The Operator Product Expansion Beyond Perturbation Theory in QCD
Dominguez, C A
2010-01-01
The Operator Product Expansion (OPE) of current correlators at short distances beyond perturbation theory in QCD, together with Cauchy's theorem in the complex energy plane, are the pillars of the method of QCD sum rules. This technique provides an analytic tool to relate QCD with hadronic physics at low and intermediate energies. It has been in use for over thirty years to determine hadronic parameters, form factors, and QCD parameters such as the quark masses, and the running strong coupling at the scale of the $\\tau$-lepton. QCD sum rules provide a powerful complement to numerical simulations of QCD on the lattice. In this talk a short review of the method is presented for non experts, followed by three examples of recent applications.
The Banks-Zaks expansion in perturbative QCD: An update
Stevenson, P. M.
2016-11-01
The recent QCD calculations of the five-loop β-function and of Re+e- to O(αs4) provide one more term in the Banks-Zaks (BZ) expansion in (161 2 - nf). There is no longer any hope that the expansion could extend, even crudely, to low nf. Above nf ˜ 9, however, the results appear to be reasonably consistent from order to order.
The Banks-Zaks expansion in perturbative QCD: an update
Stevenson, P M
2016-01-01
The recent QCD calculations of the five-loop beta function and of R(e+e-) to O(alpha_s^4) provide one more term in the Banks-Zaks expansion in (16.5-nf). There is no longer any hope that the expansion could extend, even crudely, to low nf. Above nf=9, however, the results appear to be reasonably consistent from order to order.
Sudakov Safety in Perturbative QCD
Larkoski, Andrew J; Thaler, Jesse
2015-01-01
Traditional calculations in perturbative quantum chromodynamics (pQCD) are based on an order-by-order expansion in the strong coupling $\\alpha_s$. Observables that are calculable in this way are known as "safe". Recently, a class of unsafe observables was discovered that do not have a valid $\\alpha_s$ expansion but are nevertheless calculable in pQCD using all-orders resummation. These observables are called "Sudakov safe" since singularities at each $\\alpha_s$ order are regulated by an all-orders Sudakov form factor. In this letter, we give a concrete definition of Sudakov safety based on conditional probability distributions, and we study a one-parameter family of momentum sharing observables that interpolate between the safe and unsafe regimes. The boundary between these regimes is particularly interesting, as the resulting distribution can be understood as the ultraviolet fixed point of a generalized fragmentation function, yielding a leading behavior that is independent of $\\alpha_s$.
Death to perturbative QCD in exclusive processes?
Energy Technology Data Exchange (ETDEWEB)
Eckardt, R.; Hansper, J.; Gari, M.F. [Institut fuer Theoretische Physik, Bochum (Germany)
1994-04-01
The authors discuss the question of whether perturbative QCD is applicable in calculations of exclusive processes at available momentum transfers. They show that the currently used method of determining hadronic quark distribution amplitudes from QCD sum rules yields wave functions which are completely undetermined because the polynomial expansion diverges. Because of the indeterminacy of the wave functions no statement can be made at present as to whether perturbative QCD is valid. The authors emphasize the necessity of a rigorous discussion of the subject and the importance of experimental data in the range of interest.
New Methods in Non-Perturbative QCD
Energy Technology Data Exchange (ETDEWEB)
Unsal, Mithat [North Carolina State Univ., Raleigh, NC (United States)
2017-01-31
In this work, we investigate the properties of quantum chromodynamics (QCD), by using newly developing mathematics and physics formalisms. Almost all of the mass in the visible universe emerges from a quantum chromodynamics (QCD), which has a completely negligible microscopic mass content. An intimately related issue in QCD is the quark confinement problem. Answers to non-perturbative questions in QCD remained largely elusive despite much effort over the years. It is also believed that the usual perturbation theory is inadequate to address these kinds of problems. Perturbation theory gives a divergent asymptotic series (even when the theory is properly renormalized), and there are non-perturbative phenomena which never appear at any order in perturbation theory. Recently, a fascinating bridge between perturbation theory and non-perturbative effects has been found: a formalism called resurgence theory in mathematics tells us that perturbative data and non-perturbative data are intimately related. Translating this to the language of quantum field theory, it turns out that non-perturbative information is present in a coded form in perturbation theory and it can be decoded. We take advantage of this feature, which is particularly useful to understand some unresolved mysteries of QCD from first principles. In particular, we use: a) Circle compactifications which provide a semi-classical window to study confinement and mass gap problems, and calculable prototypes of the deconfinement phase transition; b) Resurgence theory and transseries which provide a unified framework for perturbative and non-perturbative expansion; c) Analytic continuation of path integrals and Lefschetz thimbles which may be useful to address sign problem in QCD at finite density.
Understanding Theoretical Uncertainties in Perturbative QCD Computations
DEFF Research Database (Denmark)
Jenniches, Laura Katharina
effective field theories and perturbative QCD to predict the effect of New Physics on measurements at the LHC and at other future colliders. We use heavy-quark, heavy-scalar and soft-collinear effective theory to calculate a three-body cascade decay at NLO QCD in the expansion-by-regions formalism...... discuss an extension of the Cacciari-Houdeau approach to observables with hadrons in the initial state....
Basics of QCD perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Soper, D.E. [Univ. of Oregon, Eugene, OR (United States). Inst. of Theoretical Science
1997-06-01
This is an introduction to the use of QCD perturbation theory, emphasizing generic features of the theory that enable one to separate short-time and long-time effects. The author also covers some important classes of applications: electron-positron annihilation to hadrons, deeply inelastic scattering, and hard processes in hadron-hadron collisions. 31 refs., 38 figs.
Seven topics in perturbative QCD
Energy Technology Data Exchange (ETDEWEB)
Buras, A.J.
1980-09-01
The following topics of perturbative QCD are discussed: (1) deep inelastic scattering; (2) higher order corrections to e/sup +/e/sup -/ annihilation, to photon structure functions and to quarkonia decays; (3) higher order corrections to fragmentation functions and to various semi-inclusive processes; (4) higher twist contributions; (5) exclusive processes; (6) transverse momentum effects; (7) jet and photon physics.
Consistent Perturbative Fixed Point Calculations in QCD and Supersymmetric QCD.
Ryttov, Thomas A
2016-08-12
We suggest how to consistently calculate the anomalous dimension γ_{*} of the ψ[over ¯]ψ operator in finite order perturbation theory at an infrared fixed point for asymptotically free theories. If the n+1 loop beta function and n loop anomalous dimension are known, then γ_{*} can be calculated exactly and fully scheme independently in a Banks-Zaks expansion through O(Δ_{f}^{n}), where Δ_{f}=N[over ¯]_{f}-N_{f}, N_{f} is the number of flavors, and N[over ¯]_{f} is the number of flavors above which asymptotic freedom is lost. For a supersymmetric theory, the calculation preserves supersymmetry order by order in Δ_{f}. We then compute γ_{*} through O(Δ_{f}^{2}) for supersymmetric QCD in the dimensional reduction scheme and find that it matches the exact known result. We find that γ_{*} is astonishingly well described in perturbation theory already at the few loops level throughout the entire conformal window. We finally compute γ_{*} through O(Δ_{f}^{3}) for QCD and a variety of other nonsupersymmetric fermionic gauge theories. Small values of γ_{*} are observed for a large range of flavors.
Short distance repulsion in 3 nucleon forces from perturbative QCD
Aoki, Sinya; Balog, Janos; Weisz, Peter
2011-01-01
We investigate the short distance behavior of 3 nucleon forces (3NF) defined through Nambu--Bethe--Salpeter wave functions, using the operator product expansion(OPE) and calculating anomalous dimensions of 9--quark operators in perturbative QCD. As is the case of NN forces previously considered, we show that 3NF have repulsions at short distance at 1--loop, which becomes exact in the short distance limit thanks to the asymptotic freedom of QCD. Moreover these behaviors are universal in the se...
Picturing perturbative parton cascades in QCD matter
Directory of Open Access Journals (Sweden)
Aleksi Kurkela
2015-01-01
Full Text Available Based on parametric reasoning, we provide a simple dynamical picture of how a perturbative parton cascade, in interaction with a QCD medium, fills phase space as a function of time.
Constituent quark masses from modified perturbative QCD
Energy Technology Data Exchange (ETDEWEB)
Cabo Montes de Oca, A. [Instituto de Cibernetica, Matematica y Fisica, La Habana (Cuba); International Institute for Theoretical and Applied Physics (IITAP), UNESCO and Iowa State University, Ames, IA (United States); Rigol Madrazo, M. [Centro de Estudios Aplicados al Desarrollo Nuclear, La Habana (Cuba)
2002-03-01
A recently proposed modified perturbative expansion for QCD incorporating gluon condensation is employed to evaluate the quark and gluon self-energy corrections in first approximation. The results predict mass values of 1/3 of the nucleon mass for the light quarks u, d, and s and a monotonously growing variation with the current mass. The only phenomenological input is that left angle G{sup 2} right angle is evaluated up to order g{sup 2} as a function of the unique parameter C defining the modified propagator, and then C is fixed to give a current estimate of left angle g{sup 2}G{sup 2} right angle. The light quarks u and d as a result are found to be confined and the s, c, b and t ones show damped propagation modes, suggesting a model for the large differences in stability between the nucleons and the higher resonances. The above properties of quark modes diverge from the fully confinement result following from the similar gluon propagator previously considered by Munczek and Nemirovski. On the other hand, the condensate effects on the gluon self-energy furnish a tachyonic mass shell as predicted by the Fukuda analysis of gluon condensation in QCD. (orig.)
Non-perturbative QCD and hadron physics
Cobos-Martínez, J. J.
2016-10-01
A brief exposition of contemporary non-perturbative methods based on the Schwinger-Dyson (SDE) and Bethe-Salpeter equations (BSE) of Quantum Chromodynamics (QCD) and their application to hadron physics is given. These equations provide a non-perturbative continuum formulation of QCD and are a powerful and promising tool for the study of hadron physics. Results on some properties of hadrons based on this approach, with particular attention to the pion distribution amplitude, elastic, and transition electromagnetic form factors, and their comparison to experimental data are presented.
Perturbative QCD at finite temperature and density
Niégawa, A
1997-01-01
This is a comprehensive review on the perturbative hot QCD including the recent developments. The main body of the review is concentrated upon dealing with physical quantities like reaction rates. Contents: \\S1. Introduction, \\S2. Perturbative thermal field theory: Feynman rules, \\S3. Reaction-rate formula, \\S4. Hard-thermal-loop resummation scheme in hot QCD, \\S5. Effective action, \\S6. Hard modes with $|P^2| \\leq O (g^2 T^2)$, hard-thermal-loop resummation scheme, \\S9. Conclusions.
Analytic Approach to Perturbative QCD
Magradze, B
2000-01-01
The two-loop invariant (running) coupling of QCD is written in terms of the Lambert W function. The analyticity structure of the coupling in the complex Q^2-plane is established. The corresponding analytic coupling is reconstructed via a dispersion relation. We also consider some other approximations to the QCD beta-function, when the corresponding couplings are solved in terms of the Lambert function. The Landau gauge gluon propagator has been considered in the renormalization group invariant analytic approach (IAA). It is shown that there is a nonperturbative ambiguity in determination of the anomalous dimension function of the gluon field. Several analytic solutions for the propagator at the one-loop order are constructed. Properties of the obtained analytical solutions are discussed.
Chiral perturbation theory for lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Baer, Oliver
2010-07-21
The formulation of chiral perturbation theory (ChPT) for lattice Quantum Chromodynamics (QCD) is reviewed. We start with brief summaries of ChPT for continuum QCD as well as the Symanzik effective theory for lattice QCD. We then review the formulation of ChPT for lattice QCD. After an additional chapter on partial quenching and mixed action theories various concrete applications are discussed: Wilson ChPT, staggered ChPT and Wilson ChPT with a twisted mass term. The remaining chapters deal with the epsilon regime with Wilson fermions and selected results in mixed action ChPT. Finally, the formulation of heavy vector meson ChPT with Wilson fermions is discussed. (orig.)
Explaining jet quenching with perturbative QCD alone
Zapp, Korinna C; Wiedemann, Urs A
2011-01-01
We present a new formulation of jet quenching in perturbative QCD beyond the eikonal approximation. Multiple scattering in the medium is modelled through infra-red-continued (2 -> 2) scattering matrix elements in QCD and the parton shower describing further emissions. The interplay between these processes is arranged in terms of a formation time constraint such that coherent emissions can be treated consistently. Emerging partons are hadronised by the Lund string model, tuned to describe LEP data in conjunction with the parton shower. Based on this picture we obtain a good description of the nuclear modification factor R_AA at RHIC and LHC.
Perturbative and nonperturbative renormalization in lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Goeckeler, M. [Regensburg Univ. (Germany). Institut fuer Theoretische Physik; Horsley, R. [University of Edinburgh (United Kingdom). School of Physics and Astronomy; Perlt, H. [Leipzig Univ. (DE). Institut fuer Theoretische Physik] (and others)
2010-03-15
We investigate the perturbative and nonperturbative renormalization of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields (quark-antiquark operators). These include operators which are relevant to the calculation of moments of hadronic structure functions. The nonperturbative computations are based on Monte Carlo simulations with two flavors of clover fermions and utilize the Rome-Southampton method also known as the RI-MOM scheme. We compare the results of this approach with various estimates from lattice perturbation theory, in particular with recent two-loop calculations. (orig.)
Comparing the QCD potential in Perturbative QCD and Lattice QCD at large distances
Recksiegel, S
2003-01-01
We compare the perturbatively calculated QCD potential to that obtained from lattice calculations in the theory without light quark flavours. We examine E_tot(r) = 2 m_pole + V_QCD(r) by re-expressing it in the MSbar mass m = m^MSbar(m^MSbar) and by choosing specific prescriptions for fixing the scale mu (dependent on r and m). By adjusting m so as to maximise the range of convergence, we show that perturbative and lattice calculations agree up to 3 r_0 ~ 7.5 GeV^-1 (r_0 is the Sommer scale) within the perturbative uncertainty of order Lambda^3 r^2.
Unsafe but Calculable: Ratios of Angularities in Perturbative QCD
Larkoski, Andrew J
2013-01-01
Infrared- and collinear-safe (IRC-safe) observables have finite cross sections to each fixed-order in perturbative QCD. Generically, ratios of IRC-safe observables are themselves not IRC safe and do not have a valid fixed-order expansion. Nevertheless, in this paper we present an explicit method to calculate the cross section for a ratio observable in perturbative QCD with the help of resummation. We take the IRC-safe jet angularities as an example and consider the ratio formed from two angularities with different angular exponents. While the ratio observable is not IRC safe, it is "Sudakov safe", meaning that the perturbative Sudakov factor exponentially suppresses the singular region of phase space. At leading logarithmic (LL) order, the distribution is finite but has a peculiar expansion in the square root of the strong coupling constant, a consequence of IRC unsafety. The accuracy of the LL distribution can be further improved with higher-order resummation and fixed-order matching. Non-perturbative effect...
Consistent Perturbative Fixed Point Calculations in QCD and Supersymmetric QCD
DEFF Research Database (Denmark)
Ryttov, Thomas A.
2016-01-01
We suggest how to consistently calculate the anomalous dimension $\\gamma_*$ of the $\\bar{\\psi}\\psi$ operator in finite order perturbation theory at an infrared fixed point for asymptotically free theories. If the $n+1$ loop beta function and $n$ loop anomalous dimension are known then $\\gamma......_*$ can be calculated exactly and fully scheme independently through $O(\\Delta_f^n )$ where $\\Delta_f = \\bar{N_f} - N_f$ and $N_f$ is the number of flavors and $\\bar{N}_f$ is the number of flavors above which asymptotic freedom is lost. For a supersymmetric theory the calculation preserves supersymmetry...... order by order in $\\Delta_f$. We then compute $\\gamma_*$ through $O(\\Delta_f^2)$ for supersymmetric QCD in the $\\overline{\\text{DR}}$ scheme and find that it matches the exact known result. We find that $\\gamma_*$ is astonishingly well described in perturbation theory already at the few loops level...
Non-perturbative study of QCD correlators
Lokhov, A Y
2006-01-01
This PhD dissertation is devoted to a non-perturbative study of QCD correlators. The main tool that we use is lattice QCD. We concentrated our efforts on the study of the main correlators of the pure Yang - Mills theory in the Landau gauge, namely the ghost and the gluon propagators. We are particularly interested in determining the $\\Lqcd$ parameter. It is extracted by means of perturbative predictions available up to NNNLO. The related topic is the influence of non-perturbative effects that show up as appearance of power-corrections to the low-momentum behaviour of the Green functions. A new method of removing these power corrections allows a better estimate of $\\Lqcd$. Our result is $\\Lambda^{n_f=0}_{\\ms} = 269(5)^{+12}_{-9}$ MeV. Another question that we address is the infrared behaviour of Green functions, at momenta of order and below $\\Lqcd$. At low energy the momentum dependence of the propagators changes considerably, and this is probably related to confinement. The lattice approach allows to check t...
Towards finite density QCD with Taylor expansions
Karsch, Frithjof; Wagner, Mathias; Wambach, Jochen
2010-01-01
Convergence properties of Taylor expansions of observables, which are also used in lattice QCD calculations at non-zero chemical potential, are analyzed in an effective N_f = 2+1 flavor Polyakov-quark-meson model. A recently developed algorithmic technique allows the calculation of higher-order Taylor expansion coefficients in functional approaches. This novel technique is for the first time applied to an effective N_f = 2+1 flavor Polyakov-quark-meson model and the findings are compared with the full model solution at finite densities. The results are used to discuss prospects for locating the QCD phase boundary and a possible critical endpoint in the phase diagram.
Baryonic Resonances Mass Spectrum from a Modified Perturbative QCD
Cabo-Montes de Oca, Alejandro; Oca, Alejandro Cabo Montes de; Madrazo, Marcos Rigol
2001-01-01
A recently proposed modified perturbation expansion for QCD incorporating gluon condensation effects is employed to evaluate the quark self-energy in the simplest approximation. One of the solutions of the modified mass shell predicts mass values which increases monotonically with the corresponding Lagrangian mass for each kind of flavour. The mass spectrum of the ground states within the various groups of hadronic resonances and a class of mesonic ones is well predicted by the simple addition of the calculated constituent quark masses. These results suggest the gluon condensate nature of many baryonic resonances and the possibility of their description by a modified perturbative theory. Finally, it is conjectured that this procedure, after also introducing quark condensates in a same token as the gluonic ones, could predict the Lagrangian quark masses as well as the non-colored fermion (leptons and neutrinos) mass spectrum, through higher order radiative correction. Such a picture, if verified, would furnish...
Lattice-motivated holomorphic nearly perturbative QCD
Ayala, César; Cvetič, Gorazd; Kögerler, Reinhart
2017-07-01
Newer lattice results indicate that, in the Landau gauge at low spacelike momenta, the gluon propagator and the ghost dressing function are finite nonzero. This leads to a definition of the QCD running coupling, in a specific scheme, that goes to zero at low spacelike momenta. We construct a running coupling which fulfills these conditions, and at the same time reproduces to a high precision the perturbative behavior at high momenta. The coupling is constructed in such a way that it reflects qualitatively correctly the holomorphic (analytic) behavior of spacelike observables in the complex plane of the squared momenta, as dictated by the general principles of quantum field theories. Further, we require the coupling to reproduce correctly the nonstrange semihadronic decay rate of tau lepton which is the best measured low-momentum QCD observable with small higher-twist effects. Subsequent application of the Borel sum rules to the V + A spectral functions of tau lepton decays, as measured by OPAL Collaboration, determines the values of the gluon condensate and of the V + A six-dimensional condensate, and reproduces the data to a significantly higher precision than the usual \\overline{{MS}} running coupling.
Lattice-motivated holomorphic nearly perturbative QCD
Ayala, Cesar; Kogerler, Reinhart
2016-01-01
Newer lattice results indicate that, in the Landau gauge at low spacelike momenta, the gluon propagator and the ghost dressing function are finite nonzero. This leads to a definition of the QCD running coupling, in a specific scheme, that goes to zero at low spacelike momenta. We construct a running coupling which fulfills these conditions, and at the same time reproduces to a high precision the perturbative behavior at high momenta. The coupling is constructed in such a way that it reflects qualitatively correctly the holomorphic (analytic) behavior of spacelike observables in the complex plane of the squared momenta, as dictated by the general principles of Quantum Field Theories. Further, we require the coupling to reproduce correctly the nonstrange semihadronic decay rate of tau lepton which is the best measured low-momentum QCD observable with negligible higher-twist effects. Subsequent application of the Borel sum rules to the V+A spectral functions of tau lepton decays, as measured by OPAL Collaboratio...
On a Modified Initial State for Perturbative QCD
Madrazo, M R; Madrazo, Marcos Rigol; Oca, Alejandro Cabo Montes de
2000-01-01
A particular initial state for the construction of the perturbative expansion of QCD is investigated. It is formed as a coherent superposition of zero momentum gluon pairs and shows Lorentz as well as global SU3 symmetries. It follows that the gluon and ghost propagators determined by it, coincides with the ones used in an alternative of the usual perturbation theory proposed in a previous work. Therefore, the ability of such a procedure of producing a finite gluon condensation parameter already in the first orders of perturbation theory is naturally explained. It also follows that this state satisfies the physicality condition of the BRST procedure in its Kugo and Ojima formulation. The BRST quantization is done for the value alpha=1 of the gauge parameter where the procedure is greatly simplified. Therefore, after assuming that the adiabatic connection of the interaction does not takes out the state from the interacting physical space, the predictions of the perturbation expansion, at the value alpha=1 , fo...
Perturbative QCD contributions to inclusive processes
Energy Technology Data Exchange (ETDEWEB)
Ritbergen, T. van
1996-09-24
This thesis treats the calculation of quantum corrections to a number of high energy processes that are measured in current and future accelerator experiments. The main objective of these experiments is to accurately verify the generally accepted theory of electro-weak and strong interactions, known as the Standard model, and to look for possible deviations. Most of the processes that are treated in this thesis are of a type for which the final state of of a highly energetic scattering or decay process is measured inclusively. The higher order quantum corrections discussed in this thesis are due to strong interactions. To the inclusive decay rate of Z{sup 0} bosons into all possible final states consisting of hadrons third order QCD contributions have been obtained. Also in the third order QCD an expansion for the inclusive hadronic decay rate of a {tau}-lepton was obtained. Then the top-quark-mass effects on the decay channels of a Higgs boson: Higgs{yields}b-quarks and Higgs{yields}gluons, were investigated. Thereafter the calculation of 3-loop contributions to the deep-inelastic lepton-nucleon scattering process is discussed. Finally the 3-loop contributions to the q{sup 2}-dependence of the lower moments {integral}{sub 0}{sup 1}x{sup N-1}F(x,q{sup 2})dx, N=2,4,6,8 of the structure functions F{sub 2} and F{sub L} were obtained. (orig./HSI).
Towards finite density QCD with Taylor expansions
Karsch, Frithjof; Wagner, Mathias; Wambach, Jochen
2011-01-01
We analyze general convergence properties of the Taylor expansion of observables to finite chemical potential in the framework of an effective 2+1 flavor Polyakov-quark-meson model. To compute the required higher order coefficients a novel technique based on algorithmic differentiation has been developed. Results for thermodynamic observables as well as the phase structure obtained through the series expansion up to 24th order are compared to the full model solution at finite chemical potential. The available higher order coefficients also allow for resummations, e.g. Pade series, which improve the convergence behavior. In view of our results we discuss the prospects for locating the QCD phase boundary and a possible critical endpoint with the Taylor expansion method.
Computation of Heavy Quarkonium Spectrum in Perturbative QCD
Sumino, Yukinari
2016-01-01
Non-relativistic bound state theories for QED and QCD have become fairly mature and amenable to a textbook-level understanding and computation. In this talk we give an introductory review of the following subjects related to the recent computation of the heavy quarkonium spectrum using perturbative QCD: (1) Technological developments in higher-order computation, (2) Physics predictions, (3) Challenge towards analytic evaluation of the 3-loop static QCD potential.
B -> phi K decays in perturbative QCD approach
Mishima, S
2001-01-01
We calculate the branching ratios and CP asymmetries of the $B\\to \\phi K$ decays using perturbative QCD approach, which includes $k_T$ and threshold resummations. Our results of branching ratios are consistent with the experimental data and larger than those obtained from the naive factorization assumption and QCD-improved factorization approach.
Pure annihilation type $ D\\to PP(V)$ decays in the perturbative QCD approach
Zou, Zhi-Tian; Lü, Cai-Dian
2013-01-01
The annihilation type diagrams are difficult to calculate in any kind of models or method. Encouraged by the the successful calculation of pure annihilation type B decays in the perturbative QCD factorization approach, we calculate the pure annihilation type $D\\to PP(V)$ decays in the perturbative QCD approach based on the $k_T$ factorization. Although the expansion parameter $1/m_D$ is not very small, our leading order numerical results agree with the existing experiment data for most channels. We expect the more accurate observation from experiments, which can help us learn about the dynamics of $D$ meson weak decays.
Perturbative QCD analysis of $B \\to \\phi K^* $ decays
Chen Chuan Hung; Li, H; Chen, Chuan-Hung; Keum, Yong-Yeon; Li, Hsiang-nan
2002-01-01
We study the first observed charmless $B\\to VV$ modes, the $B\\to\\phi K^*$ decays, in perturbative QCD formalism. The obtained branching ratios $B(B\\to\\phi K^*)\\sim 15 \\times 10^{-6}$ are larger than $\\sim 9\\times 10^{-6}$ from QCD factorization. The comparison of the predicted magnitudes and phases of the different helicity amplitudes, and branching ratios with experimental data can test the power counting rules, the evaluation of annihilation contributions, and the mechanism of dynamical penguin enhancement in perturbative QCD, respectively.
Applications Of Chiral Perturbation Theory To Lattice Qcd
Van de Water, R S
2005-01-01
Quantum chromodynamics (QCD) is the fundamental theory that describes the interaction of quarks and gluons. Thus, in principle, one should be able to calculate all properties of hadrons from the QCD Lagrangian. It turns out, however, that such calculations can only be performed numerically on a computer using the nonperturbative method of lattice QCD, in which QCD is simulated on a discrete spacetime grid. Because lattice simulations use unphysically heavy quark masses (for computational reasons), lattice results must be connected to the real world using expressions calculated in chiral perturbation theory (χPT), the low-energy effective theory of QCD. Moreover, because real spacetime is continuous, they must be extrapolated to the continuum using an extension of χPT that includes lattice discretization effects, such as staggered χPT. This thesis is organized as follows. We motivate the need for lattice QCD and present the basic methodology in Chapter 1. We describe a common approximat...
About an Alternative Vacuum State for Perturbative QCD
Rigol, M
1999-01-01
A particular initial state for the construction of a perturbative QCD expansion is investigated. It is formed as a coherent superposition of zero momentum gluon pairs and shows Lorentz as well as global $SU(3)$ symmetries. The general form of the Wick theorem is discussed, and it follows that the gluon and ghost propagators determined by the proposed vacuum state, coincides with the ones used in an alternative of the usual perturbation theory proposed in a previous work, and reviewed here. Therefore, the ability of such a procedure of producing a finite gluon condensation parameter already in the first orders of perturbation theory is naturally explained. It also follows that this state satisfies the physicality condition of the BRST procedure in its Kugo and Ojima formulation. A brief review of the canonical quantization for gauge fields, developed by Kugo and Ojima, is done and the value of the gauge parameter $\\alpha$ is fixed to $\\alpha=1$ where the procedure is greatly simplified. Therefore, after assumi...
Perturbative expansion of Chern-Simons theory
SAWON, Justin
2005-01-01
An overview of the perturbative expansion of the Chern--Simons path integral is given. The main goal is to describe how trivalent graphs appear: as they already occur in the perturbative expansion of an analogous finite-dimensional integral, we discuss this case in detail.
Optimal RG-Improvement of Perturbative Calculations in QCD
Elias, V
2003-01-01
Using renormalization-group methods, differential equations can be obtained for the all-orders summation of leading and subsequent non-leading logarithmic corrections to QCD perturbative series for a number of processes and correlation functions. For a QCD perturbative series known to four orders, such as the e+ e- annihilation cross-section, explicit solutions to these equations are obtained for the summation to all orders in alpha_s of the leading set and the subsequent two non-leading sets of logarithms. Such summations are shown for a number of processes to lead to a substantial reduction in sensitivity to the renormalization scale parameter. Surprisingly, such summations are also shown to lower the infrared singularity within the perturbative expression for the e+ e- annihilation cross-section to coincide with the Landau pole of the naive one-loop running QCD couplant.
On the ambiguity of field correlators represented by asymptotic perturbation expansions
Energy Technology Data Exchange (ETDEWEB)
Caprini, Irinel [National Institute of Physics and Nuclear Engineering, Bucharest POB MG-6, R-077125 Romania (Romania); Fischer, Jan [Institute of Physics, Academy of Sciences of the Czech Republic, CZ-182 21 Prague 8 (Czech Republic); Vrkoc, Ivo [Mathematical Institute, Academy of Sciences of the Czech Republic, CZ-115 67 Prague 1 (Czech Republic)
2009-10-02
Starting from the divergence pattern of perturbation expansions in quantum field theory and the (assumed) asymptotic character of the series, we address the problem of ambiguity of a function determined by the perturbation expansion. We consider functions represented by an integral of the Laplace-Borel type along a general contour in the Borel complex plane. Proving a modified form of Watson's lemma, we obtain a large class of functions having the same asymptotic perturbation expansion. Some remarks on perturbative QCD are made, using the particular case of the Adler function.
Non-perturbative QCD amplitudes in quenched and eikonal approximations
Energy Technology Data Exchange (ETDEWEB)
Fried, H.M. [Physics Department, Brown University, Providence, RI 02912 (United States); Grandou, T., E-mail: Thierry.Grandou@inln.cnrs.fr [Université de Nice-Sophia Antipolis, Institut Non Linéaire de Nice, UMR 6618 CNRS 7335, 1361 routes des Lucioles, 06560 Valbonne (France); Sheu, Y.-M., E-mail: ymsheu@alumni.brown.edu [Université de Nice-Sophia Antipolis, Institut Non Linéaire de Nice, UMR 6618 CNRS 7335, 1361 routes des Lucioles, 06560 Valbonne (France)
2014-05-15
Even though approximated, strong coupling non-perturbative QCD amplitudes remain very difficult to obtain. In this article, in eikonal and quenched approximations at least, physical insights are presented that rely on the newly-discovered property of effective locality. The present article also provides a more rigorous mathematical basis for the crude approximations used in the previous derivation of the binding potential of quarks and nucleons. Furthermore, the techniques of Random Matrix calculus along with Meijer G-functions are applied to analyze the generic structure of fermionic amplitudes in QCD. - Highlights: • We discuss the physical insight of effective locality to QCD fermionic amplitudes. • We show that an unavoidable delta function goes along with the effective locality property. • The generic structure of QCD fermion amplitudes is obtained through Random Matrix calculus.
Three-body nonleptonic B decays in perturbative QCD
Chen, C H; Chen, Chuan-Hung; Li, Hsiang-nan
2003-01-01
We develop perturbative QCD formalism for three-body nonleptonic $B$ meson decays. Leading contributions are identified by defining the power counting rules for various topologies of amplitudes. The analysis is simplified into the one for two-body decays by introducing two-pion distribution amplitudes. This formalism predicts both nonresonant and resonant contributions, and can be generalized to baryonic decays.
Constituent quark and baryon spectra from a modified Perturbative QCD
Cabo-Montes de Oca, Alejandro; Cabo Montes de Oca, Alejandro; Madrazo, Marcos Rigol
2000-01-01
A recently proposed perturbative expansion for QCD incorporating gluon condensation is employed to evaluate the quark and gluon self-energy corrections in the simplest approximations. The results predict mass values of the order of 1/3 of the nucleon mass for the light quarks u,d and s and a monotonously growing variation with the current mass values. The mass spectrum of the ground states within the various groups of baryonic resonances and a class of vector meson ones is well predicted by the simple addition of the calculated constituent quark masses. In connection with the self-energy, it follows that the gluonic mass shell becomes tachyonic in the considered approximation. In order to obtain the above mentioned results was evaluated as a function of the condensate paramater up to order g^2 and then this parameter fixed to give the accepted numerical value of . The discussion leads us to conjecture that the procedure, after also introducing quark condensates in the same token as the gluonic ones, could a...
Exploring arbitrarily high orders of optimized perturbation theory in QCD with nf -> 16.5
Stevenson, P M
2016-01-01
Perturbative QCD with nf flavours of massless quarks becomes simple in the hypothetical limit nf -> 16.5, where the leading beta-function coefficient vanishes. The Banks-Zaks (BZ) expansion in a0=(8/321)(16.5-nf) is straightforward to obtain from perturbative results in MSbar or any renormalization scheme (RS) whose nf dependence is `regular.' However, `irregular' RS's are perfectly permissible and should ultimately lead to the same BZ results. We show here that the `optimal' RS determined by the Principle of Minimal Sensitivity does yield the same BZ-expansion results when all orders of perturbation theory are taken into account. The BZ limit provides an arena for exploring optimized perturbation theory at arbitrarily high orders. These explorations are facilitated by a `master equation' expressing the optimization conditions in the fixed-point limit. We find an intriguing strong/weak coupling duality a -> a*^2/a about the fixed point a*.
Taming Landau singularities in QCD perturbation theory: The analytic approach
Stefanis, N G
2013-01-01
The aim of this topical article is to outline the fundamental ideas underlying the recently developed Fractional Analytic Perturbation Theory (FAPT) of QCD and present its main calculational tools. For this, it is first necessary to review previous methods to apply QCD perturbation theory at low spacelike momentum scales, where the influence of the Landau singularities becomes inevitable. Several concepts are considered and their limitations are pointed out. The usefulness of FAPT is discussed in terms of two characteristic hadronic quantities: the perturbatively calculable part of the pion's electromagnetic form factor in the spacelike region and the Higgs-boson decay into a b\\bar b pair in the timelike region. In the first case, the focus is on the optimization of the prediction with respect to the choice of the renormalization scheme and the dependence on the renormalization and the factorization scales. The second case serves to show that the application of FAPT to this reaction reaches already at the fou...
Testing QCD in the non-perturbative regime
Energy Technology Data Exchange (ETDEWEB)
A.W. Thomas
2007-01-01
This is an exciting time for strong interaction physics. We have a candidate for a fundamental theory, namely QCD, which has passed all the tests thrown at it in the perturbative regime. In the non-perturbative regime it has also produced some promising results and recently a few triumphs but the next decade will see enormous progress in our ability to unambiguously calculate the consequences of non-perturbative QCD and to test those predictions experimentally. Amongst the new experimental facilities being constructed, the hadronic machines at JPARC and GSI-FAIR and the 12 GeV Upgrade at Jefferson Lab, the major new electromagnetic facility worldwide, present a beautifully complementary network aimed at producing precise new measurements which will advance our knowledge of nuclear systems and push our ability to calculate the consequences of QCD to the limit. We will first outline the plans at Jefferson Lab for doubling the energy of CEBAF. The new facility presents some wonderful opportunities for discovery in strong interaction physics, as well as beyond the standard model. Then we turn to the theoretical developments aimed at extracting precise results for physical hadron properties from lattice QCD simulations. This discussion will begin with classical examples, such as the mass of the nucleon and ?, before dealing with a very recent and spectacular success involving information extracted from modern parity violating electron scattering.
Non-perturbative QCD amplitudes in quenched and eikonal approximations
Fried, H. M.; Grandou, T.; Sheu, Y.-M.
2014-05-01
Even though approximated, strong coupling non-perturbative QCD amplitudes remain very difficult to obtain. In this article, in eikonal and quenched approximations at least, physical insights are presented that rely on the newly-discovered property of effective locality. The present article also provides a more rigorous mathematical basis for the crude approximations used in the previous derivation of the binding potential of quarks and nucleons. Furthermore, the techniques of Random Matrix calculus along with Meijer G-functions are applied to analyze the generic structure of fermionic amplitudes in QCD.
Non-perturbative studies of QCD at small quark masses
Energy Technology Data Exchange (ETDEWEB)
Wennekers, J.
2006-07-15
We investigate the quenched approximation of lattice QCD with numerical simulations of Ginsparg-Wilson fermions, which are a fermion discretisation with exact chiral symmetry. We compute the renormalisation constant of the scalar density, which allows to extrapolate the chiral condensate to the continuum limit. Furthermore we match lattice results of matrix elements describing hadronic kaon decays to Chiral Perturbation Theory in finite volume and at almost vanishing quark mass. The resulting low-energy constants in the considered SU(4)-flavour symmetric case indicate a substantial contribution of low scale QCD effects to the {delta}I = 1/2 rule. (Orig.)
A Non-Perturbative Gauge-Invariant QCD: Ideal vs. Realistic QCD
Fried, H M; Sheu, Y -M
2011-01-01
A basic distinction, long overlooked, between the conventional, "idealistic" formulation of QCD, and a more "realistic" formulation is brought into focus by a rigorous, non-perturbative, gauge-invariant evaluation of the Schwinger solution for the QCD generating functional in terms of exact Fradkin representations for the Green's functional $\\mathbf{G}_{c}(x,y|A)$ and the vacuum functional $\\mathbf{L}[A]$. The quanta of all (Abelian) quantized fields may be expected to obey standard quantum-mechanical measurement properties, perfect position dependence at the cost of unknown momenta, and vice-versa, but this is impossible for quarks since they always appear asymptotically in bound states, and their transverse position or momenta can never, in principle, be exactly measured. Violation of this principle produces an absurdity in the exact evaluation of each and every QCD amplitude. We here suggest a phenomenological change in the basic QCD Lagrangian, such that a limitation of transverse precision is automatical...
Kato expansion in quantum canonical perturbation theory
Nikolaev, A S
2015-01-01
This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. The corresponding computational algorithm is more efficient for high perturbative orders than the algorithms of Van Vleck and Magnus methods.
Kato expansion in quantum canonical perturbation theory
Nikolaev, Andrey
2016-06-01
This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson's ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.
Lattice QCD for Baryon Rich Matter - Beyond Taylor Expansions
Bornyakov, V.; Boyda, D.; Goy, V.; Molochkov, A.; Nakamura, A.; Nikolaev, A.; Zakharov, V. I.
2016-12-01
We discuss our study for exploring the QCD phase diagram based on the lattice QCD. To go beyond the Taylor expansion and to reach higher density regions, we employ the canonical approach. In order to produce lattice data which meet experimental situation as much as possible, we propose a canonical approach with the charge and baryon number. We present our lattice QCD GPU code for this project which employs the clover improved Wilson fermions and Iwasaki gauge action to investigate pure imaginary chemical potential.
Lattice QCD for Baryon Rich Matter – Beyond Taylor Expansions
Energy Technology Data Exchange (ETDEWEB)
Bornyakov, V. [ITEP, B. Cheremushkinskaya 25, Moscow, 117218 (Russian Federation); School of Biomedicine, Far Eastern Federal University, Sukhanova 8, Vladivostok 690950 (Russian Federation); Boyda, D. [School of Biomedicine, Far Eastern Federal University, Sukhanova 8, Vladivostok 690950 (Russian Federation); Goy, V. [School of Natural Sciences, Far Eastern Federal University, Sukhanova 8, Vladivostok 690950 (Russian Federation); Molochkov, A. [School of Biomedicine, Far Eastern Federal University, Sukhanova 8, Vladivostok 690950 (Russian Federation); Nakamura, A. [School of Biomedicine, Far Eastern Federal University, Sukhanova 8, Vladivostok 690950 (Russian Federation); Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki, Osaka, 567-0047 (Japan); Theoretical Research Division, Nishina Center, RIKEN, Wako 351-0198 (Japan); Nikolaev, A. [School of Biomedicine, Far Eastern Federal University, Sukhanova 8, Vladivostok 690950 (Russian Federation); Zakharov, V.I. [ITEP, B. Cheremushkinskaya 25, Moscow, 117218 (Russian Federation); School of Biomedicine, Far Eastern Federal University, Sukhanova 8, Vladivostok 690950 (Russian Federation); Moscow Inst Phys & Technol, Dolgoprudny, Moscow Region, 141700 (Russian Federation)
2016-12-15
We discuss our study for exploring the QCD phase diagram based on the lattice QCD. To go beyond the Taylor expansion and to reach higher density regions, we employ the canonical approach. In order to produce lattice data which meet experimental situation as much as possible, we propose a canonical approach with the charge and baryon number. We present our lattice QCD GPU code for this project which employs the clover improved Wilson fermions and Iwasaki gauge action to investigate pure imaginary chemical potential.
Importance of Non-Perturbative QCD Parameters for Bottom Mesons
Upadhyay, A
2015-01-01
The importance of non-perturbative Quantum Chromodynamics [QCD] parameters is discussed in context to the predicting power for bottom meson masses and isospin splitting. In the framework of heavy quark effective theory, the work presented here focuses on the different allowed values of the two non perturbative QCD parameters used in heavy quark effective theory formula and using the best fitted parameter, masses of the excited bottom meson states in JP=(1/2)+ doublet in strange as well as non-strange sector are calculated here. The calculated masses are found to be matching well with experiments and other phenomenological models. The mass and hyperfine splitting has also been analyzed for both strange and non-strange heavy mesons with respect to spin and flavor symmetries.
The accuracy of QCD perturbation theory at high energies
Dalla Brida, Mattia; Korzec, Tomasz; Ramos, Alberto; Sint, Stefan; Sommer, Rainer
2016-01-01
We discuss the determination of the strong coupling $\\alpha_\\mathrm{\\overline{MS}}^{}(m_\\mathrm{Z})$ or equivalently the QCD $\\Lambda$-parameter. Its determination requires the use of perturbation theory in $\\alpha_s(\\mu)$ in some scheme, $s$, and at some energy scale $\\mu$. The higher the scale $\\mu$ the more accurate perturbation theory becomes, owing to asymptotic freedom. As one step in our computation of the $\\Lambda$-parameter in three-flavor QCD, we perform lattice computations in a scheme which allows us to non-perturbatively reach very high energies, corresponding to $\\alpha_s = 0.1$ and below. We find that perturbation theory is very accurate there, yielding a three percent error in the $\\Lambda$-parameter, while data around $\\alpha_s \\approx 0.2$ is clearly insufficient to quote such a precision. It is important to realize that these findings are expected to be generic, as our scheme has advantageous properties regarding the applicability of perturbation theory.
Threshold resummation in SCET vs. perturbative QCD. An analytic comparison
Energy Technology Data Exchange (ETDEWEB)
Bonvini, Marco [Genoa Univ. (Italy). Dipt. di Fisica; Istituto Nazionale di Fisica Nucleare, Genoa (Italy); Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Forte, Stefano [Milano Univ. (Italy). Dipt. di Fisica; Istituto Nazionale di Fisica Nucleare, Milan (Italy); Ghezzi, Margherita [Milano Univ. (Italy). Dipt. di Fisica; Istituto Nazionale di Fisica Nucleare, Milan (Italy); Rome Univ. (Italy). Dipt. di Fisica; Istituto Nazionale di Fisica Nucleare, Rome (Italy); Ridolfi, Giovanni [Genoa Univ. (Italy). Dipt. di Fisica; Istituto Nazionale di Fisica Nucleare, Genoa (Italy)
2012-01-15
We compare threshold resummation in QCD, as performed using soft-collinear effective theory (SCET), to the standard perturbative QCD formalism based on factorization and resummation of Mellin moments of partonic cross-sections. We consider various forms of the SCET result, which correspond to different choices of the soft scale {mu}{sub s} that characterizes this approach. We derive a master formula that relates the SCET resummation to the QCD result for any choice of {mu}{sub s}. We then use it first, to show that if SCET resummation is performed in N-Mellin moment space by suitable choice of {mu}{sub s} it is equivalent to the standard perturbative approach. Next, we show that if SCET resummation is performed by choosing for {mu}{sub s} a partonic momentum variable, the perturbative result for partonic resummed cross-sections is again reproduced, but like its standard perturbative counterpart it is beset by divergent behaviour at the endpoint. Finally, using the master formula we show that when {mu}{sub s} is chosen as a hadronic momentum variable the SCET and standard approach are related through a multiplicative (convolutive) factor, which contains the dependence on the Landau pole and associated divergence. This factor depends on the luminosity in a non-universal way; it lowers by one power of log the accuracy of the resummed result, but it is otherwise subleading if one assumes the luminosity not to contain logarithmically enhanced terms. Therefore, the SCET approach can be turned into a prescription to remove the Landau pole from the perturbative result, but the price to pay for this is the reduction by one logarithmic power of the accuracy at each order and the need to make assumptions on the parton luminosity. (orig.)
On the Interface between Perturbative and Nonperturbative QCD
Deur, A; de Teramond, G F
2016-01-01
The QCD running coupling $\\alpha_s(Q^2)$ sets the strength of the interactions of quarks and gluons as a function of the momentum transfer $Q$. The $Q^2$ dependence of the coupling is required to describe hadronic interactions at both large and short distances. In this article we adopt the light-front holographic approach to strongly-coupled QCD, a formalism which incorporates confinement, predicts the spectroscopy of hadrons composed of light quarks, and describes the low-$Q^2$ analytic behavior of the strong coupling $\\alpha_s(Q^2)$. The high-$Q^2$ dependence of the coupling $\\alpha_s(Q^2)$ is specified by perturbative QCD and its renormalization group equation. The matching of the high and low $Q^2$ regimes of $\\alpha_s(Q^2)$ then determines the scale $Q_0$ which sets the interface between perturbative and nonperturbative hadron dynamics. The value of $Q_0$ can be used to set the factorization scale for DGLAP evolution of hadronic structure functions and the ERBL evolution of distribution amplitudes. We di...
Non-perturbative QCD effects in jets at hadron colliders
Dasgupta, Mrinal; Salam, Gavin P
2008-01-01
We discuss non-perturbative QCD contributions to jet observables, computing their dependence on the jet radius R, and on the colour and transverse momentum of the parton initiating the jet. We show, using analytic QCD models of power corrections as well as Monte Carlo simulations, that hadronisation corrections grow at small values of R, behaving as 1/R, while underlying event contributions grow with the jet area as R^2. We highlight the connection between hadronisation corrections to jets and those for event shapes in e^+e^- and DIS; we note the limited dependence of our results on the choice of jet algorithm; finally, we propose several measurements in the context of which to test or implement our predictions. The results presented here reinforce the motivation for the use of a range of R values, as well as a plurality of infrared-safe jet algorithms, in precision jet studies at hadron colliders.
On the interface between perturbative and nonperturbative QCD
Energy Technology Data Exchange (ETDEWEB)
Deur, Alexandre; Brodsky, Stanley J.; de Téramond, Guy F.
2016-06-01
The QCD running coupling αs(Q2) sets the strength of the interactions of quarks and gluons as a function of the momentum transfer Q . The Q2 dependence of the coupling is required to describe hadronic interactions at both large and short distances. In this article we adopt the light-front holographic approach to strongly-coupled QCD, a formalism which incorporates confinement, predicts the spectroscopy of hadrons composed of light quarks, and describes the low-Q2 analytic behavior of the strong coupling αs(Q2). The high-Q2 dependence of the coupling αs(Q2) is specified by perturbative QCD and its renormalization group equation. The matching of the high and low Q2 regimes of αs(Q2) then determines the scale Q0 which sets the interface between perturbative and nonperturbative hadron dynamics. The value of Q0 can be used to set the factorization scale for DGLAP evolution of hadronic structure functions and the ERBL evolution of distribution amplitudes. We discuss the scheme-dependence of the value of Q0 and the infrared fixed-point of the QCD coupling. Our analysis is carried out for the View the MathML source, g1, MOM and V renormalization schemes. Our results show that the discrepancies on the value of αs at large distance seen in the literature can be explained by different choices of renormalization schemes. We also provide the formulae to compute αs(Q2) over the entire range of space-like momentum transfer for the different renormalization schemes discussed in this article.
The heavy quark expansion of QCD
Energy Technology Data Exchange (ETDEWEB)
Falk, A.F. [Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Physics and Astronomy
1997-06-01
These lectures contain an elementary introduction to heavy quark symmetry and the heavy quark expansion. Applications such as the expansion of heavy meson decay constants and the treatment of inclusive and exclusive semileptonic B decays are included. Heavy hadron production via nonperturbative fragmentation processes is also discussed. 54 refs., 7 figs.
Geometric scaling in ultrahigh energy neutrinos and nonlinear perturbative QCD
Machado, M V T
2011-01-01
The ultrahigh energy neutrino cross section is a crucial ingredient in the calculation of the event rate in high energy neutrino telescopes. Currently there are several approaches which predict different behaviors for its magnitude for ultrahigh energies. In this contribution is presented a summary of current predictions based on the non-linear QCD evolution equations, the so-called perturbative saturation physics. In particular, predictions are shown based on the parton saturation approaches and the consequences of geometric scaling property at high energies are discussed. The scaling property allows an analytical computation of the neutrino scattering on nucleon/nucleus at high energies, providing a theoretical parameterization.
Non-perturbative QCD Modeling and Meson Physics
Nguyen, T; Tandy, P C
2009-01-01
Using a ladder-rainbow kernel previously established for light quark hadron physics, we explore the extension to masses and electroweak decay constants of ground state pseudoscalar and vector quarkonia and heavy-light mesons in the c- and b-quark regions. We make a systematic study of the effectiveness of a constituent mass concept as a replacement for a heavy quark dressed propagator for such states. The difference between vector and axial vector current correlators is explored within the same model to provide an estimate of the four quark chiral condensate and the leading distance scale for the onset of non-perturbative phenomena in QCD.
Casimir operator dependences of non-perturbative fermionic QCD amplitudes
Fried, H M; Hofmann, R
2015-01-01
In eikonal and quenched approximation, it is argued that the strong coupling fermionic QCD Green's functions and related amplitudes, when based on the newly discovered effective locality property, depart from a sole dependence on the SUc(3) quadratic Casimir operator, evaluated over the fundamental gauge group representation.Though noticed in non-relativistic Quark Models, an additional dependence on the cubic Casimir operator is in contradistinction with perturbation theory, and also with a number of non-perturbative approaches such as the MIT Bag, the Stochastic Vacuum Models and lattice simulations. It accounts for the full algebraic content of the rank-2 Lie algebra of SUc(3). We briefly discuss the orders of magnitude of quadratic and cubic Casimir operator contributions.
Consistent Perturbative Fixed Point Calculations in QCD and SQCD
Ryttov, Thomas A
2016-01-01
We suggest how to consistently calculate the anomalous dimension $\\gamma_*$ of the $\\bar{\\psi}\\psi$ operator in finite order perturbation theory at an infrared fixed point for asymptotically free theories. If the $n+1$ loop beta function and $n$ loop anomalous dimension are known then $\\gamma_*$ can be calculated exactly and fully scheme independently through $O(\\Delta_f^n )$ where $\\Delta_f = \\bar{N_f} - N_f$ and $N_f$ is the number of flavors and $\\bar{N}_f$ is the number of flavors above which asymptotic freedom is lost. For a supersymmetric theory the calculation preserves supersymmetry order by order in $\\Delta_f$. We then compute $\\gamma_*$ through $O(\\Delta_f^2)$ for supersymmetric QCD in the $\\overline{\\text{DR}}$ scheme and find that it matches the exact known result. We find that $\\gamma_*$ is astonishingly well described in perturbation theory already at the few loops level throughout the entire conformal window. We finally compute $\\gamma_*$ through $O(\\Delta_f^3)$ for QCD and a variety of other n...
On a realization of $\\{\\beta\\}$-expansion in QCD
Mikhailov, S V
2016-01-01
We suggest a simple algebraic approach to fix the elements of the $\\{ \\beta \\}$-expansion for renormalization group invariant quantities, which uses additional degrees of freedom. The approach is discussed in detail for N$^2$LO calculations in QCD with the MSSM gluino -- an additional degree of freedom. We derive the formulae of the $\\{ \\beta \\}$-expansion for the nonsinglet Adler $D$-function and Bjorken polarized sum rules in the actual N$^3$LO within this quantum field theory scheme with the MSSM gluino and the scheme with the second additional degree of freedom.
A Modern View of Perturbative QCD and Application to Heavy Quarkonium Systems
Sumino, Y
2014-01-01
Perturbative QCD has made significant progress over the last few decades. In the first part, we present an introductory overview of perturbative QCD as seen from a modern viewpoint. We explain the relation between purely perturbative predictions and predictions based on Wilsonian effective field theories. We also review progress of modern computational technologies and discuss intersection with frontiers of mathematics. Analyses of singularities in Feynman diagrams play key roles towards developing a unified view. In the second part, we discuss application of perturbative QCD, based on the formulation given in the first part, to heavy quarkonium systems and the interquark force between static color charges. We elucidate impacts on order Lambda_QCD physics in the quark mass and interquark force, which used to be considered inaccessible by perturbative QCD.
The B-meson mass splitting from non-perturbative quenched lattice QCD
Grozin, A G; Marquard, P; Meyer, H B; Piclum, J H; Sommer, R; Steinhauser, M
2007-01-01
We perform the non-perturbative (quenched) renormalization of the chromo-magnetic operator in Heavy Quark Effective Theory and its three-loop matching to QCD. At order 1/m of the expansion, the operator is responsible for the mass splitting between the pseudoscalar and vector B-mesons. These new computed factors are affected by an uncertainty negligible in comparison to the known bare matrix element of the operator between B-states. Furthermore, they push the quenched determination of the spin splitting for the Bs-meson much closer to its experimental value than the previous perturbatively renormalized computations. The renormalization factor for three commonly used heavy quark actions and the Wilson gauge action and useful parametrizations of the matching coefficient are provided.
Exploring arbitrarily high orders of optimized perturbation theory in QCD with nf→1612
Directory of Open Access Journals (Sweden)
P.M. Stevenson
2016-09-01
Full Text Available Perturbative QCD with nf flavours of massless quarks becomes simple in the hypothetical limit nf→1612, where the leading β-function coefficient vanishes. The Banks–Zaks (BZ expansion in a0≡8321(1612−nf is straightforward to obtain from perturbative results in MS‾ or any renormalization scheme (RS whose nf dependence is ‘regular’. However, ‘irregular’ RS's are perfectly permissible and should ultimately lead to the same BZ results. We show here that the ‘optimal’ RS determined by the Principle of Minimal Sensitivity does yield the same BZ-expansion results when all orders of perturbation theory are taken into account. The BZ limit provides an arena for exploring optimized perturbation theory at arbitrarily high orders. These explorations are facilitated by a ‘master equation’ expressing the optimization conditions in the fixed-point limit. We find an intriguing strong/weak coupling duality a→a⁎2/a about the fixed point a⁎.
Exploring arbitrarily high orders of optimized perturbation theory in QCD with nf → 161/2
Stevenson, P. M.
2016-09-01
Perturbative QCD with nf flavours of massless quarks becomes simple in the hypothetical limit nf → 161/2, where the leading β-function coefficient vanishes. The Banks-Zaks (BZ) expansion in a0 ≡8/321 (161/2 -nf) is straightforward to obtain from perturbative results in MS ‾ or any renormalization scheme (RS) whose nf dependence is 'regular'. However, 'irregular' RS's are perfectly permissible and should ultimately lead to the same BZ results. We show here that the 'optimal' RS determined by the Principle of Minimal Sensitivity does yield the same BZ-expansion results when all orders of perturbation theory are taken into account. The BZ limit provides an arena for exploring optimized perturbation theory at arbitrarily high orders. These explorations are facilitated by a 'master equation' expressing the optimization conditions in the fixed-point limit. We find an intriguing strong/weak coupling duality a →a*2 / a about the fixed point a*.
Perturbative QCD analysis of $B \\to \\phi K$ decays
Chen Chuan Hung; Li, H; Chen, Chuan-Hung; Keum, Yong-Yoen; Li, Hsiang-nan
2001-01-01
We investigate exclusive nonleptonic $B$ meson decays $B\\to\\phi K$ in perturbative QCD formalism. It is shown that the end-point (logarithmic and linear) singularities in decay amplitudes do not exist, after $k_T$ and threshold resummations are included. Power counting for emission and annihilation topologies of diagrams, including both factorizable and nonfactorizable ones, is discussed with Sudakov effects taken into account. Our predictions for the branching ratios $B(B\\to\\phi K)\\sim 10 \\times 10^{-6}$ are larger than those ($\\sim 4 \\times 10^{-6}$) from the factorization approach because of dynamical enhancement of penguin contributions. Whether this enhancement is essential for penguin-dominated modes can be justified by experimental data.
Infrared singularities of scattering amplitudes in perturbative QCD
Energy Technology Data Exchange (ETDEWEB)
Becher, Thomas [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Neubert, Matthias [Johannes Gutenberg-Universitaet Mainz, Mainz (Germany)
2013-11-01
An exact formula is derived for the infrared singularities of dimensionally regularized scattering amplitudes in massless QCD with an arbitrary number of legs, valid at any number of loops. It is based on the conjecture that the anomalous-dimension matrix of n-jet operators in soft-collinear effective theory contains only a single non-trivial color structure, whose coefficient is the cusp anomalous dimension of Wilson loops with light-like segments. Its color-diagonal part is characterized by two anomalous dimensions, which are extracted to three-loop order from known perturbative results for the quark and gluon form factors. This allows us to predict the three-loop coefficients of all 1/epsilon^k poles for an arbitrary n-parton scattering amplitudes, generalizing existing two-loop results.
Gluon, Quark and Hadron Masses from a Modified Perturbative QCD
Rigol, M
2000-01-01
The development of a Modified Perturbation Theory for QCD, introduced in previous works, is continued. The gluon propagator is modified as consequence of a soft gluon pairs condensate in the vacuum. The modified Feynman rules for $\\alpha=1$ are shown, and some physical magnitudes calculated with them. The mean value of $G^{2}$, gluon masses and the effective potential are calculated up to the $g^2$ order, improving previous calculations. In connection with the gluon self-energy it follows that the gluonic mass shell becomes tachyonic in the considered approximation. The constituent quarks masses, produced by the influence of the condensate, are also calculated. Results of the order of 1/3 of the nucleon mass, are obtained for the constituent masses of the up and down quarks. In addition, the predicted flavour dependence of the calculated quarks masses turns out to be the appropriate to reproduce the spectrum of the ground states within the various groups of hadronic resonances, through the simple addition of ...
Penguin-dominated B -> PV decays in NLO perturbative QCD
Li, H; Li, Hsiang-nan; Mishima, Satoshi
2006-01-01
We study the penguin-dominated B -> PV decays, with P (V) representing a pseudo-scalar (vector) meson, in the next-to-leading-order (NLO) perturbative QCD (PQCD) formalism, concentrating on the B -> K phi, pi K^*, rho K, and omega K modes. It is found that the NLO corrections dramatically enhance the B -> rho K, \\omega K branching ratios, which were estimated to be small under the naive factorization assumption. The patterns of the direct CP asymmetries A_{CP}(B^0 -> rho^\\mp K^\\pm) \\approx A_{CP}(B^\\pm -> rho^0 K^\\pm) and |A_{CP}(B^0 -> pi^\\mp K^{*\\pm})| > |A_{CP}(B^\\pm -> pi^0 K^{*\\pm})| are predicted, differing from |A_{CP}(B^0 -> pi^\\mp K^\\pm)| >> |A_{CP}(B^\\pm -> pi^0 K^\\pm)|. The above patterns, if confirmed by data, will support the source of strong phases from the scalar penguin annihilation in PQCD. The results for the mixing-induced CP asymmetries S_f are consistent with those obtained in the literature, except that our S_{rho^0 K_S} is as low as 0.5.
Quark masses from quark-gluon condensates in a modified perturbative QCD
Cabo-Montes de Oca, Alejandro
2003-01-01
In this note, it is argued that the mass matrix for the six quarks can be generated in first approximation by introducing fermion condensates on the same lines as was done before for gluons, within the modified perturbative expansion for QCD proposed in former works. Thus, the results point in the direction of the conjectured link of the approximate `Democratic' symmetry of the quark mass matrix and `gap' effects similar to the ones occuring in superconductivity. The condensates are introduced here non-dynamically and therefore the question of the possibility for their spontaneous generation remains open. However, possible ways out of the predicted lack of the `Democratic' symmetry of the condensates resulting from the spontaneous breaking of the flavour symmetry are suggested. They come from an analysis based on the Cornwall--Jackiw--Tomboulis (CJT) effective potential for composite operators
Perturbative expansions for area-preserving maps
Energy Technology Data Exchange (ETDEWEB)
Servizi, G.; Turchetti, G.
1986-10-11
The structure of perturbation series for area-preserving maps is investigated. A basically different behaviour is found between the Birkhoff series, which formally conjugate with circles all the orbits in a neighbourhood of the origin, and the series which map into circles the individual invariant curves with fixed diophantine winding number. The former series exhibit an asymptotic character, the latter a convergent one, as one should expect from the KAM theorem. The source of this difference is found to be the different way in which the contributions of the relevant resonances propagate. In the first case, if epsilon is the size of the divisor associated to a resonance M/N, then at each order n>N an epsilon/sup -1/ contribution occurs, in the second case subtle cancellations provide a new epsilon/sup -1/ only when a harmonic (that is n=pN) is reached. This precise asymptotic statement and the properties of the relevant resonances obtained from the continued fraction expansion allow us, in the case of quadratic irrationals, to understand the limit process which leads to divergence or convergence. In the divergent case the asymptotic properties of the series are exhaustively described.
A NOTE ON DELTA-PERTURBATION EXPANSION METHOD
Institute of Scientific and Technical Information of China (English)
何吉欢
2002-01-01
The Delta-perturbation expansion method, a kind of new perturbation technique depending upon an artificial parameter Delta was studied. The study reveals that the method exits some advantages, but also exits some limitations. To overcome the limitations, the socalled linearized perturbation method proposed by HE Ji-huan can be powerfully applied.
Scalar coupling evolution in a non-perturbative QCD resummation scheme
Energy Technology Data Exchange (ETDEWEB)
Gomez, J.D., E-mail: jgomez@ufabc.edu.br [Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, 09210-170, Santo André, SP (Brazil); Natale, A.A., E-mail: natale@ift.unesp.br [Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, 09210-170, Santo André, SP (Brazil); Instituto de Física Teórica, UNESP, Rua Dr. Bento T. Ferraz, 271, Bloco II, 01140-070, São Paulo, SP (Brazil)
2015-07-30
We compute the Standard Model scalar coupling (λ) evolution in a particular QCD resummation scheme, where the QCD coupling becomes infrared finite due to the presence of a dynamically generated gluon mass, leading to the existence of a non-perturbative infrared fixed point. We discuss how this scheme can be fixed taking recourse to phenomenological considerations in the infrared region. The QCD β function associated to this non-perturbative coupling when introduced into the SM renormalization group equations increases the λ values at high energies.
Computational Aspects of Normal Form Perturbation Expansions.
Murray, Diana
The method of normal forms is used to develop analytic solutions to weakly nonlinear ordinary differential equations about an equilibrium solution of the system. Such equations arise in a broad spectrum of areas where one models vibrations and oscillations of mechanical systems, oscillations and feedback in biological and ecological systems, tracking of particles in an accelerator and long -time planetary motion in astronomy. An approximation to the true solution is sought that is valid for a long time with a prescribed error. It is constructed by means of a near-identity transformation from the original system to a nearby one. The transformation is determined by a perturbation expansion as a power series in a small parameter. The method of normal forms, introduced by Poincare in his Ph.D. thesis, was further expanded by Bruno, Arnold, Kummer and others who have emphasized the nonuniqueness of the transformation. Recently, Kahn and Zarmi (1991) developed the method of minimal normal forms (MNF) which uses the nonuniqueness to terminate the normal form equation in an early order of the expansion. In the past, investigators may have missed exploiting this "freedom" because traditionally calculations were carried only to first or second order and for Hamiltonian systems this nonuniqueness is fixed when one requires that the transformation be canonical. The work presented in this thesis centers on three main aspects: (1) establishing the numerical efficacy of MNF for conservative planar systems (Kahn, Murray and Zarmi (1993)), (2) displaying the computational and conceptual simplicity of MNF for dissipative systems (Murray 1994a)), (3) and demonstrating the utility of computer algebra programs in performing very high-order calculations (Forest and Murray) and in exploring the different dynamical features of a system (Kahn, Murray and Zarmi (1994a and b)). In sections 4-11 we have included many examples in order to illustrate the wide applicability of the method of MNF
A study on the interplay between perturbative QCD and CSS/TMD formalism in SIDIS processes
Energy Technology Data Exchange (ETDEWEB)
Boglione, M. [Univ. di Torino, Torino (Italy); INFN, Torino (Italy); Gonzalez Hernandez, J. O. [INFN, Torino (Italy); Melis, S. [Univ. di Torino, Torino (Italy); Prokudin, A. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
2015-02-16
We study the Semi-Inclusive Deep Inelastic Scattering (SIDIS) cross section as a function of the transverse momentum, _{qT}. In order to describe it over a wide region of _{qT}, soft gluon resummation has to be performed. Here we will use the original Collins-Soper-Sterman (CSS) formalism; however, the same procedure would hold within the improved Transverse Momentum Dependent (TMD) framework. We study the matching between the region where fixed order perturbative QCD can successfully be applied and the region where soft gluon resummation is necessary. We find that the commonly used prescription of matching through the so-called Y-factor cannot be applied in the SIDIS kinematical configurations we examine. In particular, the non-perturbative component of the resummed cross section turns out to play a crucial role and should not be overlooked even at relatively high energies. As a result, the perturbative expansion of the resummed cross section in the matching region is not as reliable as it is usually believed and its treatment requires special attention.
SVZ + 1/q2 expansion versus some QCD holographic Models
Jugeau, F; Ratsimbarison, H
2013-01-01
Considering the classical two-point correlators built from (axial)-vector, scalar \\bar qq and gluonium currents, we confront results obtained using the SVZ + 1/q2 expansion to the ones from some QCD holographic models in the Euclidian region. We conclude that the presence of the 1/q2-term in the SVZ-expansion due to a tachyonic gluon mass appears naturally in the Minimum Soft Wall (MSW) and the Gauge/String Dual (GSD) models which can also reproduce semi-quantitatively some of the higher dimension condensate contributions appearing in the OPE. The Hard-Wall model shows a large departure from the SVZ + 1/q2 expansion in the vector, scalar and gluonium channels due to the absence of any power corrections. The equivalence of the MSW and GSD models is manifest in the vector channel through the relation of the dilaton parameter with the tachyonic gluon mass. For approximately reproducing the phenomenological values of the dimension d = 4, 6 condensates, the holographic models require a tachyonic gluon mass (alpha_...
Mojaza, Matin; Brodsky, Stanley J; Wu, Xing-Gang
2013-05-10
We introduce a generalization of the conventional renormalization schemes used in dimensional regularization, which illuminates the renormalization scheme and scale ambiguities of perturbative QCD predictions, exposes the general pattern of nonconformal {β(i)} terms, and reveals a special degeneracy of the terms in the perturbative coefficients. It allows us to systematically determine the argument of the running coupling order by order in perturbative QCD in a form which can be readily automatized. The new method satisfies all of the principles of the renormalization group and eliminates an unnecessary source of systematic error.
Perturbative QCD tests from the LEP, HERA, and TEVATRON colliders
Energy Technology Data Exchange (ETDEWEB)
Kuhlmann, S. [Argonne National Lab., IL (United States)
1994-09-01
A review of QCD tests from LEP, HERA and the TEVATRON colliders is presented. This includes jet production, quark/gluon jet separation, quark/gluon propagator spin, {alpha}{sub s} updates, photon production, and rapidity gap experiments.
Non-perturbative improvement of quark mass renormalization in two-flavour lattice QCD
Fritzsch, Patrick; Tantalo, Nazario
2010-01-01
We non-perturbatively determine the renormalization constant and the improvement coefficients relating the renormalized current and subtracted quark mass in O(a) improved two-flavour lattice QCD. We employ the Schr\\"odinger functional scheme and fix the physical extent of the box by working at a constant value of the renormalized coupling. Our calculation yields results which cover two regions of bare parameter space. One is the weak-coupling region suitable for volumes of about half a fermi. By making simulations in this region, quarks as heavy as the bottom can be propagated with the full relativistic QCD action and renormalization problems in HQET can be solved non-perturbatively by a matching to QCD in finite volume. The other region refers to the common parameter range in large-volume simulations of two-flavour lattice QCD, where our results have particular relevance for charm physics applications.
A New Approach to Analytic, Non-Perturbative and Gauge-Invariant QCD
Fried, H M; Sheu, Y -M
2012-01-01
Following a previous calculation of quark scattering in eikonal approximation, this paper presents a new, analytic and rigorous approach to the calculation of QCD phenomena. In this formulation a basic distinction between the conventional "idealistic" description of QCD and a more "realistic" description is brought into focus by a non-perturbative, gauge-invariant evaluation of the Schwinger solution for the QCD generating functional in terms of the exact Fradkin representations of the Green's functional and the vacuum functional. Because quarks exist asymptotically only in bound states, their transverse coordinates can never be measured with arbitrary precision; the non-perturbative neglect of this statement leads to obstructions that are easily corrected by invoking in the basic Lagrangian a probability amplitude which describes such transverse imprecision. The second result of this non-perturbative analysis is the appearance of a new and simplifying output called "Effective Locality", in which the interact...
Series Expansion of Functions with He's Homotopy Perturbation Method
Khattri, Sanjay Kumar
2012-01-01
Finding a series expansion, such as Taylor series, of functions is an important mathematical concept with many applications. Homotopy perturbation method (HPM) is a new, easy to use and effective tool for solving a variety of mathematical problems. In this study, we present how to apply HPM to obtain a series expansion of functions. Consequently,…
Controlling quark mass determinations non-perturbatively in three-flavour QCD
Directory of Open Access Journals (Sweden)
Campos Isabel
2017-01-01
Full Text Available The determination of quark masses from lattice QCD simulations requires a non-perturbative renormalization procedure and subsequent scale evolution to high energies, where a conversion to the commonly used MS¯$\\overline {{\\rm{MS}}} $ scheme can be safely established. We present our results for the non-perturbative running of renormalized quark masses in Nf = 3 QCD between the electroweak and a hadronic energy scale, where lattice simulations are at our disposal. Recent theoretical advances in combination with well-established techniques allows to follow the scale evolution to very high statistical accuracy, and full control of systematic effects.
Controlling quark mass determinations non-perturbatively in three-flavour QCD
Campos, Isabel; Pena, Carlos; Preti, David; Ramos, Alberto; Vladikas, Anastassios
2016-01-01
The determination of quark masses from lattice QCD simulations requires a non-perturbative renormalization procedure and subsequent scale evolution to high energies, where a conversion to the commonly used MS-bar scheme can be safely established. We present our results for the non-perturbative running of renormalized quark masses in Nf=3 QCD between the electroweak and a hadronic energy scale, where lattice simulations are at our disposal. Recent theoretical advances in combination with well-established techniques allows to follow the scale evolution to very high statistical accuracy, and full control of systematic effects.
Finite Volume Cumulant Expansion in QCD-Colorless Plasma
Ladrem, M; Al-Full, Z; Cherif, S
2015-01-01
Due to the finite size effects, the localisation of the phase transition in finite systems and the determination of its order, become an extremely difficult task, even in the simplest known cases. In order to identify and locate the finite volume transition point $T_{0}(V)$ of the QCD deconfinement phase transition to a Colorless QGP, we have developed a new approach using the finite size cumulant expansion of the order parameter and the $L_{mn}$-method. The first six cumulants $C_{1,2,3,4,5,6}$ with the corresponding under-normalized ratios(skewness $\\Sigma$, kurtosis $\\kappa$ ,pentosis $\\Pi_{\\pm}$ and hexosis $\\mathcal{H}_{1,2,3}$) and three unnormalized combinations of them ($\\mathcal{O}={\\mathcal{\\sigma }^{2} \\mathcal{\\kappa } }{\\mathbf{\\Sigma }^{-1} }$, $\\mathcal{U} ={\\mathcal{\\sigma }^{-2} \\mathbf{\\Sigma }^{-1} }$, $\\mathcal{N} = \\mathcal{\\sigma }^{2} \\mathcal{\\kappa }$) are calculated and studied as functions of $(T,V)$. A new approach, unifying in a clear and consistent way the definitions of cumulant...
On causality, unitarity and perturbative expansions
Energy Technology Data Exchange (ETDEWEB)
Danilkin, Igor; Gasparyan, Ashot; Lutz, Matthias [GSI, Planck Str. 1, 64291 Darmstadt (Germany)
2011-07-01
We present a pedagogical case study how to combine micro-causality and unitarity based on a perturbative approach. The method we advocate constructs an analytic extrapolation of partial-wave scattering amplitudes that is constrained by the unitarity condition. Suitably constructed conformal mappings help to arrive at a systematic approximation of the scattering amplitude. The technique is illustrated at hand of a Yukawa interaction. The typical case of a superposition of strong short-range and weak long-range forces is investigated.
On causality, unitarity and perturbative expansions
Energy Technology Data Exchange (ETDEWEB)
Danilkin, I.V.; Gasparyan, A.M. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Planck Str. 1, 64291 Darmstadt (Germany); Institute for Theoretical and Experimental Physics, 117259, B. Cheremushkinskaya 25, Moscow (Russian Federation); Lutz, M.F.M., E-mail: m.lutz@gsi.d [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Planck Str. 1, 64291 Darmstadt (Germany)
2011-02-28
We present a pedagogical case study how to combine micro-causality and unitarity based on a perturbative approach. The method we advocate constructs an analytic extrapolation of partial-wave scattering amplitudes that is constrained by the unitarity condition. Suitably constructed conformal mappings help to arrive at a systematic approximation of the scattering amplitude in a quantum-field theoretical context. The technique is illustrated at hand of a Yukawa interaction. The typical case of a superposition of strong short-range and weak long-range forces is investigated.
Quark Matter Equation of State from Perturbative QCD
Vuorinen, Aleksi
2016-01-01
In this proceedings contribution, we discuss recent developments in the perturbative determination of the Equation of State of dense quark matter, relevant for the microscopic description of neutron star cores. First, we introduce the current state of the art in the problem, both at zero and small temperatures, and then present results from two recent perturbative studies that pave the way towards extending the EoS to higher orders in perturbation theory.
Light-Front Holography and Non-Perturbative QCD
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; /SLAC; de Teramond, Guy F.; /Costa Rica U.
2009-12-09
The combination of Anti-de Sitter space (AdS) methods with light-front holography leads to a semi-classical first approximation to the spectrum and wavefunctions of meson and baryon light-quark bound states. Starting from the bound-state Hamiltonian equation of motion in QCD, we derive relativistic light-front wave equations in terms of an invariant impact variable {zeta} which measures the separation of the quark and gluonic constituents within the hadron at equal light-front time. These equations of motion in physical space-time are equivalent to the equations of motion which describe the propagation of spin-J modes in anti-de Sitter (AdS) space. Its eigenvalues give the hadronic spectrum, and its eigenmodes represent the probability distribution of the hadronic constituents at a given scale. Applications to the light meson and baryon spectra are presented. The predicted meson spectrum has a string-theory Regge form M{sup 2} = 4{kappa}{sup 2}(n + L + S = 2); i.e., the square of the eigenmass is linear in both L and n, where n counts the number of nodes of the wavefunction in the radial variable {zeta}. The space-like pion form factor is also well reproduced. One thus obtains a remarkable connection between the description of hadronic modes in AdS space and the Hamiltonian formulation of QCD in physical space-time quantized on the light-front at fixed light-front time {tau}. The model can be systematically improved by using its complete orthonormal solutions to diagonalize the full QCD light-front Hamiltonian or by applying the Lippmann-Schwinger method in order to systematically include the QCD interaction terms.
Minijet initial state of heavy-ion collisions from next-to-leading order perturbative QCD
Paatelainen, Risto
2014-01-01
The aim of this thesis is to calculate field-theoretically as rigorously as possible the initial state of partonic matter produced in ultrarelativistic heavy-ion collisions at CERN-LHC and BNL-RHIC colliders. The computed minijet initial conditions are then used in the initialization of the relativistic hydrodynamical modeling of these collisions. In the theoretical introduction part the computation of parton production cross section at next-to-leading order (NLO) perturbative QCD (pQCD) is discussed. Furthermore, the full analytical calculation for the squared quark-quark scattering matrix element including the systematic ultraviolet renormalization is presented. Finally, the subtraction method allowing for the cancellation of the infrared and collinear singularities in the partonic QCD cross section at NLO is discussed. In the more phenomenological part of the thesis the original EKRT model, which combines collinearly factorized leading-order pQCD minijet production with gluon saturation, is introduced. Nex...
Non-perturbative gluon-hadron inputs for all available forms of QCD factorization
Ermolaev, B I
2016-01-01
Description of hadronic reactions at high energies is conventionally done on basis of QCD factoriza- tion so that factorization convolutions involve non-perturbative inputs mimicking non-perturbative contributions and perturbative evolution of those inputs. We construct the inputs for the gluon- hadron scattering amplitudes in the forward kinematics and, using the Optical theorem, convert them into inputs for gluon distributions in the both polarized and unpolarized hadrons. Firstly, we derive general mathematical criteria which any model for the inputs should obey and then suggest a Resonance Model satisfying those criteria. This model is inspired by a simple observation: after emitting an active parton off the hadron, the remaining ensemble of spectators becomes unstable and therefore it can be described through factors of the resonance type. Exploiting Resonance Model, we obtain non-perturbative inputs for gluon distributions in unpolarized and polarized hadrons for all available forms of QCD factorization...
Determination of the QCD Λ Parameter and the Accuracy of Perturbation Theory at High Energies.
Dalla Brida, Mattia; Fritzsch, Patrick; Korzec, Tomasz; Ramos, Alberto; Sint, Stefan; Sommer, Rainer
2016-10-28
We discuss the determination of the strong coupling α_{MS[over ¯]}(m_{Z}) or, equivalently, the QCD Λ parameter. Its determination requires the use of perturbation theory in α_{s}(μ) in some scheme s and at some energy scale μ. The higher the scale μ, the more accurate perturbation theory becomes, owing to asymptotic freedom. As one step in our computation of the Λ parameter in three-flavor QCD, we perform lattice computations in a scheme that allows us to nonperturbatively reach very high energies, corresponding to α_{s}=0.1 and below. We find that (continuum) perturbation theory is very accurate there, yielding a 3% error in the Λ parameter, while data around α_{s}≈0.2 are clearly insufficient to quote such a precision. It is important to realize that these findings are expected to be generic, as our scheme has advantageous properties regarding the applicability of perturbation theory.
The Feynman-Schwinger (world-line) representation in perturbative QCD
Simonov, Yu. A.; Tjon, J. A.
2002-01-01
Abstract: The proper time path integral representation is derived explicitly for an arbitrary $n$-point amplitude in QCD. In the standard perturbation theory the formalism allows to sum up the leading subseries, e.g. yielding double-logarithm Sudakov asymptotics for form factors. Correspondence with
Finite-volume cumulant expansion in QCD-colorless plasma
Energy Technology Data Exchange (ETDEWEB)
Ladrem, M. [Taibah University, Physics Department, Faculty of Science, Al-Madinah, Al-Munawwarah (Saudi Arabia); Physics Department, Algiers (Algeria); ENS-Vieux Kouba (Bachir El-Ibrahimi), Laboratoire de Physique et de Mathematiques Appliquees (LPMA), Algiers (Algeria); Ahmed, M.A.A. [Taibah University, Physics Department, Faculty of Science, Al-Madinah, Al-Munawwarah (Saudi Arabia); ENS-Vieux Kouba (Bachir El-Ibrahimi), Laboratoire de Physique et de Mathematiques Appliquees (LPMA), Algiers (Algeria); Taiz University in Turba, Physics Department, Taiz (Yemen); Alfull, Z.Z. [Taibah University, Physics Department, Faculty of Science, Al-Madinah, Al-Munawwarah (Saudi Arabia); Cherif, S. [ENS-Vieux Kouba (Bachir El-Ibrahimi), Laboratoire de Physique et de Mathematiques Appliquees (LPMA), Algiers (Algeria); Ghardaia University, Sciences and Technologies Department, Ghardaia (Algeria)
2015-09-15
Due to the finite-size effects, the localization of the phase transition in finite systems and the determination of its order, become an extremely difficult task, even in the simplest known cases. In order to identify and locate the finite-volume transition point T{sub 0}(V) of the QCD deconfinement phase transition to a colorless QGP, we have developed a new approach using the finite-size cumulant expansion of the order parameter and the L{sub mn}-method. The first six cumulants C{sub 1,2,3,4,5,6} with the corresponding under-normalized ratios (skewness Σ, kurtosis κ, pentosis Π{sub ±}, and hexosis H{sub 1,2,3}) and three unnormalized combinations of them, (O = σ{sup 2}κΣ{sup -1},U = σ{sup -2}Σ{sup -1},N = σ{sup 2}κ) are calculated and studied as functions of (T, V). A new approach, unifying in a clear and consistent way the definitions of cumulant ratios, is proposed.Anumerical FSS analysis of the obtained results has allowed us to locate accurately the finite-volume transition point. The extracted transition temperature value T{sub 0}(V) agrees with that expected T{sub 0}{sup N}(V) from the order parameter and the thermal susceptibility χ{sub T} (T, V), according to the standard procedure of localization to within about 2%. In addition to this, a very good correlation factor is obtained proving the validity of our cumulants method. The agreement of our results with those obtained by means of other models is remarkable. (orig.)
Perturbative thermodynamics at nonzero isospin density for cold QCD
Graf, Thorben; Fraga, Eduardo S
2015-01-01
We use next-to-leading-order in perturbation theory to investigate the effects of a finite isospin density on the thermodynamics of cold strongly interacting matter. Our results include nonzero quark masses and are compared to lattice data.
Perturbative thermodynamics at nonzero isospin density for cold QCD
Graf, Thorben; Schaffner-Bielich, Juergen; Fraga, Eduardo S.
2016-04-01
We use next-to-leading order in perturbation theory to investigate the effects of a finite isospin density on the thermodynamics of cold strongly interacting matter. Our results include nonzero quark masses and are compared to lattice data.
BRST analysis of QCD$_{2}$ as a perturbed WZW theory
Cabra, D C; Schaposnik, F A
1995-01-01
Integrability of Quantum Chromodynamics in 1+1 dimensions has recently been suggested by formulating it as a perturbed conformal Wess-Zumino-Witten Theory. The present paper further elucidates this formulation, by presenting a detailed BRST analysis.
Pire, B
2009-01-01
QCD is the theory of strong interactions and non-perturbative methods have been developed to address the confinement property of QCD. Many experimental measurements probe the confining dynamics, and it is well-known that hard scattering processes allow the extraction of non perturbative hadronic matrix elements. To study exclusive hard processes, such as electromagnetic form factors and reactions like gamma* N -> gamma N', gamma* N -> pi N', gamma* gamma -> pi pi, antiproton proton ->gamma* pi in particular kinematics (named as generalized Bjorken regime), one introduces specific non-perturbative objects, namely generalized parton distributions (GPDs), distribution amplitudes (DA) and transition distribution amplitudes (TDA), which are Fourier transformed non-diagonal matrix elements of non-local operators on the light-cone. We review here a selected sample of exclusive amplitudes in which the quark and gluon content of hadrons is probed, and emphasize that much remains to be done to successfully compute thei...
Ben-Haim, E; Roudeau, Patrick; Savoy-Navarro, Aurore; Stocchi, A; Bambade, Ph.
2004-01-01
Using recent measurements of the b-quark fragmentation distribution obtained in $e^+e^- \\to b \\bar{b}$ events registered at the Z pole, the non-perturbative QCD component of the distribution has been extracted independently of any hadronic physics modelling. This distribution depends only on the way the perturbative QCD component has been defined. When the perturbative QCD component is taken from a parton shower Monte-Carlo, the non-perturbative QCD component is rather similar with those obtained from the Lund or Bowler models. When the perturbative QCD component is the result of an analytic NLL computation, the non-perturbative QCD component has to be extended in a non-physical region and thus cannot be described by any hadronic modelling. In the two examples used to characterize these two situations, which are studied at present, it happens that the extracted non-perturbative QCD distribution has the same shape, being simply translated to higher-x values in the second approach, illustrating the ability of t...
Approach to Perturbative QCD Results in Transition Amplitudes of Nucleon Negative-Parity Resonances
Institute of Scientific and Technical Information of China (English)
DONG Yu-Bing
2004-01-01
The scaling behaviors of the nucleon resonance transition amplitudes from perturbative QCD (PQCD) are utilized to parametrize the amplitudes of the first negative-parity nucleon resonance S11 (1535). Our analysis indicates that the constraints of the transition amplitude for the S11 resonance at the limit Q2 →∞ by QCD sum rule calculations are not applicable at a moderate Q2 range of 2.5 ～ 4 Ge V2 compared with the present available data if the contribution of S11 is dominant in the Q2 limit.
QCD With A Chemical Potential, Topology, And The 't Hooft 1/N Expansion
Armoni, Adi
2012-01-01
We discuss the dependence of observables on the chemical potential in 't Hooft's large-N QCD. To this end we use the worldline formalism to expand the fermionic determinant in powers of 1/N. We consider the hadronic as well as the deconfining phase of the theory. We discuss the origin of the sign problem in the worldline approach and elaborate on the planar equivalence between QCD with a baryon chemical potential and QCD with an isospin chemical potential. We show that for C-even observables the sign problem occurs at a subleading order in the 1/N expansion of the fermionic determinant. Finally, we comment on the finite N theory.
The theory and phenomenology of perturbative QCD based jet quenching
Majumder, A.; van Leeuwen, M.
2010-01-01
The study of the structure of strongly interacting dense matter via hard jets is reviewed. High momentum partons produced in hard collisions produce a shower of gluons prior to undergoing the non-perturbative process of hadronization. In the presence of a dense medium this shower is modified due to
The triple pomeron interaction in the perturbative QCD
Braun, M
1995-01-01
The triple pomeron interaction is studied in the perturbative approach of BFKL-Bartels. At finite momentum transfers \\sqrt{-t} the contribution factorizes in the standard manner with a triple-pomeron vertex proportional to 1/\\sqrt{-t}. At t=0 the contribution is finite, although it grows faster with energy than for finite t and does not factorize.
Perturbative QCD effects observed in 490 GeV deep-inelastic muon scattering
Energy Technology Data Exchange (ETDEWEB)
Adams, M.R.; Aied, S.; Anthony, P.L.; Baker, M.D.; Bartlett, J.; Bhatti, A.A.; Braun, H.M.; Busza, W.; Conrad, J.M.; Coutrakon, G.; Davisson, R.; Derado, I.; Dhawan, S.K.; Dougherty, W.; Dreyer, T.; Dziunikowska, K.; Eckardt, V.; Ecker, U.; Erdmann, M.; Eskreys, A.; Figiel, J.; Gebauer, H.J.; Geesaman, D.F.; Gilman, R.; Green, M.C.; Haas, J.; Halliwell, C.; Hanlon, J.; Hantke, D.; Hughes, V.W.; Jackson, H.E.; Jaffe, D.E.; Jancso, G.; Jansen, D.M.; Kaufman, S.; Kennedy, R.D.; Kirk, T.; Kobrak, H.G.E.; Krzywdzinski, S.; Kunori, S.; Lord, J.J.; Lubatti, H.J.; McLeod, D.; Magill, S.; Malecki, P.; Manz, A.; Melanson, H.; Michael, D.G.; Mohr, W.; Montgomery, H.E.; Morfin, J.G.; Nickerson, R.B.; O' Day, S.; Olkiewicz, K.; Osborne, L.; Papavassiliou, V.; Pawlik, B.; Pipkin, F.M.; Ramberg, E.J.; Roeser, A.; Ryan, J.J.; Salgado, C.W.; Salvarani, A.; Schellman, H.; Schmitt, M.; Schmitz, N.; Schueler, K.P.; Skuja, A.; Snow, G.A.; Soeldner-Rembold, S.; Steinberg, P.H.; Stier, H.E.; Stopa, P.; Swanso; (Fermilab E665 Collaboration)
1993-12-01
Results on forward charged hadrons in 490 GeV deep-inelastic muon scattering are presented. The transverse momenta, azimuthal asymmetry, and energy flow of events with four or more forward charged hadrons are studied. The range of the invariant hadronic mass squared 300[lt][ital W][sup 2][lt]900 GeV[sup 2]/[ital c][sup 4] extends higher than previous deep-inelastic muon scattering experiments. Data are compared to the predictions of the Lund Monte Carlo model with perturbative QCD simulated by matrix elements, parton showers, and color dipole radiation. All of the QCD-based models are consistent with the data while a model without QCD processes is not. Correlations with the multiplicity-independent event variable [Pi][congruent][summation][vert bar][ital p][sub [ital T
Non-perturbative QCD effects in forward scattering at LHC
Bahia, C A S; Luna, E G S
2015-01-01
We study infrared contributions to semihard parton-parton interactions by considering an effective charge whose finite infrared behavior is constrained by a dynamical mass scale. Using an eikonal QCD-based model in order to connect this semihard parton-level dynamics to the hadron-hadron scattering, we obtain predictions for the proton-proton ($pp$) and antiproton-proton ($\\bar{p}p$) total cross sections, $\\sigma_{tot}^{pp,\\bar{p}p}$, and the ratios of the real to imaginary part of the forward scattering amplitude, $\\rho^{pp,\\bar{p}p}$. We discuss the theoretical aspects of this formalism and consider the phenomenological implications of a class of energy-dependent form factors in the high-energy behavior of the forward amplitude. We introduce integral dispersion relations specially tailored to relate the real and imaginary parts of eikonals with energy-dependent form factors. Our results, obtained using a group of updated sets of parton distribution functions (PDFs), are consistent with the recent data from ...
The role of quark mass in cold and dense perturbative QCD
Fraga, E S; Fraga, Eduardo S.; Romatschke, Paul
2004-01-01
We consider the equation of state of QCD at high density and zero temperature in perturbation theory to first order in the coupling constant $\\alpha_s$. We compute the thermodynamic potential including the effect of a non-vanishing mass for the strange quark and show that corrections are sizable. Renormalization group running of the coupling and the strange quark mass plays a crucial role. The structure of quark stars is dramatically modified.
Niemi, H; Paatelainen, R
2015-01-01
We introduce an event-by-event perturbative-QCD + saturation + hydro ("EKRT") framework for ultrarelativistic heavy-ion collisions, where we compute the produced fluctuating QCD-matter energy densities from next-to-leading order perturbative QCD using a saturation conjecture to control soft particle production, and describe the space-time evolution of the QCD matter with dissipative fluid dynamics, event by event. We perform a simultaneous comparison of the centrality dependence of hadronic multiplicities, transverse momentum spectra, and flow coefficients of the azimuth-angle asymmetries, against the LHC and RHIC measurements. We compare also the computed event-by-event probability distributions of relative fluctuations of elliptic flow, and event-plane angle correlations, with the experimental data from Pb+Pb collisions at the LHC. We show how such a systematic multi-energy and multi-observable analysis tests the initial state calculation and the applicability region of hydrodynamics, and in particular how ...
Determination of the QCD Λ-parameter and the accuracy of perturbation theory at high energies
Energy Technology Data Exchange (ETDEWEB)
Dalla Brida, Mattia [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Fritzsch, Patrick [Univ. Autonoma de Madrid (Spain). Inst. de Fisica Teorica UAM/CSIC; Korzec, Tomasz [Wuppertal Univ. (Germany). Dept. of Physics; Ramos, Alberto [CERN - European Organization for Nuclear Research, Geneva (Switzerland). Theory Div.; Sint, Stefan [Trinity College Dublin (Ireland). School of Mathematics; Sommer, Rainer [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Collaboration: ALPHA Collaboration
2016-04-15
We discuss the determination of the strong coupling α{sub MS}(m{sub Z}) or equivalently the QCD Λ-parameter. Its determination requires the use of perturbation theory in α{sub s}(μ) in some scheme, s, and at some energy scale μ. The higher the scale μ the more accurate perturbation theory becomes, owing to asymptotic freedom. As one step in our computation of the Λ-parameter in three-flavor QCD, we perform lattice computations in a scheme which allows us to non-perturbatively reach very high energies, corresponding to α{sub s}=0.1 and below. We find that (continuum) perturbation theory is very accurate there, yielding a three percent error in the Λ-parameter, while data around α{sub s}∼0.2 is clearly insufficient to quote such a precision. It is important to realize that these findings are expected to be generic, as our scheme has advantageous properties regarding the applicability of perturbation theory.
Lattice QCD at finite temperature and density from Taylor expansion
Steinbrecher, Patrick
2017-01-01
In the first part, I present an overview of recent Lattice QCD simulations at finite temperature and density. In particular, we discuss fluctuations of conserved charges: baryon number, electric charge and strangeness. These can be obtained from Taylor expanding the QCD pressure as a function of corresponding chemical potentials. Our simulations were performed using quark masses corresponding to physical pion mass of about 140 MeV and allow a direct comparison to experimental data from ultra-relativistic heavy ion beams at hadron colliders such as the Relativistic Heavy Ion Collider at Brookhaven National Laboratory and the Large Hadron Collider at CERN. In the second part, we discuss computational challenges for current and future exascale Lattice simulations with a focus on new silicon developments from Intel and NVIDIA.
Towards a non-perturbative matching of HQET and QCD with dynamical light quarks
Della Morte, Michele; Heitger, Jochen; Meyer, Harvey B.; Simma, Hubert; Sommer, Rainer
2007-01-01
We explain how the strategy of solving renormalization problems in HQET non-perturbatively by a matching to QCD in finite volume can be implemented to include dynamical fermions. As a primary application, some elements of an HQET computation of the mass of the b-quark beyond the leading order with N_f=2 are outlined. In particular, the matching of HQET and QCD requires relativistic QCD simulations in a volume with L ~ 0.5 fm, which will serve to quantitatively determine the heavy quark mass dependence of heavy-light meson observables in the continuum limit of finite-volume two-flavour lattice QCD. As a preparation for the latter, we report on our determination of the renormalization constants and improvement coefficients relating the renormalized current and subtracted bare quark mass in the relevant weak coupling region. The calculation of these coefficients employs a constant physics condition in the Schroedinger functional scheme, where the box size L is fixed by working at a prescribed value of the renorm...
Non-perturbative renormalization of static-light four-fermion operators in quenched lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Palombi, F. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Papinutto, M.; Pena, C. [CERN, Geneva (Switzerland). Physics Dept., Theory Div.; Wittig, H. [Mainz Univ. (Germany). Inst. fuer Kernphysik
2007-06-15
We perform a non-perturbative study of the scale-dependent renormalization factors of a multiplicatively renormalizable basis of {delta}B=2 parity-odd four-fermion operators in quenched lattice QCD. Heavy quarks are treated in the static approximation with various lattice discretizations of the static action. Light quarks are described by nonperturbatively O(a) improved Wilson-type fermions. The renormalization group running is computed for a family of Schroedinger functional (SF) schemes through finite volume techniques in the continuum limit. We compute non-perturbatively the relation between the renormalization group invariant operators and their counterparts renormalized in the SF at a low energy scale. Furthermore, we provide non-perturbative estimates for the matching between the lattice regularized theory and all the SF schemes considered. (orig.)
A perturbative QCD study of dijets in p+Pb collisions at the LHC
Eskola, Kari J; Salgado, Carlos A
2013-01-01
Inspired by the recent measurements of the CMS collaboration, we report a QCD study of dijet production in proton+lead collisions at the LHC involving large-transverse-momentum jets, $p_T \\gtrsim 100$ GeV. Examining the inherent uncertainties of the next-to-leading order perturbative QCD calculations and their sensitivity to the free proton parton distributions (PDFs), we observe a rather small, typically much less than 5% clearance for the shape of the dijet rapidity distribution within approximately 1.5 units around the midrapidity. Even a more stable observable is the ratio between the yields in the positive and negative dijet rapidity, for which the baseline uncertainty can be made negligible by imposing a symmetric jet rapidity acceptance. Both observables prove sensitive to the nuclear modifications of the gluon distributions, the corresponding uncertainties clearly exceeding the estimated baseline uncertainties from the free-proton PDFs and scale dependence. From a theoretical point of view, these obse...
Perturbative aspects of the phase diagram of QCD with heavy quarks
Serreau, Julien; Reinosa, Urko
2017-03-01
We report on recent progress in the description of the phase diagram of QCD with heavy quarks at nonzero temperature and chemical potential in the context of a modified perturbative approach. The latter is based on a simple massive extension of the QCD Lagrangian in the Landau-DeWitt gauge, the background field generalization of the Landau gauge. Here, the background field plays the role of an order parameter for the center symmetry, relevant for confinement-deconfinement transition. One-loop results in this approach give a fairly accurate description of the phase diagram both at real and imaginary chemical potential. We comment on issues related to the sign problem in continuum approaches. Based on works in collaboration with Matthieu Tissier and Nicolás Wschebor.
QCD Multipole Expansion and Hadronic Transitions in Heavy Quarkonium Systems
Institute of Scientific and Technical Information of China (English)
KUANG Yu-ping
2006-01-01
We review the developments of the multipole expansion approach in quantum chromodynamics and its applications to hadronic transitions and some radiative decays of heavy quarkonia.Theoretical predictions are compared with updated experimental results.
Studies of QCD at the Intersection of the Perturbative and Non-Perturbative Regimes
Energy Technology Data Exchange (ETDEWEB)
Liuti, Simonetta [Univ. of Virginia, Charlottesville, VA (United States). Physics Dept.
2013-12-31
New sets of spin observables and relations/sum rules were developed that could be tested in a class of experiments including exclusive deeply virtual electron and neutrino proton/nucleus scattering. Advancements in the phenomenology for the following outstanding problems at the next QCD frontier of nuclear physics were obtained: (1) the origin of the proton spin and its decomposition into quark and gluon spin and orbital angular momentum components; (2) the size of the hadronic matrix elements entering processes at the Intensity Frontier, from neutron and nuclear beta decay, to the experimental extraction of the neutron Electric Dipole Moment; (3) Monitoring the transition of quarks and gluons into protons, neutrons and pions to form the atomic nucleus.
Taylor- and fugacity expansion for the effective Z(3) spin model of QCD at finite density
Grünwald, Eva; Gattringer, Christof
2014-01-01
Series expansions in the chemical potential mu are studied for an effective theory of QCD which has a flux representation where the complex action is overcome. In particular we consider fugacity series, Taylor expansion and a modified Taylor expansion and compare the outcome of these series to the reference results from a Monte Carlo simulation in the flux representation where arbitrary mu is accessible. It is shown that for most parameter values the fugacity expansion gives the best approximation to the data from the flux simulation, followed by our newly proposed modified Taylor expansion. For the conventional Taylor expansion we find that the results coincide with the flux data only for very small mu.
$CP$ violation for $B^+_{c}\\rightarrow D_{(s)}^+\\pi^+\\pi^-$ in Perturbative QCD
Lü, Gang; Wang, Yu-Ting
2016-01-01
In the perturbative QCD (PQCD) approach we study the direct $CP$ violation in $B^+_{c}\\rightarrow D_{(s)}^+\\rho^0(\\omega) \\rightarrow D_{(s)}^+\\pi^+\\pi^-$ via the $\\rho-\\omega$ mixing mechanism. We find that the $CP$ violation can be enhanced by $\\rho-\\omega$ mixing when the invariant masses of the $\\pi^+\\pi^-$ pairs are in the vicinity of the $\\omega$ resonance. For the decay process $B^+_{c}\\rightarrow D^+\\rho^0(\\omega) \\rightarrow D^+\\pi^+\\pi^-$, the maximum $CP$ violation can reach 7.5 {\\%}.
Dijet azimuthal decorrelations for $\\Delta \\phi_{\\rm dijet} < 2\\pi/3$ in perturbative QCD
Wobisch, M
2015-01-01
We point out an inconsistency in perturbative QCD predictions previously used for dijet azimuthal decorrelations for azimuthal angles of $\\Delta\\phi_{\\rm dijet} < 2\\pi/3$ between the two jets. We show how the inconsistency arises and how the calculations can be modified to provide more accurate results that exhibit a smaller scale dependence and give a better description of the data than the inconsistent results. We also explain how the quality of the predictions strongly depends on a perceivedly minor detail in the definition of the dijet phase space and give recommendations for future measurements.
A Perturbative QCD Analysis of the Nucleon's Pauli Form Factor F_2(Q^2)
Belitsky, A V; Yuan, F; Belitsky, Andrei V.; Ji, Xiangdong; Yuan, Feng
2003-01-01
We perform a perturbative QCD analysis of the nucleon's Pauli form factor $F_2(Q^2)$ in the asymptotically large $Q^2$ limit. We find that the leading contribution to $F_2(Q^2)$ goes like $1/Q^6$, consistent with the well-known folklore. Its coefficient is expressed in terms of an overlap integral involving the leading and subleading light-cone wave functions of the nucleon, the latter describing the quark state with one unit of orbital angular momentum. We estimate the numerical size of the coefficient and comment on the contribution from the end-point region.
Khellat, M
2016-01-01
We first consider the idea of renormalization group-induced estimates, in the context of optimization procedures, for the Brodsky-Lepage-Mackenzie approach to generate higher-order contributions for QCD perturbative series. Secondly, we develop the deviation pattern approach (DPA) in which through a series of comparisons between lower-order RG-induced estimates and the corresponding analytical calculations, we modify higher-order RG-induced estimates. Finally, using the normal estimation procedure and DPA, we get estimates of $\\alpha_s^4$ corrections for the Bjorken sum rule of polarized deed-inelastic scattering and for the non-singlet contribution to the Adler function.
Non-perturbative test of the Witten-Veneziano formula from lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Cichy, Krzysztof [Goethe-Universität, Institut für Theoretische Physik,Max-von-Laue-Straße 1, Frankfurt a.M., D-60438 (Germany); NIC, DESY,Platanenallee 6, Zeuthen, D-15738 (Germany); Adam Mickiewicz University, Faculty of Physics,Umultowska 85, Poznan, 61-614 (Poland); Garcia-Ramos, Elena [NIC, DESY,Platanenallee 6, Zeuthen, D-15738 (Germany); Humboldt Universität zu Berlin,Newtonstr. 15, Berlin, D-12489 (Germany); Jansen, Karl [NIC, DESY,Platanenallee 6, Zeuthen, D-15738 (Germany); Ottnad, Konstantin [Institut für Strahlen- und Kernphysik (Theorie),Nussallee 14-16, Bonn 53115 Germania (Germany); Urbach, Carsten [Institut für Strahlen- und Kernphysik (Theorie),Nussallee 14-16, Bonn 53115 Germania (Germany); Bethe Center for Theoretical Physics,Nussallee 12, Universität Bonn, Bonn, D-53115 (Germany); Collaboration: The ETM collaboration
2015-09-03
We compute both sides of the Witten-Veneziano formula using lattice techniques. For the one side we perform dedicated quenched simulations and use the spectral projector method to determine the topological susceptibility in the pure Yang-Mills theory. The other side we determine in lattice QCD with N{sub f}=2+1+1 dynamical Wilson twisted mass fermions including for the first time also the flavour singlet decay constant. The Witten-Veneziano formula represents a leading order expression in the framework of chiral perturbation theory and we also employ leading order chiral perturbation theory to relate the flavor singlet decay constant to the relevant decay constant parameters in the quark flavor basis and flavor non-singlet decay constants. After taking the continuum and the SU(2) chiral limits we compare both sides and find good agreement within uncertainties.
Heavy quark fragmentation functions at next-to-leading perturbative QCD
Nejad, S M Moosavi
2016-01-01
It is well-known that the dominant mechanism to produce hadronic bound states with large transverse momentum is fragmentation. This mechanism is described by the fragmentation functions (FFs) which are the universal and process-independent functions. Here, we review the perturbative FFs formalism as an appropriate tool for studying these hadronization processes and detail the extension of this formalism at next-to-leading order (NLO). Using the Suzuki's model, we calculate the perturbative QCD FF for a heavy quark to fragment into a S-wave heavy meson at NLO. As an example, we study the LO and NLO FFs for a charm quark to split into the S-wave $D$-meson and compare our analytic results both with experimental data and well-known phenomenological models.
Non-perturbative test of the Witten-Veneziano formula from lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Cichy, Krzysztof [Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Poznan Univ. (Poland). Faculty of Physics; Garcia-Ramos, Elena [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Humboldt-Universitaet, Berlin (Germany); Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Ottnad, Konstantin; Urbach, Carsten [Bonn Univ. (Germany). Institut fuer Strahlen- und Kernphysik; Bonn Univ. (Germany). Bethe Center for Theoretical Physics; Collaboration: The ETM collaboration
2015-10-15
We compute both sides of the Witten-Veneziano formula using lattice techniques. For the one side we perform dedicated quenched simulations and use the spectral projector method to determine the topological susceptibility in the pure Yang-Mills theory. The other side we determine in lattice QCD with N{sub f}=2 +1+1 dynamical Wilson twisted mass fermions including for the first time also the flavour singlet decay constant. The Witten-Veneziano formula represents a leading order expression in the framework of chiral perturbation theory and we also employ leading order chiral perturbation theory to relate the flavor singlet decay constant to the relevant decay constant parameters in the quark flavor basis and flavor non-singlet decay constants. After taking the continuum and the SU(2) chiral limits we compare both sides and find good agreement within uncertainties.
Heavy-quark fragmentation functions at next-to-leading perturbative QCD
Energy Technology Data Exchange (ETDEWEB)
Moosavi Nejad, S.M. [Yazd University, Faculty of Physics, Yazd (Iran, Islamic Republic of); Institute for Research in Fundamental Sciences (IPM), School of Particles and Accelerators, Tehran (Iran, Islamic Republic of); Sartipi Yarahmadi, P. [Yazd University, Faculty of Physics, Yazd (Iran, Islamic Republic of)
2016-10-15
It is well known that the dominant mechanism to produce hadronic bound states with large transverse momentum is fragmentation. This mechanism is described by the fragmentation functions (FFs) which are the universal and process-independent functions. Here, we review the perturbative FFs formalism as an appropriate tool for studying these hadronization processes and detail the extension of this formalism at next-to-leading order (NLO). Using Suzuki's model, we calculate the perturbative QCD FF for a heavy quark to fragment into a S-wave heavy meson at NLO. As an example, we study the LO and NLO FFs for a charm quark to split into the S-wave D-meson and compare our analytic results both with experimental data and well-known phenomenological models. (orig.)
Non-Perturbative QCD Coupling and Beta Function from Light Front Holography
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins; de Teramond, Guy F.; /Costa Rica U.; Deur, Alexandre; /Jefferson Lab
2010-05-26
The light-front holographic mapping of classical gravity in AdS space, modified by a positive-sign dilaton background, leads to a non-perturbative effective coupling {alpha}{sub s}{sup AdS} (Q{sup 2}). It agrees with hadron physics data extracted from different observables, such as the effective charge defined by the Bjorken sum rule, as well as with the predictions of models with built-in confinement and lattice simulations. It also displays a transition from perturbative to nonperturbative conformal regimes at a momentum scale {approx} 1 GeV. The resulting {beta}-function appears to capture the essential characteristics of the full {beta}-function of QCD, thus giving further support to the application of the gauge/gravity duality to the confining dynamics of strongly coupled QCD. Commensurate scale relations relate observables to each other without scheme or scale ambiguity. In this paper we extrapolate these relations to the nonperturbative domain, thus extending the range of predictions based on {alpha}{sub s}{sup AdS} (Q{sup 2}).
AdS/QCD, LIight-Front Holography, and the Non-perturbative Running Coupling
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; /SLAC; de Teramond, Guy; /Costa Rica U.; Deur, Alexandre; /Jefferson Lab
2010-04-29
The combination of Anti-de Sitter space (AdS) methods with light-front (LF) holography provides a remarkably accurate first approximation for the spectra and wavefunctions of meson and baryon light-quark bound states. The resulting bound-state Hamiltonian equation of motion in QCD leads to relativistic light-front wave equations in terms of an invariant impact variable {zeta} which measures the separation of the quark and gluonic constituents within the hadron at equal light-front time. These equations of motion in physical space-time are equivalent to the equations of motion which describe the propagation of spin-J modes in anti-de Sitter (AdS) space. The eigenvalues give the hadronic spectrum, and the eigenmodes represent the probability distributions of the hadronic constituents at a given scale. A positive-sign confining dilaton background modifying AdS space gives a very good account of meson and baryon spectroscopy and form factors. The light-front holographic mapping of this model also leads to a non-perturbative effective coupling {alpha}{sub s}{sup Ads} (Q{sup 2}) which agrees with the effective charge defined by the Bjorken sum rule and lattice simulations. It displays a transition from perturbative to nonperturbative conformal regimes at a momentum scale {approx} 1 GeV. The resulting {beta}-function appears to capture the essential characteristics of the full {beta}-function of QCD, thus giving further support to the application of the gauge/gravity duality to the confining dynamics of strongly coupled QCD.
Cosmology on all scales: a two-parameter perturbation expansion
Goldberg, Sophia R; Malik, Karim A
2016-01-01
We propose and construct a two-parameter perturbative expansion around a Friedmann-Lema\\^{i}tre-Robertson-Walker geometry that can be used to model high-order gravitational effects in the presence of non-linear structure. This framework reduces to the weak-field and slow-motion post-Newtonian treatment of gravity in the appropriate limits, but also includes the low-amplitude large-scale fluctuations that are important for cosmological modelling. We derive a set of field equations that can be applied to the late Universe, where non-linear structure exists on supercluster scales, and perform a detailed investigation of the associated gauge problem. This allows us to identify a consistent set of perturbed quantities in both the gravitational and matter sectors, and to construct a set of gauge-invariant quantities that correspond to each of them. The field equations, written in terms of these quantities, take on a relatively simple form, and allow the effects of small-scale structure on the large-scale properties...
Catani, S; Soper, Davison Eugene; Stirling, William James; Tapprogge, Stefan; Alekhin, S I; Aurenche, Patrick; Balázs, C; Ball, R D; Battistoni, G; Berger, E L; Binoth, T; Brock, R L; Casey, D; Corcella, Gennaro; Del Duca, V; Fabbro, A D; de Roeck, A; Ewerz, C; de Florian, D; Fontannaz, M; Frixione, Stefano; Giele, W T; Grazzini, Massimiliano; Guillet, J P; Marlen-Heinrich, G; Huston, J; Kalk, J; Kataev, A L; Kato, K; Keller, S; Klasen, M; Kosower, D A; Kulesza, A; Kunszt, Zoltán; Kupco, A; Ilyin, V A; Magnea, L; Mangano, Michelangelo L; Martin, A D; Mazumdar, K; Miné, P; Moretti, M; van Neerven, W L; Parente, G; Perret-Gallix, D; Pilon, E; Pukhov, A E; Puljak, I; Pumplin, Jon; Richter-Was, Elzbieta; Roberts, R G; Salam, Gavin P; Seymour, Michael H; Skachkov, N B; Sidorov, A V; Stenzel, H; Stump, D R; Thorne, R S; Treleani, D; Tung, W K; Vogt, A; Webber, Bryan R; Werlen, M; Zmouchko, S; Mine, Ph.
2000-01-01
We discuss issues of QCD at the LHC including parton distributions, Monte Carlo event generators, the available next-to-leading order calculations, resummation, photon production, small x physics, double parton scattering, and backgrounds to Higgs production.
Resummation of Cactus Diagrams in Lattice QCD
Panagopoulos, H
1998-01-01
We show how to perform a resummation, to all orders in perturbation theory, of a certain class of gauge invariant diagrams in Lattice QCD. These diagrams are often largely responsible for lattice artifacts. Our resummation leads to an improved perturbative expansion. Applied to a number of cases of interest, this expansion yields results remarkably close to corresponding nonperturbative estimates.
Non-perturbative renormalization of the static axial current in two-flavour QCD
Della Morte, M; Heitger, J; Fritzsch, Patrick; Heitger, Jochen; Morte, Michele Della
2007-01-01
We perform the non-perturbative renormalization of matrix elements of the static-light axial current by a computation of its scale dependence in lattice QCD with two flavours of massless O(a) improved Wilson quarks. The regularization independent factor that relates any running renormalized matrix element of the axial current in the static effective theory to the renormalization group invariant one is evaluated in the Schroedinger functional scheme, where in this case we find a significant deviation of the non-perturbative running from the perturbative prediction. An important technical ingredient to improve the precision of the results consists in the use of modified discretizations of the static quark action introduced earlier by our collaboration. As an illustration how to apply the renormalization of the static axial current presented here, we connect the bare matrix element of the current to the B_s-meson decay constant in the static approximation for one value of the lattice spacing, a ~ 0.08 fm, employ...
Particle Production In Relativistic Heavy-ion Collisions With Perturbative Qcd
Zhang, Y
2003-01-01
The commissioning of the Relativistic Heavy Ion Collider (RHIC) opened new era in nuclear collision physics, with the study of excited strongly-interacting matter becoming a reality. A primary motivation for studying high-p T hadron production in ultrarelativistic heavy ion collisions is to gain insight into the gluon density of the quark-gluon medium via jet energy loss. The sensitivity of high-pT hadron spectra to initial gluon density may be a probe of the formation of quark-gluon-plasma (QGP). However, a thorough understanding of ultrarelativistic nuclear (AA ) collisions requires the accurate description of proton-proton ( pp) and proton-nucleus (pA) collisions in the same framework. In the present dissertation we follow the evolution of high-p T hadron production in relativistic collisions from pp to pA to AA reactions. The perturbative Quantum Chromodynamics (pQCD) improved parton model is used for the study. We apply leading- order (LO) pQCD throughout, and augment the standard one- dimensional cross ...
Improved estimates of the B{sub (s)}→VV decays in perturbative QCD approach
Energy Technology Data Exchange (ETDEWEB)
Zou, Zhi-Tian; Li, Ying [Yantai Univ. (China). Dept. of Physics; Ali, Ahmed [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Lue, Cai-Dian [Institute of High Energy Physics, Beijing, BJ (China); Theoretical Physics Center for Science Facilities, CAS, Beijing (China); Liu, Xin [Jiangsu Normal Univ., Xuzhou (China). School of Physics and Electronic Engineering
2015-01-15
We reexamine the branching ratios, CP-asymmetries, and other observables in a large number of B{sub q}→VV(q=u,d,s) decays in the perturbative QCD (PQCD) approach, where V denotes a light vector meson (ρ,K{sup *},ω,φ). The essential difference between this work and the earlier similar works is of parametric origin and in the estimates of the power corrections related to the ratio r{sup 2}{sub i}=m{sup 2}{sub V{sub i}}/m{sup 2}{sub B} (i=2,3) (m{sub V} and m{sub B} denote the masses of the vector and B meson, respectively). In particular, we use up-to-date distribution amplitudes for the final state mesons and keep the terms proportional to the ratio r{sup 2}{sub i} in our calculations. Our updated calculations are in agreement with the experimental data, except for a limited number of decays which we discuss. We emphasize that the penguin annihilation and the hard-scattering emission contributions are essential to understand the polarization anomaly, such as in the B→φK{sup *} and B{sub s}→φφ decay modes. We also compare our results with those obtained in the QCD factorization (QCDF) approach and comment on the similarities and differences, which can be used to discriminate between these approaches in future experiments.
Longitudinal Conductivity in Strong Magnetic Field in Perturbative QCD: Complete Leading Order
Hattori, Koichi; Satow, Daisuke; Yee, Ho-Ung
2016-01-01
We compute the longitudinal electrical conductivity in the presence of strong background magnetic field in complete leading order of perturbative QCD, based on the assumed hierarchy of scales $\\alpha_s eB\\ll (m_q^2,T^2)\\ll eB$. We formulate an effective kinetic theory of lowest Landau level quarks with the leading order QCD collision term arising from 1-to-2 processes that become possible due to 1+1 dimensional Landau level kinematics. In small $m_q/T\\ll 1$ regime, the longitudinal conductivity behaves as $\\sigma_{zz}\\sim e^2(eB)T/(\\alpha_s m_q^2\\log(m_q/T))$, where the quark mass dependence can be understood from the chiral anomaly with the axial charge relaxation provided by a finite quark mass $m_q$. We also present parametric estimates for the longitudinal and transverse "color conductivities" in the presence of strong magnetic field, by computing dominant damping rates for quarks and gluons that are responsible for color charge transportation. We observe that the longitudinal color conductivity is enhanc...
Non-perturbative running of quark masses in three-flavour QCD
Campos, Isabel; Pena, Carlos; Preti, David; Ramos, Alberto; Vladikas, Anastassios
2016-01-01
We present our preliminary results for the computation of the non-perturbative running of renormalized quark masses in $N_f = 3$ QCD, between the electroweak and hadronic scales, using standard finite-size scaling techniques. The computation is carried out to very high precision, using massless $\\mathcal{O}(a)$-improved Wilson quarks. Following the strategy adopted by the ALPHA Collaboration for the running coupling, different schemes are used above and below a scale $\\mu_0 \\sim m_b$, which differ by using either the Schr\\"odinger Functional or Gradient Flow renormalized coupling. We discuss our results for the running in both regions, and the procedure to match the two schemes.
Revisiting the $B^{0} \\to \\pi^{0}\\pi^{0} $ decays in the perturbative QCD approach
Li, Yun-Feng
2016-01-01
We recalculate the branching ratio and CP asymmetry for $\\bar{B}^{0} (B^{0})\\to \\pi^{0}\\pi^{0}$ decays in the Perturbative QCD approach. In this approach, we consider all the possible diagrams including non-factorizable contributions and annihilation contributions, and identity principle is also taken into account. We obtain the branching ratio of $B^{0}\\to\\pi^{0}\\pi^{0}$ is about $1.2\\times10^{-6}$. Our result is in agreement with the latest measured branching ratio of $B^{0}\\to\\pi^{0}\\pi^{0}$ by the Belle and HFAG Collaborations. We also predict large direct CP asymmetry and mixing CP asymmetry in $B^{0}\\to\\pi^{0}\\pi^{0}$ decays, which can be tested by the running LHC-b experiments.
Charmless chiral perturbation theory for N_f=2+1+1 twisted mass lattice QCD
Bar, Oliver
2014-01-01
The chiral Lagrangian describing the low-energy behavior of N_f=2+1+1 twisted mass lattice QCD is constructed through O(a^2). In contrast to existing results the effects of a heavy charm quark are consistently removed, leaving behind a charmless 3-flavor Lagrangian. This Lagrangian is used to compute the pion and kaon masses to one loop in a regime where the pion mass splitting is large and taken as a leading order effect. In comparison with continuum chiral perturbation theory additional chiral logarithms are present in the results. In particular, chiral logarithms involving the neutral pion mass appear. These predict rather large finite volume corrections in the kaon mass which roughly account for the finite volume effects observed in lattice data.
Tackling the sign problem with a moment expansion and application to Heavy dense QCD
Garron, Nicolas
2016-01-01
Heavy-Dense QCD (HDQCD) is a popular theory to investigate the sign problem in quantum field theory. Besides its physical applications, HDQCD is relatively easy to implement numerically: the fermionic degrees of freedom are integrated out, and the fermion determinant factorises into local ones. The theory has a sign problem, the severeness of which depends on the value of the chemical potential, which makes this theory ideal to test the reach of new algorithms. We use the LLR approach to obtain the probability distribution of the phase of the fermion determinant. Our goal is the calculation of the phase factor expectation value, which appears as Fourier transform of this probability distribution. We here propose a new and systematic moment expansion for this phase factor. We compare the answer from the moment expansion order by order with the exact answer. We find that this expansion converge quickly and works very well in the strong sign problem region.
FAPT: A Mathematica package for calculations in QCD Fractional Analytic Perturbation Theory
Bakulev, Alexander P.; Khandramai, Vyacheslav L.
2013-01-01
We provide here all the procedures in Mathematica which are needed for the computation of the analytic images of the strong coupling constant powers in Minkowski (A(s;nf) and Aνglob(s)) and Euclidean (A(Q2;nf) and Aνglob(Q2)) domains at arbitrary energy scales (s and Q2, correspondingly) for both schemes — with fixed number of active flavours nf=3,4,5,6 and the global one with taking into account all heavy-quark thresholds. These singularity-free couplings are inevitable elements of Analytic Perturbation Theory (APT) in QCD, proposed in [10,69,70], and its generalization — Fractional APT, suggested in [42,46,43], needed to apply the APT imperative for renormalization-group improved hadronic observables. Program summaryProgram title: FAPT Catalogue identifier: AENJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENJ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1985 No. of bytes in distributed program, including test data, etc.: 1895776 Distribution format: tar.gz Programming language: Mathematica. Computer: Any work-station or PC where Mathematica is running. Operating system: Windows XP, Mathematica (versions 5 and 7). Classification: 11.5. Nature of problem: The values of analytic images A(Q2) and A(s) of the QCD running coupling powers αsν(Q2) in Euclidean and Minkowski regions, correspondingly, are determined through the spectral representation in the QCD Analytic Perturbation Theory (APT). In the program FAPT we collect all relevant formulas and various procedures which allow for a convenient evaluation of A(Q2) and A(s) using numerical integrations of the relevant spectral densities. Solution method: FAPT uses Mathematica functions to calculate different spectral densities and then performs numerical integration of these spectral integrals
Transition Form Factors: A Unique Opportunity to Connect Non-Perturbative Strong Interactions to QCD
Energy Technology Data Exchange (ETDEWEB)
Gothe, Ralf W. [University of South Carolina, Columbia, SC (United States)
2014-01-01
Meson-photoproduction measurements and their reaction-amplitude analyses can establish more sensitively, and in some cases in an almost model-independent way, nucleon excitations and non-resonant reaction amplitudes. However, to investigate the strong interaction from explored — where meson-cloud degrees of freedom contribute substantially to the baryon structure — to still unexplored distance scales — where quark degrees of freedom dominate and the transition from dressed to current quarks occurs — we depend on experiments that allow us to measure observables that are probing this evolving non-perturbative QCD regime over its full range. Elastic and transition form factors are uniquely suited to trace this evolution by measuring elastic electron scattering and exclusive single-meson and double-pion electroproduction cross sections off the nucleon. These exclusive measurements will be extended to higher momentum transfers with the energy-upgraded CEBAF beam at JLab to study the quark degrees of freedom, where their strong interaction is responsible for the ground and excited nucleon state formations. After establishing unprecedented high-precision data, the imminent next challenge is a high-quality analysis to extract these relevant electrocoupling parameters for various resonances that then can be compared to state-of-the-art models and QCD-based calculations. Recent results will demonstrate the status of the analysis and of their theoretical descriptions, and an experimental and theoretical outlook will highlight what shall and may be achieved in the new era of the 12-GeV upgraded transition form factor program.
Stability of $SU(N_c)$ QCD3 from the $\\epsilon$-Expansion
Goldman, Hart
2016-01-01
QCD with gauge group $SU(N_c)$ flows to an interacting conformal fixed point in three spacetime dimensions when the number of four-component Dirac fermions $N_f \\gg N_c$. We study the stability of this fixed point via the $\\epsilon$-expansion about four dimensions. We find that when the number of fermions is lowered to $N_f^{\\rm crit} \\approx {11 \\over 2} N_c + (6 + {4 \\over N_c}) \\epsilon$, a certain four-fermion operator becomes relevant and the theory flows to a new infrared fixed point (massless or massive). F-theorem or entanglement monotonicity considerations complement our $\\epsilon$-expansion calculation.
Brodsky, Stanley J.; de Téramond, Guy F.; Deur, Alexandre; Dosch, Hans Günter
2015-09-01
The valence Fock-state wavefunctions of the light-front (LF) QCD Hamiltonian satisfy a relativistic equation of motion, analogous to the nonrelativistic radial Schrödinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. If one requires that the effective action which underlies the QCD Lagrangian remains conformally invariant and extends the formalism of de Alfaro, Fubini and Furlan to LF Hamiltonian theory, the potential U has a unique form of a harmonic oscillator potential, and a mass gap arises. The result is a nonperturbative relativistic LF quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories with the same slope in the radial quantum number n and orbital angular momentum L. Only one mass parameter κ appears. The corresponding LF Dirac equation provides a dynamical and spectroscopic model of nucleons. The same LF equations arise from the holographic mapping of the soft-wall model modification of AdS5 space with a unique dilaton profile to QCD (3+1) at fixed LF time. LF holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of Anti-de Sitter (AdS) space and the boost-invariant LFWFs describing the internal structure of hadrons in physical space-time. We also show how the mass scale underlying confinement and the masses of light-quark hadrons determines the scale controlling the evolution of the perturbative QCD coupling. The relation between scales is obtained by matching the nonperturbative dynamics, as described by an effective conformal theory mapped to the LF and its embedding in AdS space, to the perturbative QCD regime computed to four-loop order. The data for the effective coupling defined from the Bjorken sum rule are remarkably consistent with the
Dorney, Brian Lee
2013-01-01
Beauty quarks are pair-produced by strong interactions in multi-TeV proton- proton (pp) collisions at the CERN Large Hadron Collider (LHC). Such interactions allow for a test of perturbative Quantum Chromodynamics (QCD) in a new energy regime. The primary beauty-antibeauty quark b b pair production mechanisms in perturbative QCD are referred to as avor creation, avor excitation, and gluon splitting. These three mechanisms produce b b pairs with characteristic kinematic behavior, which contribute dierently to the shape of the dierential b b production cross section with respect to the dierence in the azimuthal angle and the combined separation variable R = p 2 + 2 between the beauty and antibeauty quarks ( b and b , respectively); with being the change in the pseudorapidity = ln ( tan ( = 2)), being the polar angle. These and R variables are collectively referred to as angular correlation variables and hence forth referred to as A . By measuring the shape and absolute normalization of the dierential prod...
Final state interaction and $B\\to KK$ decays in perturbative QCD
Chen Chuan Hung; Chen, Chuan-Hung; Li, Hsiang-nan
2001-01-01
We predict branching ratios and CP asymmetries of the $B\\to KK$ decays using perturbative QCD factorization theorem, in which tree, penguin, and annihilation contributions, including both factorizable and nonfactorizable ones, are expressed as convolutions of hard six-quark amplitudes with universal meson wave functions. The unitarity angle $\\phi_3= 90^o$ and the $B$ and $K$ meson wave functions extracted from experimental data of the $B\\to K\\pi$ and $\\pi\\pi$ decays are employed. Since the $B\\to KK$ decays are sensitive to final-state-interaction effects, the comparision of our predictions with future data can test the neglect of these effects in the above formalism. The CP asymmetry in the $B^\\pm\\to K^\\pm K^0$ modes and the $B_d^0\\to K^\\pm K^\\mp$ branching ratios depend on annihilation and nonfactorizable amplitudes. The $B\\to KK$ data can also verify the evaluation of these contributions.
Indian Academy of Sciences (India)
M E ZOMORRODIAN; M HASHEMINIA; S M ZABIHINPOUR; A MIRJALILI
2016-08-01
Inclusive momentum distributions of charged particles are measured in dijet events. Events were produced at the AMY detector with a centre of mass energy of 60 ${\\rm GeV}$. Our results were compared, on the one hand to those obtained from other $e^+ e^-$, $ep$ as well as CDF data, and on the other hand to the perturbative QCD calculations carried out in the framework of the modified leading log approximation (MLLA) and assuming local parton--hadron duality (LPHD). A fit of the shape of the distributions yields $\\scr Q_{eff} = 263 \\pm 13 {\\rm MeV}$ for the AMY data. In addition, a fit to the evolution of the peak position with dijet mass using all data from different experiments gives $\\scr Q_{eff} = 226 \\pm 18 {\\rm MeV}$. Next, αs was extracted using the shape of the distribution at the Z0 scale, with a value of 0.118 \\pm 0.013. This is consistent, within the statistical errors, with many accurate measurements. We conclude that it is the success of LPHD + MLLA that the extracted value of $\\alpha_{s}$ is correct. Possible explanations for all these features will be presented in this paper.
Improved Estimates of The $B_{(s)}\\to V V$ Decaysin Perturbative QCD Approach
Zou, Zhi-Tian; Lu, Cai-Dian; Liu, Xin; Li, Ying
2015-01-01
We reexamine the branching ratios, $CP$-asymmetries, and other observables in a large number of $B_q\\to VV(q=u,d,s)$ decays in the perturbative QCD (PQCD) approach, where $V$ denotes a light vector meson $(\\rho, K^*, \\omega, \\phi)$. The essential difference between this work and the earlier similar works is of parametric origin and in the estimates of the power corrections related to the ratio $r_i^2=m_{V_i}^2/m_B^2(i=2,3)$ ($m_V$ and $m_B$ denote the masses of the vector and $B$ meson, respectively). In particular, we use up-to-date distribution amplitudes for the final state mesons and keep the terms proportional to the ratio $r_i^2$ in our calculations. Our updated calculations are in agreement with the experimental data, except for a limited number of decays which we discuss. We emphasize that the penguin annihilation and the hard-scattering emission contributions are essential to understand the polarization anomaly, such as in the $B\\to \\phi K^*$ and $B_s \\to \\phi\\phi$ decay modes. We also compare our re...
Exotic-Hadron Signature by Constituent-Counting Rule in Perturbative QCD
Chang, Wen-Chen; Kumano, S; Sekihara, T
2016-01-01
We explain a method to find internal quark configurations of exotic hadron candidates by using the constituent counting rule. The counting rule was theoretically predicted in perturbative QCD for hard exclusive hadron reactions, and it has been tested in experiments for stable hadrons including compound systems of hadrons such as the deuteron, $^3$H, and $^3$He. It indicates that the cross section scales as $d\\sigma /dt \\sim 1/s^{n-2}$, where $s$ is the center-of-mass energy squared and $n$ is the total number of constituents. We apply this method for finding internal configurations of exotic hadron candidates, especially $\\Lambda (1405)$. There is a possibility that $\\Lambda (1405)$ could be five-quark state or a $\\bar K N$ molecule, and scaling properties should be different between the ordinary three-quark state or five-quark one. We predict such a difference in $\\pi^- + p \\to K^0 + \\Lambda (1405)$, and it could be experimentally tested, for example, at J-PARC. On the other hand, there are already measurem...
Probing the finite density equation of state of QCD via resummed perturbation theory
Mogliacci, Sylvain
2014-01-01
In this Ph.D. thesis, the primary goal is to present a recent investigation of the finite density thermodynamics of hot and dense quark-gluon plasma. As we are interested in a temperature regime, in which naive perturbation theory is known to lose its predictive power, we clearly need to use a refined approach. To this end, we adopt a resummed perturbation theory point of view and employ two different frameworks. We first use hard-thermal-loop perturbation theory (HLTpt) at leading order to obtain the pressure for nonvanishing quark chemical potentials, and next, inspired by dimensional reduction, resum the known four-loop weak coupling expansion for the quantity. We present and analyze our findings for various cumulants of conserved charges. This provides us with information, through correlations and fluctuations, on the degrees of freedom effectively present in the quark-gluon plasma right above the deconfinement transition. Moreover, we compare our results with state-of-the-art lattice Monte Carlo simulati...
Resumming QCD vacuum fluctuations in three-flavour Chiral Perturbation Theory
Descotes-Genon, S; Girlanda, L; Stern, J
2003-01-01
Due to its light mass of order Lambda_QCD, the strange quark can play a special role in Chiral Symmetry Breaking (ChSB): differences in the pattern of ChSB in the limits N_f=2 (m_u,m_d->0, m_s physical) and N_f=3 (m_u,m_d,m_s->0) may arise due to vacuum fluctuations of s-bar s pairs, related to the violation of the Zweig rule in the scalar sector and encoded in particular in the O(p^4) low-energy constants L_4 and L_6. In case of large fluctuations, we show that the customary treatment of SU(3)xSU(3) chiral expansions generate instabilities upsetting their convergence. We develop a systematic program to cure these instabilities by resumming nonperturbatively vacuum fluctuations of s-bar s pairs, in order to extract information about ChSB from experimental observations even in the presence of large fluctuations. We advocate a Bayesian framework for treating the uncertainties due to the higher orders. As an application, we present a three-flavour analysis of the low-energy pi-pi scattering and show that the rec...
Large mass expansion in two-loop QCD corrections of para-charmonium decay
Hasegawa, K; Pak, Alexey
2006-01-01
We calculate the light-by-light scattering type two-loop QCD corrections due to the light quark loops in the para-charmonium decays $eta_{c} rightarrow gamma gamma$ and $eta_{c} rightarrow g g$. We replace the mass of the internal charm quarks by an artificial large mass and obtain the result as a series in the large mass. The obtained series can be transformed into the good convergent ones by a change of the expansion parameter. The results are supported by two other methods to improve the convergence. We also observe that the color singlet state of $eta_{c}$ eliminates the potential divergences in the two-loop QCD corrections. The obtained corrections to the modes $eta_{c} rightarrow gamma gamma$ and $eta_{c} rightarrow g g$ account for -1.25% and -0.73% of the tree level values, respectively. Comparing the ratio of the decay rates with the experimental value, we find the constrains on the unknown contribution to these decays.
Convergence of high order perturbative expansions in open system quantum dynamics
Xu, Meng; Song, Linze; Song, Kai; Shi, Qiang
2017-02-01
We propose a new method to directly calculate high order perturbative expansion terms in open system quantum dynamics. They are first written explicitly in path integral expressions. A set of differential equations are then derived by extending the hierarchical equation of motion (HEOM) approach. As two typical examples for the bosonic and fermionic baths, specific forms of the extended HEOM are obtained for the spin-boson model and the Anderson impurity model. Numerical results are then presented for these two models. General trends of the high order perturbation terms as well as the necessary orders for the perturbative expansions to converge are analyzed.
On the asymptotic expansion of the curvature of perturbations of the $L_{2}$ connection
DEFF Research Database (Denmark)
De, Amit
We establish that the Hitchin connection is a perturbation of the $L_{2}$-connection. We notice that such a formulation of the Hitchin connection does not necessarily require the manifold in question possessing a rigid family of Kähler structures. We then proceed to calculate the asymptotic...... expansion of general perturbations of the $L_{2}$-connection, and see when under certain assumptions such perturbations are flat and projectively flat. During the calculations we also found an asymptotic expansion of the projection operator $\\pi_{\\sigma}^{\\left(k\\right)}$ which projects onto the holomorphic...
Cluster expansions and chiral symmetry at large density in 2-color QCD
Tomboulis, E T
2015-01-01
$SU(N_c)$ lattice gauge theories with $N_f$ flavors of massless staggered fermions are considered at high quark chemical potential $\\mu$ and any temperature $T$. In the strong coupling regime (sufficiently small $\\beta$) they have been shown to possess a chiral phase of intact global $U(N_f)\\times U(N_f)$ symmetry. The proof is by cluster expansions which converge in the infinite volume limit. Extension to weaker coupling does not appear feasible in the presence of complex fermion determinant. For theories with real determinant, however, such as 2-color QCD with fundamental fermions, or any $N_c$ with even $N_f$ and adjoint fermions, such large $\\mu$ cluster expansions can be used to show chiral behavior of fermionic lattice observables at any gauge coupling. Unfortunately, this absence of color superfluidity/superconductivity at high $\\mu$ appears to be a lattice artifact due to lattice saturation, a serious problem plaguing the standard finite density formalism on the lattice. Some possible ways of circumve...
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J. [SLAC National Accelerator Lab., Menlo Park, CA (United States); de Teramond, Guy F. [Univ. of Costa Rica, San Pedro (Costa Rica); Deur, Alexandre P. [Jefferson La.b, Newport News, VA (United States); Dosch, Hans G. [Institut fur Theoretische Physik, Heidelberg (Germany)
2015-09-01
The valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a relativistic equation of motion with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. If one requires that the effective action which underlies the QCD Lagrangian remains conformally invariant and extends the formalism of de Alfaro, Fubini and Furlan to light front Hamiltonian theory, the potential U has a unique form of a harmonic oscillator potential, and a mass gap arises. The result is a nonperturbative relativistic light-front quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories with the same slope in the radial quantum number n and orbital angular momentum L. Only one mass parameter κ appears. Light-front holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. We also show how the mass scale κ underlying confinement and hadron masses determines the scale Λ_{{ovr MS}} controlling the evolution of the perturbative QCD coupling. The relation between scales is obtained by matching the nonperturbative dynamics, as described by an effective conformal theory mapped to the light-front and its embedding in AdS space, to the perturbative QCD regime computed to four-loop order. The result is an effective coupling defined at all momenta. The predicted value Λ_{{ovr MS}}=0.328±0.034 GeV is in agreement with the world average 0.339±0.010 GeV. The analysis applies to any renormalization scheme.
Flow in a Circular Expansion Pipe Flow: Effect of a Vortex Perturbation on Localized Turbulence
Selvam, Kamal; Willis, Ashley P
2016-01-01
We report the results of three-dimensional direct numerical simulations for incompressible viscous fluid in a circular pipe flow with a sudden expansion. At the inlet, a parabolic velocity profile is applied together with a finite amplitude perturbation in the form of a vortex with its axis parallel to the axis of the pipe. At sufficiently high Reynolds numbers the recirculation region breaks into a turbulent patch that changes position axially depending on the strength of the perturbation. This vortex perturbation is believed to produce a less abrupt transition than in previous studies with a tilt perturbation, as the localized turbulence is observed via the formation of a wavy structure at a low order azimuthal mode, which resembles an optimally amplified perturbation. For higher amplitude, the localized turbulence remains at a constant axial position. It is further investigated using proper orthogonal decomposition, which indicates that the centre region close to the expansion is highly energetic.
Flow in a circular expansion pipe flow: effect of a vortex perturbation on localised turbulence
Selvam, Kamal; Peixinho, Jorge; Willis, Ashley P.
2016-12-01
We report the results of three-dimensional direct numerical simulations for incompressible viscous fluid in a circular pipe flow with a sudden expansion. At the inlet, a parabolic velocity profile is applied together with a finite amplitude perturbation in the form of a vortex with its axis parallel to the axis of the pipe. At sufficiently high Reynolds numbers the recirculation region breaks into a turbulent patch that changes position axially, depending on the strength of the perturbation. This vortex perturbation is believed to produce a less abrupt transition than in previous studies, which applied a tilt perturbation, as the localised turbulence is observed via the formation of a wavy structure at a low order azimuthal mode, which resembles an optimally amplified perturbation. For large vortex amplitude, the localised turbulence remains at a constant axial position. It is further investigated using proper orthogonal decomposition, which indicates that the centre region close to the expansion is highly energetic.
Comparison of Non-Perturbative, Gauge-Invariant, Realistic QCD with ISR Elastic pp Scattering Data
Fried, Herbert M; Gabellini, Yves; Grandou, Thierry; Sheu, Yeuan Ming
2016-01-01
Using previously-described, functional techniques for exact solutions to QCD processes, a simplified version of the amplitudes provides high-quality fits to the ISR data. Qualitative generalizations to initial LHC data are suggested, and are presently under consideration.
Particle production in relativistic heavy-ion collisions with perturbative QCD
Zhang, Yi
The commissioning of the Relativistic Heavy Ion Collider (RHIC) opened new era in nuclear collision physics, with the study of excited strongly-interacting matter becoming a reality. A primary motivation for studying high-p T hadron production in ultrarelativistic heavy ion collisions is to gain insight into the gluon density of the quark-gluon medium via jet energy loss. The sensitivity of high-pT hadron spectra to initial gluon density may be a probe of the formation of quark-gluon-plasma (QGP). However, a thorough understanding of ultrarelativistic nuclear (AA ) collisions requires the accurate description of proton-proton ( pp) and proton-nucleus (pA) collisions in the same framework. In the present dissertation we follow the evolution of high-p T hadron production in relativistic collisions from pp to pA to AA reactions. The perturbative Quantum Chromodynamics (pQCD) improved parton model is used for the study. We apply leading-order (LO) pQCD throughout, and augment the standard one-dimensional cross section calculation by the intrinsic transverse momentum distribution of partons. We use abundant pion production data from pp collisions at c.m. energies s≲ 60 GeV to extract the width of the transverse momentum distribution of partons in the nucleon. This gives a satisfactory fit of pion and kaon production data in pp collisions in the 2 ≤ pT ≤ 6 GeV window. For the treatment of nuclear systems, we developed a model based on the enhancement of the width of the transverse momentum distribution of partons in the nuclear medium. An additional parameter is fitted to describe the Cronin effect (cross section enhancement in pA collisions relative to pp collisions) at these energies. Shadowing and the isospin asymmetry of heavy nuclei are taken into account. We tested the model on charged pion and kaon production. In AA collisions at SPS energies we find an indication of a need for a mechanism to decrease the calculated cross section of neutral pion production
Gotsman, E
2016-01-01
In this paper, we found within the framework of perturbative QCD, that in deuteron-deuteron scattering the Bose-Einstein correlations due to two parton showers production, induce azimuthal angle correlations, with three correlation lengths: the size of the deuteron ($R_D$), the proton radius ($R_N$), and the size of the BFKL Pomeron which, is closely related to the saturation momentum ($R_c \\sim 1/Q_s$). These correlations are independent of the values of rapidities of the produced gluons (long range rapidity correlations), for large rapidities ($\\bas |y_1 - y_2| \\geq 1$), and have no symmetry with respect to $\\phi \\to \\pi - \\phi$ ($ \\vec{p}_{T1} \\to - \\vec{p}_{T1}$). Therefore, they give rise to $v_n$ for all values of $n$, not only even values. The contributions with the correlation length $R_D$ and $R_N$ crucially depend on the non-perturbative contributions, and to obtain estimates of their values, requiries a lot of modeling, while the correlations with $R_c \\sim 1/Q_s$ have a perturbative QCD origin, an...
Non-perturbative renormalization of quark mass in Nf=2+1 QCD with the Schroedinger functional scheme
Aoki, S; Ishizuka, N; Izubuchi, T; Kanaya, K; Kuramashi, Y; Murano, K; Namekawa, Y; Okawa, M; Taniguchi, Y; Ukawa, A; Ukita, N; Yoshié, T
2010-01-01
We present an evaluation of the quark mass renormalization factor for Nf=2+1 QCD. The Schroedinger functional scheme is employed as the intermediate scheme to carry out non-perturbative running from the low energy region, where renormalization of bare mass is performed on the lattice, to deep in the high energy perturbative region, where the conversion to the renormalization group invariant mass or the MS-bar scheme is safely carried out. For numerical simulations we adopted the Iwasaki gauge action and non-perturbatively improved Wilson fermion action with the clover term. Seven renormalization scales are used to cover from low to high energy regions and three lattice spacings to take the continuum limit at each scale. The regularization independent step scaling function of the quark mass for the Nf=2+1 QCD is obtained in the continuum limit. Renormalization factors for the pseudo scalar density and the axial vector current are also evaluated for the same action and the bare couplings as two recent large sca...
Su, Fang; Yang, Yi-Bo; Zhuang, Ci
2008-01-01
The charmless bottom meson decays are systematically investigated based on an approximate six quark operator effective Hamiltonian from perturbative QCD. It is shown that within this framework the naive QCD factorization method provides a simple way to evaluate the hadronic matrix elements of two body mesonic decays. The singularities caused by on mass-shell quark propagator and gluon exchanging interaction are appropriately treated. Such a simple framework allows us to make theoretical predictions for the decay amplitudes with reasonable input parameters. The resulting theoretical predictions for all the branching ratios and CP asymmetries in the charmless $B^0, B^+, B_s\\to \\pi\\pi, \\pi K, KK$ decays are found to be consistent with the current experimental data except for a few decay modes. The observed large branching ratio in $B\\to \\pi^0\\pi^0$ decay remains a puzzle though the predicted branching ratio may be significantly improved by considering the large vertex corrections in the effective Wilson coeffici...
Energy Technology Data Exchange (ETDEWEB)
Hehl, H.
2002-07-01
This thesis has studied the range of validity of the chiral random matrix theory in QCD on the example of the quenched staggered Dirac operator. The eigenvalues of this operator in the neighbourhood of zero are essential for the understanding of the spontaneous breaking of the chiral symmetry and the phase transition connected with this. The phase transition cannot be understood in the framework of perturbation theory, so that the formulation of QCD on the lattice has been chosen as the only non-perturbative approach. In order to circumvent both the problem of the fermion doubling and to study chiral properties on the lattice with acceptable numerical effort, quenched Kogut-Susskind fermions have been applied. The corresponding Dirac operator can be completely diagonalized by the Lanczos procedure of Cullum and Willoughby. Monte carlo simulations on hypercubic lattice have been performed and the Dirac operators of very much configurations diagonalized at different lattice lengths and coupling constants. The eigenvalue correlations on the microscopic scale are completely described by the chiral random matrix theory for the topological sector zero, which has been studied by means of the distribution of the smallest eigenvalue, the microscopic spectral density and the corresponding 2-point correlation function. The found universal behaviour shows, that on the scale of the lowest eigenvalue only completely general properties of the theory are important, but not the full dynamics. In order to determine the energy scale, from which the chiral random matrix theory losses its validity, - the Thouless energy - with the scalar susceptibilities observables have been analyzed, which are because of their spectral mass dependence sensitive on this. For each combination of the lattice parameter so the deviation point has been identified.
Instantaneous stochastic perturbation theory
Lüscher, Martin
2015-01-01
A form of stochastic perturbation theory is described, where the representative stochastic fields are generated instantaneously rather than through a Markov process. The correctness of the procedure is established to all orders of the expansion and for a wide class of field theories that includes all common formulations of lattice QCD.
Nakamura, Yousuke; Taniguchi, Yusuke; Collaboration, for CP-PACS
2007-01-01
We present non-perturbative renormalization factors for $\\Delta S=2$ four-quark operators in quenched domain-wall QCD using the Schroedinger functional method. Non-perturbative renormalization factor for $B_K$ is evaluated at hadronic scale. Combined with the non-perturbative RG running obtained by the Alpha collaboration, our result yields renormalization factor which converts lattice bare $B_K$ to the renormalization group invariant one. We apply the renormalization factor to bare $B_K$ pre...
Kataev, A L
2013-01-01
Conformal symmetry based relations between the concrete perturbative QED and QCD approximations of the polarized Bjorken, the Ellis-Jaffe, the Gross-Llewellyn Smith sum rules and of the Adler functions of the axial vector and vector channels are derived. They are based on application of the operator product expansion to three triangle AVV Green functions, constructed from the non-singlet axial vector-vector-vector currents, the {\\it singlet} axial-vector and two {\\it non-singlet} vector currents and the {\\it non-singlet} axial-vector-vector and {\\it singlet} vector currents, in the limit when the conformal symmetry of gauge models with fermions is unbroken. We specify the conditions when the conformal symmetry is valid in the U(1) and $SU(N_c)$ models. The identity between perturbative approximations of the Bjorken, Ellis-Jaffe and the Gross-Llewellyn Smith sum rules, which follow from this theoretical limit, is proved. The expressions for the $O(\\alpha^4)$ and $O(\\alpha_s^3)$ conformal symmetry based contrib...
Charmless hadronic $B \\to (f_1(1285),f_1(1420)) P$ decays in the perturbative QCD approach
Liu, Xin; Li, Jing-Wu; Zou, Zhi-Tian
2014-01-01
We study twenty charmless hadronic $B \\to f_1 P$ decays, with $f_1$ representing axial-vector mesons $f_1(1285)$ and $f_1(1420)$ that resulting from a mixing of quark-flavor $f_{1q}$ and $f_{1s}$ states with the angle $\\phi_{f_1}$, in the perturbative QCD(pQCD) formalism. The estimations of branching ratios and CP asymmetries of the considered $B \\to f_1 P$ decays are presented in the pQCD approach with $\\phi_{f_1} \\sim 24^\\circ$ from recently measured $B_{d/s} \\to J/\\psi f_1(1285)$ decays. It is found that (a) the tree dominant $B^+ \\to f_1 \\pi^+$ and the penguin dominant $B^+ \\to f_1 K^+$ decays with large branching ratios[${\\cal O}(10^{-6})$] and large direct CP violations(around $14\\% \\sim 28\\%$ in magnitude) simultaneously are believed to be clearly measurable at the LHCb and Super-B factory experiments; (b) the nearly pure penguin-dominated $B_d \\to f_1 K_S^0$ and $B_s \\to f_1 (\\eta, \\eta')$ modes with safely negligible tree pollution also have large decay rates in the order of $10^{-6} \\sim 10^{-5}$, w...
Perturbative Corrections to $\\Lambda_b \\to \\Lambda$ Form Factors from QCD Light-Cone Sum Rules
Wang, Yu-Ming
2015-01-01
We compute radiative corrections to $\\Lambda_b \\to \\Lambda$ from factors, at next-to-leading logarithmic accuracy, from QCD light-cone sum rules with $\\Lambda_b$-baryon distribution amplitudes. Employing the diagrammatic approach factorization of the vacuum-to-$\\Lambda_b$-baryon correlation function is justified at leading power in $\\Lambda/m_b$, with the aid of the method of regions. Hard functions entering the factorization formulae are identical to the corresponding matching coefficients of heavy-to-light currents from QCD onto soft-collinear effective theory. The universal jet function from integrating out the hard-collinear fluctuations exhibits richer structures compared with the one involved in the factorization expressions of the vacuum-to-$B$-meson correlation function. Based upon the QCD resummation improved sum rules we observe that the perturbative corrections at ${\\cal O}(\\alpha_s)$ shift the $\\Lambda_b \\to \\Lambda$ from factors at large recoil significantly and the dominant contribution originat...
Li, Shiyong; Yee, Ho-Ung
2016-01-01
We compute the jet quenching parameter $\\hat q$ of QCD plasma in the presence of strong magnetic field in both weakly and strongly coupled regimes. In weakly coupled regime, we compute $\\hat q$ in perturbative QCD at complete leading order (that is, leading log as well as the constant under the log) in QCD coupling constant $\\alpha_s$, assuming the hierarchy of scales $\\alpha_s eB\\ll T^2\\ll eB$. We consider two cases of jet orientations with respect to the magnetic field: 1) the case of jet moving parallel to the magnetic field, 2) the case jet moving perpendicular to the magnetic field. In the former case, we find $\\hat q\\sim \\alpha_s^2 (eB)T\\log(1/\\alpha_s)$, while in the latter we have $\\hat q\\sim \\alpha_s^2 (eB)T\\log(T^2/\\alpha_seB)$. In both cases, this leading order result arises from the scatterings with thermally populated lowest Landau level quarks. In strongly coupled regime described by AdS/CFT correspondence, we find $\\hat q\\sim \\sqrt{\\lambda}(eB)T$ or $\\hat q\\sim\\sqrt{\\lambda}\\sqrt{eB}T^2$ in the...
Non-perturbative renormalization of quark mass in Nf=2+1 QCD with the Schroedinger functional scheme
Taniguchi, Yusuke
2010-01-01
We present an evaluation of the quark mass renormalization factor for Nf=2+1 QCD. The Schroedinger functional scheme is employed as the intermediate scheme to carry out non-perturbative running from the low energy to deep in the high energy perturbative region. The regularization independent step scaling function of the quark mass is obtained in the continuum limit. Renormalization factors for the pseudo scalar density and the axial vector current are also evaluated for the same action and the bare couplings as two recent large scale Nf=2+1 simulations; previous work of the CP-PACS/JLQCD collaboration, which covered the up-down quark mass range heavier than m_pi=500 MeV and that of PACS-CS collaboration on the physical point using the reweighting technique.
Perturbative QCD corrections to the Z boson width and the Higgs decay rate
Chetyrkin, K G; Kwiatkowski, A
1994-01-01
Radiative QCD corrections significantly influence the theoretical predictions for the decay rates of the Z and the Higgs boson. The status of the QCD calculations to the hadronic Z width is reviewed. The role of mass corrections from bottom quark final states is emphasized. An estimate of the theoretical uncertainties is given. New results for quartic mass terms of order {\\cal O}(\\alpha_s^2) are presented. The impact of secondary radiation of bottom quarks on the determination of \\Gamma(Z\\rightarrow b\\bar{b}) is discussed. Second order QCD corrections to the partial decay rate \\Gamma(H\\rightarrow b\\bar{b}) are also presented in this talk. A recent result for the flavour singlet contribution to this quantity is presented. It includes quark mass effects and completes the otherwise massless calculations of order \\ordas^2).
Perturbative Expansion around the Gaussian Effective Potential of the Fermion Field Theory
Lee, G H; Yee, J H; Lee, Geon Hyoung; Lee, Tack Hwi; Yee, Jae Hyung
1998-01-01
We have extended the perturbative expansion method around the Gaussian effective action to the fermionic field theory, by taking the 2-dimensional Gross-Neveu model as an example. We have computed both the zero temperature and the finite temperature effective potentials of the Gross-Neveu model up to the first perturbative correction terms, and have found that the critical temperature, at which dynamically broken symmetry is restored, is significantly improved for small value of the flavour number.
What galaxy masses perturb the local cosmic expansion?
Peñarrubia, Jorge
2016-01-01
We use 12 cosmological $N$-body simulations of Local Group systems (the Apostle models; Sawala et al. 2016) to inspect the relation between the virial mass of the main haloes ($M_{\\rm vir,1}$ and $M_{\\rm vir,2}$), the mass derived from the relative motion of the halo pair ($M_{\\rm tim}$), and that inferred from the local Hubble flow ($M_{\\rm lhf}$). We show that within the Spherical Collapse Model (SCM), which provides an idealized description of structure formation in an expanding Universe, the correspondence between the three mass estimates is exact, i.e. $M_{\\rm lhf}=M_{\\rm tim}=M_{\\rm vir,1}+M_{\\rm vir,2}$. However, comparison with Apostle simulations reveals that, contrary to what the SCM states, a relatively large fraction of the mass that perturbs the local Hubble flow and drives the relative trajectory of the main galaxies is not contained within $R_{\\rm vir}$, and that the amount of "extra-virial" mass tends to increase in galaxies with a slow accretion rate. In addition, we find that modelling the p...
DEFF Research Database (Denmark)
Sannino, Francesco
2009-01-01
We uncover a novel solution of the 't Hooft anomaly matching conditions for QCD. Interestingly in the perturbative regime the new gauge theory, if interpreted as a possible QCD dual, predicts the critical number of flavors above which QCD in the nonperturbative regime, develops an infrared stable...... fixed point. Remarkably this value is identical to the maximum bound predicted in the nonpertubative regime via the all-orders conjectured beta function for nonsupersymmetric gauge theories.......We uncover a novel solution of the 't Hooft anomaly matching conditions for QCD. Interestingly in the perturbative regime the new gauge theory, if interpreted as a possible QCD dual, predicts the critical number of flavors above which QCD in the nonperturbative regime, develops an infrared stable...
SVZ⊕1/q{sup 2}-expansion versus some QCD holographic models
Energy Technology Data Exchange (ETDEWEB)
Jugeau, F., E-mail: frederic.jugeau@if.ufrj.br [Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, RJ 21941-972, Rio de Janeiro (Brazil); Narison, S., E-mail: snarison@yahoo.fr [Laboratoire Particules et Univers de Montpellier, CNRS-IN2P3, Case 070, Place Eugène Bataillon, 34095 Montpellier (France); Ratsimbarison, H., E-mail: herysedra@yahoo.fr [Institute of High-Energy Physics of Madagascar (iHEP-MAD), University of Antananarivo (Madagascar)
2013-05-13
Considering the classical two-point correlators built from (axial-) vector, scalar q{sup ¯}q and gluonium currents, we confront results obtained using the SVZ⊕1/q{sup 2}-expansion to the ones from some QCD holographic models in the Euclidean region and with negative dilaton Φ{sub i}(z)=−|c{sub i}{sup 2}|z{sup 2}. We conclude that the presence of the 1/q{sup 2}-term in the SVZ-expansion due to a tachyonic gluon mass appears naturally in the Minimum Soft-Wall (MSW) and the Gauge/String Dual (GSD) models which can also reproduce semi-quantitatively some of the higher dimension condensate contributions appearing in the OPE. The Hard-Wall model shows a large departure from the SVZ⊕1/q{sup 2}-expansion in the vector, scalar and gluonium channels due to the absence of any power corrections. The equivalence of the MSW and GSD models is manifest in the vector channel through the relation of the dilaton parameter with the tachyonic gluon mass. For approximately reproducing the phenomenological values of the dimension d=4,6 condensates, the holographic models require a tachyonic gluon mass (α{sub s}/π)λ{sup 2}≈−(0.12–0.14) GeV{sup 2}, which is about twice the fitted phenomenological value from e{sup +}e{sup −} data. The relation of the inverse length parameter c{sub i} to the tachyonic gluon mass also shows that c{sub i} is channel dependent but not universal for a given holographic model. Using the MSW model and M{sub ρ}=0.78 GeV as input, we predict a scalar q{sup ¯}q mass M{sub S}≈(0.95–1.10) GeV and a scalar gluonium mass M{sub G}≈(1.1–1.3) GeV.
Two-loop thermodynamics of warm and dense (isospin and baryo-chemical potential) perturbative QCD
Energy Technology Data Exchange (ETDEWEB)
Graf, Thorben [Institut fuer Theoretische Physik, Goethe Universitaet, Frankfurt am Main (Germany); Schaffner-Bielich, Juergen [Institut fuer Theoretische Physik, Goethe Universitaet, Frankfurt am Main (Germany); Fraga, Eduardo S. [Instituto de Fisica, Universidade Federal do Rio de Janeiro, Rio de Janeiro (Brazil)
2014-07-01
We present a perturbative calculation of the thermodynamical potential of quantum chromodynamics at nonvanishing temperatures for different values of the isospin and baryo-chemical potential. A comparison to recent lattice calculations at nonvanishing isospin is performed and the region of the break-down of the perturbative calculations are delineated. Finally, we study the thermodynamic potential at high chemical potentials and low temperatures where the perturbative scheme should be also applicable.
Nakamura, Y
2007-01-01
We present non-perturbative renormalization factors for $\\Delta S=2$ four-quark operators in quenched domain-wall QCD using the Schroedinger functional method. Non-perturbative renormalization factor for $B_K$ is evaluated at hadronic scale. Combined with the non-perturbative RG running obtained by the Alpha collaboration, our result yields renormalization factor which converts lattice bare $B_K$ to the renormalization group invariant one. We apply the renormalization factor to bare $B_K$ previously obtained by the CP-PACS collaboration with the quenched domain-wall QCD(DWQCD). We compare our result with previous ones obtained by perturbative renormalization factors, different renormalization schemes or different quark actions. We also show that chiral symmetry breaking effects in the renormalization factor are numerically small.
Towards a non-perturbative construction of the operator product expansion
Energy Technology Data Exchange (ETDEWEB)
Holland, Jan [Universitaet Leipzig (Germany)
2016-07-01
Our current understanding of Quantum Field Theory (QFT) is based to a large extent on perturbative - i.e. approximate - methods. Exact constructions in QFT are not only of fundamental conceptual interest, but they offer insights into physical phenomena that are intractable by perturbative means. In this talk, I present progress on a novel approach towards the non-perturbative construction of the Operator Product Expansion (OPE). The OPE is a structure encoding the complete algebraic skeleton as well as the short distance properties of a Quantum Field Theory. Our construction method is based on a recently found recursion formula for the OPE, which is discussed along with recent results on mathematical properties of the OPE in perturbation theory.
Conformal expansions and renormalons
Gardi, E; Gardi, Einan; Grunberg, Georges
2001-01-01
The large-order behaviour of QCD is dominated by renormalons. On the other hand renormalons do not occur in conformal theories, such as the one describing the infrared fixed-point of QCD at small beta_0 (the Banks--Zaks limit). Since the fixed-point has a perturbative realization, all-order perturbative relations exist between the conformal coefficients, which are renormalon-free, and the standard perturbative coefficients, which contain renormalons. Therefore, an explicit cancellation of renormalons should occur in these relations. The absence of renormalons in the conformal limit can thus be seen as a constraint on the structure of the QCD perturbative expansion. We show that the conformal constraint is non-trivial: a generic model for the large-order behaviour violates it. We also analyse a specific example, based on a renormalon-type integral over the two-loop running-coupling, where the required cancellation does occur.
Fried, H. M.; Tsang, P. H.; Gabellini, Y.; Grandou, T.; Sheu, Y.-M.
2016-11-01
A new non-perturbative, gauge-invariant model QCD renormalization is applied to high energy elastic pp-scattering. The differential cross-section deduced from this model displays a diffraction dip that resembles those of experiments. Comparison with ISR and LHC data is currently underway.
Fried, H M; Gabellini, Y; Grandou, T; Sheu, Y-M
2015-01-01
A new non-perturbative, gauge-invariant model QCD renormalization is applied to high energy elastic pp-scattering. The differential cross-section deduced from this model displays a diffraction dip that resembles those of experiments. Comparison with ISR and LHC data is currently underway.
Directory of Open Access Journals (Sweden)
Fried H. M.
2016-01-01
Full Text Available A new non-perturbative, gauge-invariant model QCD renormalization is applied to high energy elastic pp-scattering. The differential cross-section deduced from this model displays a diffraction dip that resembles those of experiments. Comparison with ISR and LHC data is currently underway.
Puhr, M
2016-01-01
We use exactly chiral overlap lattice fermions to investigate the Chiral Separation Effect in quenched QCD at finite density. We employ a recently developed numerical method which allows, for the first time, to address the transport properties of exactly chiral lattice fermions with non-zero chemical potential. Studying the axial current along the external magnetic field, we find a linear dependence consistent with the free fermion result for topologically trivial gauge field configurations. However, for configurations with nontrivial topology in the confinement regime the axial current is strongly suppressed due to contributions of topological modes of the Dirac operator, which suggests that non-perturbative corrections to the Chiral Separation Effect have topological origin.
Bandyopadhyay, Aritra
2016-01-01
We evaluate the electromagnetic spectral function in QCD plasma in a nonperturbative background of in-medium quark and gluon condensates by incorporating the leading order power corrections in a systematic framework within the ambit of the operator product expansion in D=4 dimension. We explicitly show that the mixing of the composite operators removes mass singularities and renders Wilson coefficients finite and well defined. As a spectral property, we then obtain the nonperturbative dilepton production rate from QCD plasma. The operator product expansion automatically restricts the dilepton rate to the intermediate mass range, which is found to be enhanced due to the power corrections. We also compare our result with those from nonperturbative calculations, e.g., lattice QCD and effective QCD models based on Polyakov loop.
Institute of Scientific and Technical Information of China (English)
李大鸣; 张红萍; 高永祥
2002-01-01
A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted. By the ameliorative asymptotic expansion matched method, the matched functions are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.
Perturbative Non-Equilibrium Thermal Field Theory to all Orders in Gradient Expansion
Millington, Peter
2013-01-01
We present a new perturbative formulation of non-equilibrium thermal field theory, based upon non-homogeneous free propagators and time-dependent vertices. The resulting time-dependent diagrammatic perturbation series are free of pinch singularities without the need for quasi-particle approximation or effective resummation of finite widths. After arriving at a physically meaningful definition of particle number densities, we derive master time evolution equations for statistical distribution functions, which are valid to all orders in perturbation theory and to all orders in a gradient expansion. For a scalar model, we perform a loopwise truncation of these evolution equations, whilst still capturing fast transient behaviour, which is found to be dominated by energy-violating processes, leading to the non-Markovian evolution of memory effects.
13. international QCD conference (QCD 06)
Energy Technology Data Exchange (ETDEWEB)
NONE
2006-07-01
This conference was organized around 5 sessions: 1) quantum chromodynamics (QCD) at colliders, 2) CP-violation, Kaon decays and Chiral symmetry, 3) perturbative QCD, 4) physics of light and heavy hadrons, 5) confinement, thermodynamics QCD and axion searches. This document gathers only the slides of the presentations.
Non-perturbative QCD Effects and the Top Mass at the Tevatron
Wicke, Daniel
2008-01-01
The modelling of non-perturbative effects is an important part of modern collider physics simulations. In hadron collisions there is some indication that the modelling of the interactions of the beam remnants, the underlying event, may require non-trivial colour reconnection effects to be present. We recently introduced a universally applicable toy model of such reconnections, based on hadronising strings. This model, which has one free parameter, has been implemented in the Pythia event generator. We then considered several parameter sets (`tunes'), constrained by fits to Tevatron minimum-bias data, and determined the sensitivity of a simplified top mass analysis to these effects, in exclusive semi-leptonic top events at the Tevatron. A first attempt at isolating the genuine non-perturbative effects gave an estimate of order +-0.5GeV from non-perturbative uncertainties. The results presented here are an update to the original study and include recent bug fixes of Pythia that influenced the tunings investigat...
Tests of perturbative QCD using CCFR data for measurements of nucleon structure functions
Energy Technology Data Exchange (ETDEWEB)
Bodek, A.; Budd, H.S.; De Barbaro, P.; Sakumoto, W.K.; Leung, W.C.; Quintas, P.Z.; Sciulli, F.; Arroyo, C.; Bachmann, K.T.; Blair, R.E.; Foudas, C.; King, B.J.; Lefmann, W.C.; Mishra, S.R.; Oltman, E.; Rabinowitz, S.A.; Seligman, W.G.; Shaevitz, M.H.; Merritt, F.S.; Oreglia, M.J.; Schumm, B.A.; Bernstein, R.H.; Borcherding, F.; Fisk, H.E.; Lamm, M.J.; Marsh, W.; Merritt, K.W.B.; Schellman, H.; Yovanovitch, D.D.; Sandler, P.H.; Smith, W.H. (Univ. of Rochester, NY (United States) Columbia Univ., New York, NY (United States) Univ. of Chicago, IL (United States) Fermilab, Batavia, IL (United States) Univ. of Wisconsin, Madison, WI (United States))
1993-04-01
We present measurements of nucleon structure functions, F[sub 2](x, Q[sup 2]) and xF[sub 3](x, Q[sup 2]), from the high-statistics, high-energy neutrino-iron scattering experiment at the Fermilab Tevatron. The existing high-statistics xF[sub 3] determination by the CDHSW collaboration is compared to our data. The data presented here constitute the first corroboration of the QCD prediction of xF[sub 3] evolution at low-x, and yields [Lambda][anti M][anti S] = 210 [+-] 28 [+-] 41 MeV, and a determination of the GLS sum rule at Q[sup 2] = 3 GeV[sup 2], S[sub GLS] = [integral][sup 1][sub x] xF[sub 3]/x dx = 2.50 [+-] 0.018(stat.) [+-]0.078 (syst.). Our value of [Lambda][anti M][anti S] yields [alpha][sub s](M[sub z]) = .111 [+-] .002 [+-] .003 [+-] .003 (scale). Comparison of the neutrino determination of F[sub 2](x, Q[sup 2]) with that obtained from the charged-lepton (e or [mu]) scattering leads to a precise test of the mean-square charge prediction by the Quark Parton Model. The SLAC-CCFR and BCDMS structure function provide a consistent and precise set of structure functions over a large range of Q[sup 2]. (orig.)
Pandharipande, Pranav P; Makhatadze, George I
2015-04-01
The main goal of this work was to provide direct experimental evidence that the expansivity of peptides, polypeptides and proteins as measured by pressure perturbation calorimetry (PPC), can serve as a proxy to characterize relative compactness of proteins, especially the denatured state ensemble. This is very important as currently only small angle X-ray scattering (SAXS), intrinsic viscosity and, to a lesser degree, fluorescence resonance transfer (FRET) experiments are capable of reporting on the compactness of denatured state ensembles. We combined the expansivity measurements with other biophysical methods (far-UV circular dichroism spectroscopy, differential scanning calorimetry, and small angle X-ray scattering). Three case studies of the effects of conformational changes on the expansivity of polypeptides in solution are presented. We have shown that expansivity appears to be insensitive to the helix-coil transition, and appears to reflect the changes in hydration of the side-chains. We also observed that the expansivity is sensitive to the global conformation of the polypeptide chain and thus can be potentially used to probe hydration of different collapsed states of denatured or even intrinsically disordered proteins. Copyright © 2015 Elsevier Inc. All rights reserved.
QCD Effective action at high temperature and small chemical potential
Villavicencio, C
2007-01-01
We present a construction of an effective Yang-Mills action for QCD, from the expansion of the fermionic determinant in terms of powers of the chemical potential at high temperature, for the case of massless quarks. We analyze this expansion in the perturbative region and find that it gives extra spurious information. We propose for the non-perturbative sector a simplified effective action which, in principle, contains only the relevant information.
Directory of Open Access Journals (Sweden)
Sharf Igor
2013-11-01
Full Text Available We consider the hadron–hadron inelastic scattering in the framework of QCD perturbation theory. It is shown that in QCD, due to conservation of color, the tree-level diagrams of inelastic scattering are prohibited and one has to deal with the diagrams with loops. We examine the simplest type of such diagrams, where the diagram can be split into blocks, so that the integration over four-momenta of virtual particles in each block can be done independently. It is shown that for these diagrams the squared absolute value of scattering amplitude has a maximum point, similar to that observed earlier in ɸ3 model, if one takes into account the relations between the arguments of scattering amplitude, imposed by the energy-momentum conservation law. This enables to apply the Laplace’s method for the calculation of cross section of hadron–hadron inelastic scattering. It is shown that the diagrams of gluon-loop exchange in QCD are equivalent to the diagrams of pion exchange in ɸ3 theory, whereby the new mechanism of cross section growth, discovered earlier in ɸ3 theory, takes place also in the perturbative QCD. The latter may explain the origin of experimentally-observed growth of cross section of hadron–hadron inelastic scattering as function of energy of colliding hadrons. The discovered mechanism can’t emerge in any Regge-based model due to the premises on the particle kinematics, made in these models.
Non-perturbative effects of vacuum energy on the recent expansion of the universe
Parker, L; Parker, Leonard; Raval, Alpan
1999-01-01
We show that the vacuum energy of a free quantized field of very low mass can significantly alter the recent expansion of the universe. The effective action of the theory is obtained from a non-perturbative sum of scalar curvature terms in the propagator. We numerically investigate the semiclassical Einstein equations derived from it. As a result of non-perturbative quantum effects, the scalar curvature of the matter-dominated universe stops decreasing and approaches a constant value. The universe in our model evolves from an open matter-dominated epoch to a mildly inflating de Sitter expansion. The Hubble constant during the present de Sitter epoch, as well as the time at which the transition occurs from matter-dominated to de Sitter expansion, are determined by the mass of the field and by the present matter density. The model provides a theoretical explanation of the observed recent acceleration of the universe, and gives a good fit to data from high-redshift Type Ia supernovae, with a mass of about 10^{-3...
Non-perturbative renormalisation of four-fermion operators in $N_f=2$ QCD
Dimopoulos, P; Palombi, Filippo; Papinutto, Mauro; Peña, C; Vladikas, A; Wittig, H
2007-01-01
We present results for the non-perturbative renormalisation of four-fermion operators with two flavours of dynamical quarks. We consider both fully relativistic left current-left current operators, and a full basis for $\\Delta B=2$ operators with static heavy quarks. The renormalisation group running of the operators to high energy scales is computed in the continuum limit for a family of Schroedinger Functional renormalisation schemes, via standard finite size scaling techniques. The total renormalisation factors relating renormalisation group invariant to bare operators are computed for a choice of lattice regularisations.
B-physics from non-perturbatively renormalized HQET in two-flavour lattice QCD
Bernardoni, Fabio; Bulava, John; Della Morte, Michele; Fritzsch, Patrick; Garron, Nicolas; Gerardin, Antoine; Heitger, Jochen; von Hippel, Georg M; Simma, Hubert
2013-01-01
We report on the ALPHA Collaboration's lattice B-physics programme based on N_f=2 O(a) improved Wilson fermions and HQET, including all NLO effects in the inverse heavy quark mass, as well as non-perturbative renormalization and matching, to fix the parameters of the effective theory. Our simulations in large physical volume cover 3 lattice spacings a ~ (0.08-0.05) fm and pion masses down to 190 MeV to control continuum and chiral extrapolations. We present the status of results for the b-quark mass and the B_(s)-meson decay constants, f_B and f_{B_s}.
Energy Technology Data Exchange (ETDEWEB)
Adams, M.R.; Arndotied, S.; Anthony, P.L.; Baker, M.D.; Bartlett, J.; Bhatti, A.A.; Braun, H.M.; Busza, W.; Conrad, J.M.; Coutrakon, G.; Davisson, R.; Derado, I.; Dhawan, S.K.; Dougherty, W.; Dreyer, T.; Dziunikowska, K.; Eckardt, V.; Ecker, U.; Erdmann, M.; Eskreys, A.; Figiel, J.; Gebauer, H.J.; Geesaman, D.F.; Gilman, R.; Green, M.C.; Haas, J.; Halliwell, C.; Hanlon, J.; Hantke, D.; Hughes, V.W.; Jackson, H.E.; Jaffe, D.E.; Jancso, G.; Jansen, D.M.; Kaufman, S.; Kennedy, R.D.; Kirk, T.; Kobrak, H.G.E.; Krzywdzinski, S.; Kunori, S.; Lord, J.J.; Lubatti, H.J.; McLeod, D.; Magill, S.; Malecki, P.; Manz, A.; Melanson, H.; Michael, D.G.; Mohr, W.; Montgomery, H.E.; Morfin, J.G.; Nickerson, R.B.; O' Day, S.; Olkiewicz, K.; Osborne, L.; Papavassiliou, V.; Pawlik, B.; Pipkin, F.M.; Ramberg, E.J.; Roeser, A.; Ryan, J.J.; Salgado, C.W.; Salvarani, A.; Schellman, H.; Schmitt, M.; Schmitz, N.; Schueler, K.P.; Skuja, A.; Snow, G.A.; Soeldner-Rembold, S.; Steinberg, P.H.; Stier, H.E.; Stopa, P.; S; (E665 Collaboration)
1994-01-24
The average squared transverse energy of jets in deep-inelastic muon-nucleon scattering is measured as a function of the momentum transfer squared ([ital Q][sup 2]), in the range 3[lt][ital Q][sup 2][lt]25 GeV[sup 2]. Perturbative QCD predicts that the average squared parton transverse energy will depend upon the strong coupling constant ([alpha][sub [ital S
Semileptonic decays of B{sub c} meson to S-wave charmonium states in the perturbative QCD approach
Energy Technology Data Exchange (ETDEWEB)
Rui, Zhou; Li, Hong; Wang, Guang-xin [North China University of Science and Technology, College of Sciences, Tangshan (China); Xiao, Ying [North China University of Science and Technology, College of Information Engineering, Tangshan (China)
2016-10-15
Inspired by the recent measurement of the ratio of B{sub c} branching fractions to J/ψπ{sup +} and J/ψμ{sup +}ν{sub μ} final states at the LHCb detector, we study the semileptonic decays of B{sub c} meson to the S-wave ground and radially excited 2S and 3S charmonium states with the perturbative QCD approach. After evaluating the form factors for the transitions B{sub c} → P,V, where P and V denote pseudoscalar and vector S-wave charmonia, respectively, we calculate the branching ratios for all these semileptonic decays. The theoretical uncertainty of hadronic input parameters are reduced by utilizing the light-cone wave function for the B{sub c} meson. It is found that the predicted branching ratios range from 10{sup -7} up to 10{sup -2} and could be measured by the future LHCb experiment. Our prediction for the ratio of branching fractions (BR(B{sub c}{sup +}→J/Ψπ{sup +}))/(BR(B{sub c}{sup +}→J/Ψμ{sup +}ν{sub μ})) is in good agreement with the data. For B{sub c} → Vlν{sub l} decays, the relative contributions of the longitudinal and transverse polarization are discussed in different momentum transfer squared regions. These predictions will be tested on the ongoing and forthcoming experiments. (orig.)
Quasi-two-body decays $B\\to K\\rho\\to K\\pi\\pi$ in perturbative QCD approach
Wang, Wen-Fei
2016-01-01
We analyze the quasi-two-body decays $B\\to K\\rho\\to K\\pi\\pi$ in the perturbative QCD (PQCD) approach, in which final-state interactions between the pions in the resonant regions associated with the $P$-wave states $\\rho(770)$ and $\\rho^\\prime(1450)$ are factorized into two-pion distribution amplitudes. Adopting experimental inputs for the time-like pion form factors involved in two-pion distribution amplitudes, we calculate branching ratios and direct $CP$ asymmetries of the $B\\to K\\rho(770),K\\rho^\\prime(1450)\\to K\\pi\\pi$ modes. It is shown that agreement of theoretical results with data can be achieved, through which Gegenbauer moments of the $P$-wave two-pion distribution amplitudes are determined. The consistency between the three-body and two-body analyses of the $B\\to K\\rho(770)\\to K\\pi\\pi$ decays supports the PQCD factorization framework for exclusive hadronic $B$ meson decays.
Wilson Loops in 2D Noncommutative Euclidean Gauge Theory: 1. Perturbative Expansion
Ambjørn, Jan; Makeenko, Y
2004-01-01
We calculate quantum averages of Wilson loops (holonomies) in gauge theories on the Euclidean noncommutative plane, using a path-integral representation of the star-product. We show how the perturbative expansion emerges from a concise general formula and demonstrate its anomalous behavior at large parameter of noncommutativity for the simplest nonplanar diagram of genus 1. We discuss various UV/IR regularizations of the two-dimensional noncommutative gauge theory in the axial gauge and, using the noncommutative loop equation, construct a consistent regularization.
Inadequacy of Taylor series for perturbation expansion: a lesson from weak measurement
Di Lorenzo, Antonio
2012-01-01
We all learnt from calculus textbooks that a Taylor expansion should be made consistently: all first-order terms should be grouped together, then all the second-order terms, etc. However, when applying perturbation theory to estimate probabilities, a common task in quantum mechanics, this automatic procedure can lead to nonpositive-definite probabilities. (Here, we are talking about probabilities that must be positive, as they can be inferred directly from the frequency of observed events, and not about intermediate functions, as Wigner quasiprobabilities, the inference of which from experimental data is a nontrivial task.) We demonstrate how to preserve the nonnegativity of probabilities at the cost of getting a bad grade in Calculus, and we show how the corrected expansion leads to a modification of the commonly accepted expressions for weak measurements, curing unphysical divergences at the same time. We provide the corrected formulas in the trivial case of an instantaneous interaction, the most commonly s...
Effects of non-perturbatively improved dynamical fermions in QCD at fixed lattice spacing
Allton, C R; Bowler, K C; Garden, J; Hart, A; Hepburn, D; Irving, A C; Joó, B; Kenway, R D; Maynard, C M; McNeile, C; Michael, C; Pickles, S M; Sexton, J C; Sharkey, K J; Sroczynski, Z; Talevi, M; Teper, M; Wittig, H
2002-01-01
We present results for the static inter-quark potential, lightest glueballs, light hadron spectrum and topological susceptibility using a non-perturbatively improved action on a $16^3\\times 32$ lattice at a set of values of the bare gauge coupling and bare dynamical quark mass chosen to keep the lattice size fixed in physical units ($\\sim 1.7$ fm). By comparing these measurements with a matched quenched ensemble, we study the effects due to two degenerate flavours of dynamical quarks. With the greater control over residual lattice spacing effects which these methods afford, we find some evidence of charge screening and some minor effects on the light hadron spectrum over the range of quark masses studied ($M_{PS}/M_{V}\\ge0.58$). More substantial differences between quenched and unquenched simulations are observed in measurements of topological quantities.
Non-perturbative QCD: renormalization, O(a)-improvement and matching to Heavy Quark Effective Theory
Sommer, R
2006-01-01
We give an introduction to three topics in lattice gauge theory: I. The Schroedinger Functional and O(a) improvement. O(a) improvement has been reviewed several times. Here we focus on explaining the basic ideas in detail and then proceed directly to an overview of the literature and our personal assessment of what has been achieved and what is missing. II. The computation of the running coupling, running quark masses and the extraction of the renormalization group invariants. We focus on the basic strategy and on the large effort that has been invested in understanding the continuum limit. We point out what remains to be done. III. Non-perturbative Heavy Quark Effective Theory. Since the literature on this subject is still rather sparse, we go beyond the basic ideas and discuss in some detail how the theory works in principle and in practice.
Non-perturbative QCD. Renormalization, O(a)-improvement and matching to heavy quark effective theory
Energy Technology Data Exchange (ETDEWEB)
Sommer, R.
2006-11-15
We give an introduction to three topics in lattice gauge theory: I. The Schroedinger Functional and O(a) improvement. O(a) improvement has been reviewed several times. Here we focus on explaining the basic ideas in detail and then proceed directly to an overview of the literature and our personal assessment of what has been achieved and what is missing. II. The computation of the running coupling, running quark masses and the extraction of the renormalization group invariants. We focus on the basic strategy and on the large effort that has been invested in understanding the continuum limit. We point out what remains to be done. III. Non-perturbative Heavy Quark Effective Theory. Since the literature on this subject is still rather sparse, we go beyond the basic ideas and discuss in some detail how the theory works in principle and in practice. (orig.)
Perturbative expansion of irreversible work in Fokker-Planck equation à la quantum mechanics
Koide, T.
2017-08-01
We discuss the systematic expansion of the solution of the Fokker-Planck equation with the help of the eigenfunctions of the time-dependent Fokker-Planck operator. The expansion parameter is the time derivative of the external parameter which controls the form of an external potential. Our expansion corresponds to the perturbative calculation of the adiabatic motion in quantum mechanics. With this method, we derive a new formula to calculate the irreversible work order by order, which is expressed as the expectation value with a pseudo density matrix. Applying this method to the case of the harmonic potential, we show that the first order term of the expansion gives the exact result. Because we do not need to solve the coupled differential equations of moments, our method simplifies the calculations of various functions such as the fluctuation of the irreversible work per unit time. We further investigate the exact optimized protocol to minimize the irreversible work by calculating its variation with respect to the control parameter itself.
EoS of finite density QCD with Wilson fermions by Multi-Parameter Reweighting and Taylor expansion
Nagata, Keitaro
2012-01-01
The equation of state (EoS), quark number density and susceptibility at nonzero quark chemical potential $\\mu$ are studied in lattice QCD simulations with a clover-improved Wilson fermion of 2-flavors and RG-improved gauge action. To access nonzero $\\mu$, we employ two methods : a multi-parameter reweighting (MPR) in $\\mu$ and $\\beta$ and Taylor expansion in $\\mu/T$. The use of a reduction formula for the Wilson fermion determinant enables to study the reweighting factor in MPR explicitly and heigher-order coefficients in Taylor expansion free from errors of noise method, although calculations are limited to small lattice size. As a consequence, we can study the reliability of the thermodynamical quantities through the consistency of the two methods, each of which has different origin of the application limit. The thermodynamical quantities are obtained from simulations on a $8^3\\times 4$ lattice with an intermediate quark mass($m_{\\rm PS}/m_{\\rm V}=0.8)$. The MPR and Taylor expansion are consistent for the E...
New lessons from the nucleon mass, lattice QCD and heavy baryon chiral perturbation theory
Walker-Loud, A
2008-01-01
I will review heavy baryon chiral perturbation theory for the nucleon delta degrees of freedom and then examine the recent dynamical lattice calculations of the nucleon mass from the BMW, ETM, JLQCD, LHP, MILC, NPLQCD, PACS-CS, QCDSF/UKQCD and RBC/UKQCD Collaborations. Performing the chiral extrapolations of these results, one finds remarkable agreement with the physical nucleon mass, from each lattice data set. However, a careful examination of the lattice data and the resulting extrapolation functions reveals some unexpected results, serving to highlight the significant challenges in performing chiral extrapolations of baryon quantities. All the N_f=2+1 dynamical results can be quantitatively described by theoretically unmotivated fit function linear in the pion mass with m_pi ~ 750 -190 MeV. When extrapolated to the physical point, the results are in striking agreement with the physical nucleon mass. I will argue that knowledge of each lattice datum of the nucleon mass is required at the 1-2% level, includ...
W -boson plus jet differential distributions at NNLO in QCD
Boughezal, Radja; Liu, Xiaohui; Petriello, Frank
2016-12-01
We present a detailed phenomenological study of W -boson production in association with a jet through next-to-next-to-leading order (NNLO) in perturbative QCD. Fiducial cross sections and differential distributions for both 8 TeV and 13 TeV LHC collisions are presented, as are results for both the inclusive one-jet bin and the exclusive one-jet bin. Two different event selection criteria are considered: a general selection with standard cuts used in experimental analyses, and a boosted selection that focuses on high transverse momentum jets. We discuss the higher-order corrections in detail and identify for which observables and phase space regions the QCD perturbative expansion is under good theoretical control, and where additional work is needed. For most distributions and phase space regions the QCD perturbative expansion exhibits good convergence after the inclusion of the NNLO corrections.
Xiao, Zhen-Jun; Lin, Dong-Ting; Fan, Ying-Ying; Ma, Ai-Jun
2014-01-01
In this paper, we calculate the branching ratios and CP violating asymmetries of the five $\\bar{B}^0_s \\to (\\pi^0\\eta^{(*)},\\eta^{(*)}\\eta^{(*)})$ decays, by employing the perturbative QCD (pQCD) factorization approach and with the inclusion of all currently known next-to-leading order (NLO) contributions. We find that (a) the NLO contributions can provide about 100% enhancements to the LO pQCD predictions for the decay rates of $\\bar{B}_s^0 \\to \\eta\\eta^\\prime$ and $\\eta^\\prime \\eta^\\prime$ decays, but result in small changes to $Br(\\bar{B}_s \\to \\pi^0 \\eta^{(*)})$ and $Br(\\bar{B}_s \\to \\eta\\eta)$; (b) the newly known NLO twist-2 and twist-3 contributions to the relevant form factors can provide about 10% enhancements to the decay rates of the considered decays; (c) for $\\bar{B}_s \\to \\pi^0 \\eta^{(*)}$ decays, their direct CP-violating asymmetries $\\cala_f^{dir}$ could be enhanced significantly by the inclusion of the NLO contributions; and (d) the pQCD predictions for $Br(\\bar{B}_s \\to \\eta \\eta^{(*)})$ and...
QCD matter in extreme environments
Fukushima, Kenji
2011-01-01
We review various theoretical approaches to the states of QCD matter out of quarks and gluons in extreme environments such as the high-temperature states at zero and finite baryon density and the dimensionally reduced state under an intense magnetic field. The topics at high temperature include the Polyakov loop and the 't Hooft loop in the perturbative regime, the Polyakov loop behaviour and the phase transition in some of non-perturbative methods; the strong-coupling expansion, the large-Nc limit and the holographic QCD models. These analyses are extended to hot and dense matter with a finite baryon chemical potential. We point out that the difficulty in the finite-density problem has similarity to that under a strong magnetic field. We make a brief summary of results related to the topological contents probed by the magnetic field and the Chiral Magnetic Effect. We also address the close connection to the (1+1) dimensional system.
Determination of $m_c$ and $m_b$ from quarkonium 1S energy levels in perturbative QCD
Kiyo, Yuichiro; Sumino, Yukinari
2015-01-01
We update determination of the $\\overline{\\rm MS}$ masses of the charm and bottom quarks, from comparisons of the masses of the charmonium and bottomonium $1S$ states with their perturbative predictions up to next-to-next-to-next-to-leading order in $\\varepsilon$ expansion and using the $\\overline{\\rm MS}$ masses. Effects of non-zero charm-quark mass in the bottomonium masses are incorporated up to next-to-next-to-leading order. We obtain $\\overline m_c=1246\\pm 2 (d_3) \\pm 4 (\\alpha_s) \\pm 23 (\\text{h.o.} )~{\\rm MeV} $ and $\\overline m_b=4197\\pm 2 (d_3) \\pm 6 (\\alpha_s) \\pm 20 (\\text{h.o.} )\\pm 5 (m_c)~ {\\rm MeV} $, which agree with the current Particle Data Group values.
Energy Technology Data Exchange (ETDEWEB)
Herbert, J.M.
1997-02-01
Perturbation theory has long been utilized by quantum chemists as a method for approximating solutions to the Schroedinger equation. Perturbation treatments represent a system`s energy as a power series in which each additional term further corrects the total energy; it is therefore convenient to have an explicit formula for the nth-order energy correction term. If all perturbations are collected into a single Hamiltonian operator, such a closed-form expression for the nth-order energy correction is well known; however, use of a single perturbed Hamiltonian often leads to divergent energy series, while superior convergence behavior is obtained by expanding the perturbed Hamiltonian in a power series. This report presents a closed-form expression for the nth-order energy correction obtained using Rayleigh-Schroedinger perturbation theory and a power series expansion of the Hamiltonian.
Resummation of Cactus Diagrams in the Clover Improved Lattice Formulation of QCD
Panagopoulos, H
1999-01-01
We extend to the clover improved lattice formulation of QCD the resummation of cactus diagrams, i.e. a certain class of tadpole-like gauge invariant diagrams. Cactus resummation yields an improved perturbative expansion. We apply it to the lattice renormalization of some two-fermion operators improving their one-loop perturbative estimates.
Bali, Gunnar S; Pineda, Antonio; Torrero, Christian
2013-01-01
We determine the infinite volume coefficients of the perturbative expansions of the self-energies of static sources in the fundamental and adjoint representations in SU(3) gluodynamics to order \\alpha^{20} in the strong coupling parameter \\alpha. We use numerical stochastic perturbation theory, where we employ a new second order integrator and twisted boundary conditions. The expansions are obtained in lattice regularization with the Wilson action and two different discretizations of the covariant time derivative within the Polyakov loop. Overall, we obtain four different perturbative series. For all of them the high order coefficients display the factorial growth predicted by the conjectured renormalon picture, based on the operator product expansion. This enables us to determine the normalization constants of the leading infrared renormalons of heavy quark and heavy gluino pole masses and to translate these into the modified minimal subtraction scheme (MS). We also estimate the four-loop \\beta-function coef...
A brief overview of hard-thermal-loop perturbation theory
Su, Nan
2012-01-01
The poor convergence of quantum field theory at finite temperature has been one of the main obstacles in the practical applications of thermal QCD for decades. Here we briefly review the progress of hard-thermal-loop perturbation theory (HTLpt) in reorganizing the perturbative expansion in order to improve the convergence. The quantum mechanical anharmonic oscillator is used as a simple example to show the breakdown of weak-coupling expansion, and variational perturbation theory is introduced as an effective resummation scheme for divergent weak-coupling expansions. We discuss HTLpt thermodynamic calculations for QED, pure-glue QCD, and QCD with N_f=3 up to three-loop order. The results suggest that HTLpt provides a systematic framework that can be used to calculate both static and dynamic quantities for temperatures relevant at LHC.
A Brief Overview of Hard-Thermal-Loop Perturbation Theory
Institute of Scientific and Technical Information of China (English)
SU Nan
2012-01-01
The poor convergence of quantum field theory at finite temperature has been one of the main obstacles in the practical applications of thermal QCD for decades. Here we briefly review the progress of hard-thermal-loop perturbation theory （HTLpt） in reorganizing the perturbative expansion in order to improve the convergence. The quantum mechanical anharmonic oscillator is used as a simple example to show the breakdown of weak-coupling expansion, and variational perturbation theory is introduced as an effective resummation scheme for divergent weak-coupling expansions. We discuss HTLpt thermodynamic calculations for QED, pure-glue QCD, and QCD with Nf = 3 up to three-loop order. The results suggest that HTLpt provides a systematic framework that can be used to calculate both static and dynamic quantities for temperatures relevant at LHC.
Chiral symmetry breaking in continuum QCD
Mitter, Mario; Pawlowski, Jan M.; Strodthoff, Nils
2015-03-01
We present a quantitative analysis of chiral symmetry breaking in two-flavor continuum QCD in the quenched limit. The theory is set up at perturbative momenta, where asymptotic freedom leads to precise results. The evolution of QCD towards the hadronic phase is achieved by means of dynamical hadronization in the nonperturbative functional renormalization group approach. We use a vertex expansion scheme based on gauge-invariant operators and discuss its convergence properties and the remaining systematic errors. In particular, we present results for the quark propagator, the full tensor structure and momentum dependence of the quark-gluon vertex, and the four-Fermi scatterings.
Volume and expansivity changes of micelle formation measured by pressure perturbation calorimetry.
Fan, Helen Y; Nazari, Mozhgan; Chowdhury, Saria; Heerklotz, Heiko
2011-03-01
We present the application of pressure perturbation calorimetry (PPC) as a new method for the volumetric characterization of the micelle formation of surfactants. The evaluation is realized by a global fit of PPC curves at different surfactant concentration ranging, if possible, from below to far above the CMC. It is based on the knowledge of the temperature dependence of the CMC, which can for example be characterized by isothermal titration calorimetry. We demonstrate the new approach for decyl-β-maltopyranoside (DM). It shows a strong volume increase upon micelle formation of 16 ± 2.5 mL/mol (+4%) at 25 °C, and changes with temperature by -0.1 mL/(mol K). The apparent molar expansivity (E(S)) decreases upon micelle formation from 0.44 to 0.31 mL/(mol K) at 25 °C. Surprisingly, the temperature dependence of the expansivity of DM in solution (as compared with that of maltose) does not agree with the principal behavior described for polar (E(S)(T) decreasing) and hydrophobic (E(S)(T) increasing) solutes or moieties before. The results are discussed in terms of changes in hydration of the molecules and internal packing of the micelles and compared with the volumetric effects of transitions of proteins, DNA, lipids, and polymers.
Chakon, Ofir; Or, Yizhar
2017-01-01
Underactuated robotic locomotion systems are commonly represented by nonholonomic constraints where in mixed systems, these constraints are also combined with momentum evolution equations. Such systems have been analyzed in the literature by exploiting symmetries and utilizing advanced geometric methods. These works typically assume that the shape variables are directly controlled, and obtain the system's solutions only via numerical integration. In this work, we demonstrate utilization of the perturbation expansion method for analyzing a model example of mixed locomotion system—the twistcar toy vehicle, which is a variant of the well-studied roller-racer model. The system is investigated by assuming small-amplitude oscillatory inputs of either steering angle (kinematic) or steering torque (mechanical), and explicit expansions for the system's solutions under both types of actuation are obtained. These expressions enable analyzing the dependence of the system's dynamic behavior on the vehicle's structural parameters and actuation type. In particular, we study the reversal in direction of motion under steering angle oscillations about the unfolded configuration, as well as influence of the choice of actuation type on convergence properties of the motion. Some of the findings are demonstrated qualitatively by reporting preliminary motion experiments with a modular robotic prototype of the vehicle.
Chakon, Ofir; Or, Yizhar
2017-08-01
Underactuated robotic locomotion systems are commonly represented by nonholonomic constraints where in mixed systems, these constraints are also combined with momentum evolution equations. Such systems have been analyzed in the literature by exploiting symmetries and utilizing advanced geometric methods. These works typically assume that the shape variables are directly controlled, and obtain the system's solutions only via numerical integration. In this work, we demonstrate utilization of the perturbation expansion method for analyzing a model example of mixed locomotion system—the twistcar toy vehicle, which is a variant of the well-studied roller-racer model. The system is investigated by assuming small-amplitude oscillatory inputs of either steering angle (kinematic) or steering torque (mechanical), and explicit expansions for the system's solutions under both types of actuation are obtained. These expressions enable analyzing the dependence of the system's dynamic behavior on the vehicle's structural parameters and actuation type. In particular, we study the reversal in direction of motion under steering angle oscillations about the unfolded configuration, as well as influence of the choice of actuation type on convergence properties of the motion. Some of the findings are demonstrated qualitatively by reporting preliminary motion experiments with a modular robotic prototype of the vehicle.
Bali, Gunnar S; Pineda, Antonio
2014-01-01
Using numerical stochastic perturbation theory, we determine the first 35 infinite volume coefficients of the perturbative expansion in powers of the strong coupling constant $\\alpha$ of the plaquette in SU(3) gluodynamics. These coefficients are obtained in lattice regularization with the standard Wilson gauge action. The on-set of the dominance of the dimension four renormalon associated to the gluon condensate is clearly observed. We determine the normalization of the corresponding singularity in the Borel plane and convert this into the $\\overline{\\mathrm{MS}}$ scheme. We also comment on the impact of the renormalon on non-perturbative determinations of the gluon condensate.
Strong Decays of Hybrid Mesons from the Heavy Quark Expansion of QCD
Page, P R
1998-01-01
We calculate the strong decays of hybrid mesons to conventional mesons for all the lowest lying J^PC hybrids of flavour uu, dd, ss, cc and bb. A decay operator developed from the heavy quark expansion of quantum chromodynamics is employed. We show that the selection rule that hybrid mesons do not decay to identical S-wave mesons, found in other models, is preserved. We predict decays of charmonium hybrids, discuss decays of J^PC=1^-+ exotic isovector hybrids of various masses, and interpret the \\pi(1800) as a hybrid meson.
Bulava, John; Heitger, Jochen; Wittemeier, Christian
2016-01-01
We non-perturbatively determine the renormalization factor of the axial vector current in lattice QCD with $N_f=3$ flavors of Wilson-clover fermions and the tree-level Symanzik-improved gauge action. The (by now standard) renormalization condition is derived from the massive axial Ward identity and it is imposed among Schr\\"{o}dinger functional states with large overlap on the lowest lying hadronic state in the pseudoscalar channel, in order to reduce kinematically enhanced cutoff effects. We explore a range of couplings relevant for simulations at lattice spacings of $\\approx 0.09$ fm and below. An interpolation formula for $Z_A(g_0^2)$, smoothly connecting the non-perturbative values to the 1-loop expression, is provided together with our final results.
Peak exclusion, stochasticity and convergence of perturbative bias expansions in 1+1 gravity
Baldauf, Tobias; Desjacques, Vincent; Pichon, Christophe
2015-01-01
The Lagrangian peaks of a 1D cosmological random field representing dark matter are used as a proxy for a catalogue of biased tracers in order to investigate the small-scale exclusion in the two-halo term. The two-point correlation function of peaks of a given height is numerically estimated and analytical approximations that are valid inside the exclusion zone are derived. The resulting power spectrum of these tracers is investigated and shows clear deviations from Poisson noise at low frequencies. On large scales, the convergence of a perturbative bias expansion is discussed. Finally, we go beyond Gaussian statistics for the initial conditions and investigate the subsequent evolution of the two-point clustering of peaks through their Zel'dovich ballistic displacement, to clarify how exclusion effects mix up with scale-dependencies induced by nonlinear gravitational evolution. While the expected large-scale separation limit is recovered, significant deviations are found in the exclusion zone that tends in pa...
Guardia, M.; Kaloshin, V.; Zhang, J.
2016-11-01
In this paper we study a so-called separatrix map introduced by Zaslavskii-Filonenko (Sov Phys JETP 27:851-857, 1968) and studied by Treschev (Physica D 116(1-2):21-43, 1998; J Nonlinear Sci 12(1):27-58, 2002), Piftankin (Nonlinearity (19):2617-2644, 2006) Piftankin and Treshchëv (Uspekhi Mat Nauk 62(2(374)):3-108, 2007). We derive a second order expansion of this map for trigonometric perturbations. In Castejon et al. (Random iteration of maps of a cylinder and diffusive behavior. Preprint available at arXiv:1501.03319, 2015), Guardia and Kaloshin (Stochastic diffusive behavior through big gaps in a priori unstable systems (in preparation), 2015), and Kaloshin et al. (Normally Hyperbolic Invariant Laminations and diffusive behavior for the generalized Arnold example away from resonances. Preprint available at http://www.terpconnect.umd.edu/vkaloshi/, 2015), applying the results of the present paper, we describe a class of nearly integrable deterministic systems with stochastic diffusive behavior.
Mohamed, Firdawati binti; Karim, Mohamad Faisal bin Abd
2015-10-01
Modelling physical problems in mathematical form yields the governing equations that may be linear or nonlinear for known and unknown boundaries. The exact solution for those equations may or may not be obtained easily. Hence we seek an analytical approximation solution in terms of asymptotic expansion. In this study, we focus on a singular perturbation in second order ordinary differential equations. Solutions to several perturbed ordinary differential equations are obtained in terms of asymptotic expansion. The aim of this work is to find an approximate analytical solution using the classical method of matched asymptotic expansion (MMAE). The Mathematica computer algebra system is used to perform the algebraic computations. The details procedures will be discussed and the underlying concepts and principles of the MMAE will be clarified. Perturbation problem for linear equation that occurs at one boundary and two boundary layers are discussed. Approximate analytical solution obtained for both cases are illustrated by graph using selected parameter by showing the outer, inner and composite solution separately. Then, the composite solution will be compare to the exact solution to show their accuracy by graph. By comparison, MMAE is found to be one of the best methods to solve singular perturbation problems in second order ordinary differential equation since the results obtained are very close to the exact solution.
Brodsky, Stanley J; Deur, Alexandre; Dosch, Hans Günter
2014-01-01
The valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a relativistic equation of motion with an effective confining potential $U$ which systematically incorporates the effects of higher quark and gluon Fock states. If one requires that the effective action which underlies the QCD Lagrangian remains conformally invariant and extends the formalism of de Alfaro, Fubini and Furlan to light front Hamiltonian theory, the potential $U$ has a unique form of a harmonic oscillator potential, and a mass gap arises. The result is a nonperturbative relativistic light-front quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories with the same slope in the radial quantum number $n$ and orbital angular momentum $L$. Only one mass parameter $\\kappa$ appears. Light-front holography thus provides a precise relation between the bound-state ...
White, G R
2000-01-01
instanton-like properties, although not statistically significant enough to draw firm conclusions. Measurements of kaons, pions and protons identified using the dE/dx technique have been made in deep-inelastic scattering ep interactions at HERA in the kinematic range 5 < Q sup 2 < 70 and 10 sup - sup 5 < x < 10 sup - sup 2. Tests of QCD were made possible through the production of transverse momenta and pseudo-rapidity spectra with comparisons made to ARIADNE and LEPTO Monte Carlo models, utilising the JETSET hadronisation model with tuning taken from DELPHI experiments, and with HERWIG using the cluster fragmentation model. Further measurements were made of the proton-antiproton asymmetry A sub B 1.(N(p)-N(p-bar)) / N(p)+N(p-bar) and compared to measurements made elsewhere using photo-production data and recent theoretical results. A search for QCD instanton induced events was also made using the kaon and pion sample. Results from kaon and pion spectra show a preference for the ARIADNE model with...
Brambilla, Michele
2013-01-01
Numerical Stochastic Perturbation Theory was able to get three- (and even four-) loop results for finite Lattice QCD renormalization constants. More recently, a conceptual and technical framework has been devised to tame finite size effects, which had been reported to be significant for (logarithmically) divergent renormalization constants. In this work we present three-loop results for fermion bilinears in the Lattice QCD regularization defined by tree-level Symanzik improved gauge action and n_f=2 Wilson fermions. We discuss both finite and divergent renormalization constants in the RI'-MOM scheme. Since renormalization conditions are defined in the chiral limit, our results also apply to Twisted Mass QCD, for which non-perturbative computations of the same quantities are available. We emphasize the importance of carefully accounting for both finite lattice space and finite volume effects. In our opinion the latter have in general not attracted the attention they would deserve.
W-boson plus jet differential distributions at NNLO in QCD
Boughezal, Radja; Petriello, Frank
2016-01-01
We present a detailed phenomenological study of W-boson production in association with a jet through next-to-next-to-leading order (NNLO) in perturbative QCD. Fiducial cross sections and differential distributions for both 8 TeV and 13 TeV LHC collisions are presented, as are results for both the inclusive one-jet bin and the exclusive one-jet bin. Two different event selection criteria are considered: a general selection with standard cuts used in experimental analyses, and a boosted selection that focuses on high transverse momentum jets. We discuss the higher-order corrections in detail and identify for which observables and phase space regions the QCD perturbative expansion is under good theoretical control, and where additional work is needed. For most distributions and phase space regions the QCD perturbative expansion exhibits good convergence after the inclusion of the NNLO corrections.
Bulava, John; Heitger, Jochen; Wittemeier, Christian
2015-01-01
The coefficient c_A required for O(a) improvement of the axial current in lattice QCD with N_f=3 flavors of Wilson fermions and the tree-level Symanzik-improved gauge action is determined non-perturbatively. The standard improvement condition using Schroedinger functional boundary conditions is employed at constant physics for a range of couplings relevant for simulations at lattice spacings of ~ 0.09 fm and below. We define the improvement condition projected onto the zero topological charge sector of the theory, in order to avoid the problem of possibly insufficient tunneling between topological sectors in our simulations at the smallest bare coupling. An interpolation formula for c_A(g_0^2) is provided together with our final results.
Hou, Wei-Shu; Li, Hsiang-nan; Mishima, Satoshi; Nagashima, Makiko
2007-03-30
We study the effect from a sequential fourth generation quark on penguin-dominated two-body nonleptonic B meson decays in the next-to-leading order perturbative QCD formalism. With an enhancement of the color-suppressed tree amplitude and possibility of a new CP phase in the electroweak penguin amplitude, we can account better for A(CP)(B(0)-->K+ pi-)-A(CP)(B+-->K+ pi0). Taking |V(t's)V(t'b)| approximately 0.02 with a phase just below 90 degrees, which is consistent with the b-->sl+ l- rate and the B(s) mixing parameter Deltam(B)(s), we find a downward shift in the mixing-induced CP asymmetries of B(0)-->K(S)(pi 0) and phi(K)(S). The predicted behavior for B(0)-->rho(0)(K)(S) is opposite.
QCD Technology: Light-Cone Quantization and Commensurate Scale Relations
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.
1999-09-03
I discuss several theoretical tools which are useful for analyzing perturbative and non-perturbative problems in quantum chromodynamics, including (a) the light-cone Fock expansion, (b) the effective charge {alpha}{sub v}, (c) conformal symmetry, and (d) commensurate scale relations. Light-cone Fock-state wavefunctions encode the properties of a hadron in terms of its fundamental quark and gluon degrees of freedom. Given the proton's light-cone wavefunctions, one can compute not only the quark and gluon distributions measured in deep inelastic lepton-proton scattering, but also the multi-parton correlations which control the distribution of particles in the proton fragmentation region and dynamical higher twist effects. Light-cone wavefunctions also provide a systematic framework for evaluating exclusive hadronic matrix elements, including timelike heavy hadron decay amplitudes and form factors. The {alpha}{sub v} coupling, defined from the QCD heavy quark potential, provides a physical expansion parameter for perturbative QCD with an analytic dependence on the fermion masses which is now known to two-loop order. Conformal symmetry provides a template for QCD predictions, including relations between observables which are present even in a theory which is not scale invariant. Commensurate scale relations are perturbative QCD predictions based on conformal symmetry relating observable to observable at fixed relative scale. Such relations have no renormalization scale or scheme ambiguity.
Mirror QCD and Cosmological Constant
Pasechnik, Roman; Teryaev, Oleg
2016-01-01
An analog of Quantum Chromo Dynamics (QCD) sector known as mirror QCD (mQCD) can affect the cosmological evolution and help in resolving the Cosmological Constant problem. In this work, we explore an intriguing possibility for a compensation of the negative QCD vacuum contribution to the ground state energy density of the universe by means of a positive contribution from the chromomagnetic gluon condensate in mQCD. The trace anomaly compensation condition and the form of the mQCD coupling constant in the infrared limit have been proposed by analysing a partial non-perturbative solution of the Einstein--Yang-Mills equations of motion.
${\\Upsilon}(1S)$ ${\\to}$ $B_{c}{\\pi}$, $B_{c}K$ decays with perturbative QCD approach
Sun, Junfeng; Yang, Yueling; Li, Haiyan; Chang, Qin; Zhang, Zhiqing
2016-01-01
With the potential prospects of the ${\\Upsilon}(1S)$ at high-luminosity dedicated heavy-flavor factories, the bottom-changing ${\\Upsilon}(1S)$ ${\\to}$ $B_{c}{\\pi}$, $B_{c}K$ weak decays are studied with the pQCD approach. It is found that branching ratio for the color-favored and CKM-favored ${\\Upsilon}(1S)$ ${\\to}$ $B_{c}{\\pi}$ decay can reach up to ${\\cal O}(10^{-11})$. So the ${\\Upsilon}(1S)$ ${\\to}$ $B_{c}{\\pi}$ decay might be measured promisingly by the future experiments.
Resummation of Cactus Diagrams in Lattice QCD, to all Orders
Panagopoulos, H
2000-01-01
We show how to perform a resummation, to all orders in perturbation theory, of a certain class of gauge invariant tadpole-like diagrams in Lattice QCD. These diagrams are often largely responsible for lattice artifacts. Our resummation leads to an improved perturbative expansion. Applied to a number of cases of interest, e.g. the lattice renormalization of some two-fermion operators, this expansion yields results remarkably close to corresponding nonperturbative estimates. We consider in our study both the Wilson and the clover action for fermions.
Zhou, Shiqi
2011-12-01
Thermodynamic and structural properties of liquids are of fundamental interest in physics, chemistry, and biology, and perturbation approach has been fundamental to liquid theoretical approaches since the dawn of modern statistical mechanics and remains so to this day. Although thermodynamic perturbation theory (TPT) is widely used in the chemical physics community, one of the most popular versions of the TPT, i.e. Zwanzig (Zwanzig, R. W. J. Chem. Phys. 1954, 22, 1420-1426) 1st-order high temperature series expansion (HTSE) TPT and its 2nd-order counterpart under a macroscopic compressibility approximation of Barker-Henderson (Barker, J. A.; Henderson, D. J. Chem. Phys. 1967, 47, 2856-2861), have some serious shortcomings: (i) the nth-order term of the HTSE is involved with reference fluid distribution functions of order up to 2n, and the higher-order terms hence progressively become more complicated and numerically inaccessible; (ii) the performance of the HTSE rapidly deteriorates and the calculated results become even qualitatively incorrect as the temperature of interest decreases. This account deals with the developments that we have made over the last five years or so to advance a coupling parameter series expansion (CPSE) and a non hard sphere (HS) perturbation strategy that has scored some of its greatest successes in overcoming the above-mentioned difficulties. In this account (i) we expatiate on implementation details of our schemes: how input information indispensable to high-order truncation of the CPSE in both the HS and non HS perturbation schemes is calculated by an Ornstein-Zernike integral equation theory; how high-order thermodynamic quantities, such as critical parameters and excess constant volume heat capacity, are extracted from the resulting excess Helmholtz free energy with irregular and inevitable numerical errors; how to select reference potential in the non HS perturbation scheme. (ii) We give a quantitative analysis on why convergence
Directory of Open Access Journals (Sweden)
Shiqi Zhou
2011-12-01
Full Text Available Thermodynamic and structural properties of liquids are of fundamental interest in physics, chemistry, and biology, and perturbation approach has been fundamental to liquid theoretical approaches since the dawn of modern statistical mechanics and remains so to this day. Although thermodynamic perturbation theory (TPT is widely used in the chemical physics community, one of the most popular versions of the TPT, i.e. Zwanzig (Zwanzig, R. W. J. Chem. Phys. 1954, 22, 1420-1426 1st-order high temperature series expansion (HTSE TPT and its 2nd-order counterpart under a macroscopic compressibility approximation of Barker-Henderson (Barker, J. A.; Henderson, D. J. Chem. Phys. 1967, 47, 2856-2861, have some serious shortcomings: (i the nth-order term of the HTSE is involved with reference fluid distribution functions of order up to 2n, and the higher-order terms hence progressively become more complicated and numerically inaccessible; (ii the performance of the HTSE rapidly deteriorates and the calculated results become even qualitatively incorrect as the temperature of interest decreases. This account deals with the developments that we have made over the last five years or so to advance a coupling parameter series expansion (CPSE and a non hard sphere (HS perturbation strategy that has scored some of its greatest successes in overcoming the above-mentioned difficulties. In this account (i we expatiate on implementation details of our schemes: how input information indispensable to high-order truncation of the CPSE in both the HS and non HS perturbation schemes is calculated by an Ornstein-Zernike integral equation theory; how high-order thermodynamic quantities, such as critical parameters and excess constant volume heat capacity, are extracted from the resulting excess Helmholtz free energy with irregular and inevitable numerical errors; how to select reference potential in the non HS perturbation scheme. (ii We give a quantitative analysis on why
Paukkunen, Hannu
2009-06-01
This is the introductory part of my PhD thesis which consists of two parts, the separate introduction and four published articles. The introduction begins by a technically detailed description of the DGLAP evolution and the fast numerical solving method for the DGLAP equations, which has been used in the numerical works of the published articles of this thesis. A write-up of the next-to-leading order (NLO) calculations for the deeply inelastic scattering (DIS) and the Drell-Yan (DY) dilepton production cross-sections is also included. The formalism of the inclusive single hadron production at NLO is described as well, although less rigorously. The introductory part ends with a discussion of the global QCD analyses in general, with a special attention paid to the major work of this thesis, the NLO analysis of nuclear parton densities and their uncertainties.
Kataev, A L
2016-01-01
The summary of the available semi-analytical results for the three-loop corrections to the QCD static potential and for the $\\mathcal{O}(\\alpha_s^4)$ contributions to the ratio of the running and pole heavy quark masses are presented. The procedure of the determination of the dependence of the four-loop contribution to the pole-running heavy quarks mass ratio on the number of quarks flavours, based on application of the least squares method is described. The necessity of clarifying the reason of discrepancy between the numerical uncertainties of the $\\alpha_s^4$ coefficients in the mass ratio, obtained by this mathematical method by the direct numerical calculations is emphasised.
Light-cone quantized QCD and novel hadron phenomenology
Energy Technology Data Exchange (ETDEWEB)
Brodsky, S.J.
1997-09-01
The authors reviews progress made in solving gauge theories such as collinear quantum chromodynamics using light-cone Hamiltonian methods. He also shows how the light-cone Fock expansion for hadron wavefunctions can be used to compute operator matrix elements such as decay amplitudes, form factors, distribution amplitudes, and structure functions, and how it provides a tool for exploring novel features of QCD. The author also reviews commensurate scale relations, leading-twist identities which relate physical observables to each other, thus eliminating renormalization scale and scheme ambiguities in perturbative QCD predictions.
Korcyl, Piotr
2016-01-01
We determine quark mass dependent order $a$ improvement terms of the form $b_Jam$ for non-singlet scalar, pseudoscalar, vector and axialvector currents using correlators in coordinate space on a set of CLS ensembles. These have been generated employing non-perturbatively improved Wilson Fermions and the tree-level L\\"uscher-Weisz gauge action at $\\beta = 3.4, 3.46, 3.55$ and $3.7$, corresponding to lattice spacings ranging from $a \\approx 0.085$ fm down to $0.05$ fm. In the $N_f=2+1$ flavour theory two types of improvement coefficients exist: $b_J$, proportional to non-singlet quark mass combinations, and $\\bar{b}_J$ (or $\\tilde{b}_J$), proportional to the trace of the quark mass matrix. Combining our non-perturbative determinations with perturbative results, we quote Pad\\'e approximants parameterizing the $b_J$ improvement coefficients within the above window of lattice spacings. We also give preliminary results for $\\tilde{b}_J$ at $\\beta=3.4$.
The pressure of deconfined QCD for all temperatures and quark chemical potentials
Ipp, A
2007-01-01
A new method for the evaluation of the perturbative expansion of the QCD pressure is presented which is valid for all temperatures and quark chemical potentials in the deconfined phase, and worked out up to and including order g^4. This new approach unifies several distinct perturbative approaches to the equation of state, and agrees with dimensional reduction, HDL and HTL resummation schemes, and the zero-temperature result in their respective ranges of validity.
One-loop effective action of QCD at high temperature using the heat kernel method
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Megias, E. [Universidad de Granada (Spain). Dept. de Fisica Moderna]. E-mail: emegias@ugr.es
2004-07-01
Perturbation theory is an important tool to describe the properties of QCD at very high temperatures. Recently a new technique has been proposed to compute the one-loop effective action of QCD at finite temperature by making a gauge covariant derivative expansion, which is fully consistent with topologically small and large gauge transformations (also time dependent transformations). This technique is based on the heat kernel expansion, and the thermal Wilson line plays an essential role. We consider a general SU(N-c) gauge group. (author)
Second-order many-body perturbation expansions of vibrational Dyson self-energies.
Hermes, Matthew R; Hirata, So
2013-07-21
Second-order many-body perturbation theories for anharmonic vibrational frequencies and zero-point energies of molecules are formulated, implemented, and tested. They solve the vibrational Dyson equation self-consistently by taking into account the frequency dependence of the Dyson self-energy in the diagonal approximation, which is expanded in a diagrammatic perturbation series up to second order. Three reference wave functions, all of which are diagrammatically size consistent, are considered: the harmonic approximation and diagrammatic vibrational self-consistent field (XVSCF) methods with and without the first-order Dyson geometry correction, i.e., XVSCF[n] and XVSCF(n), where n refers to the truncation rank of the Taylor-series potential energy surface. The corresponding second-order perturbation theories, XVH2(n), XVMP2[n], and XVMP2(n), are shown to be rigorously diagrammatically size consistent for both total energies and transition frequencies, yield accurate results (typically within a few cm(-1) at n = 4 for water and formaldehyde) for both quantities even in the presence of Fermi resonance, and have access to fundamentals, overtones, and combinations as well as their relative intensities as residues of the vibrational Green's functions. They are implemented into simple algorithms that require only force constants and frequencies of the reference methods (with no basis sets, quadrature, or matrix diagonalization at any stage of the calculation). The rules for enumerating and algebraically interpreting energy and self-energy diagrams are elucidated in detail.
Ivanov, N Ya
2012-01-01
We analyze the perturbative and parametric stability of the QCD predictions for the Callan-Gross ratio $R(x,Q^2)=F_L/F_T$ and azimuthal $\\cos(2\\varphi)$ asymmetry in heavy-quark leptoproduction. Our analysis shows that large radiative corrections to the structure functions cancel each other in their ratio $R(x,Q^2)$ and azimuthal asymmetry with good accuracy. As a result, the NLO contributions to the Callan-Gross ratio and $\\cos(2\\varphi)$ asymmetry are less than 10% in a wide region of the variables $x$ and $Q^2$. We provide compact analytic predictions for $R(x,Q^2)$ and asymmetry in the case of low $x\\ll 1$. Simple formulae connecting the high-energy behavior of the Callan-Gross ratio and azimuthal asymmetry with the low-$x$ asymptotics of the gluon density in the target are derived. It is shown that the obtained hadron-level predictions for $R(x,Q^2)$ and azimuthal asymmetry are stable at $x\\ll 1$ under the DGLAP evolution of the gluon distribution function. Concerning the experimental aspects, we propose...
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Yu, Jaehoon
1993-08-01
The D0 experiment has accumulated data for a study of inclusive W production corresponding to a total integrated luminosity of 14.3 {plus_minus} 1.7 pb{sup {minus}1} during the 1992--1993 Fermilab Tevatron collider run. The total number of W {yields} e + {nu} candidates is 9770. The ratio of the number of W + 1 jet events to that of W + 0 jet events has been measured as a function of jet minimum E{sub T}. Using this ratio the strong coupling constant, {alpha}{sub s} at Q{sup 2} = M{sub W}{sup 2} is measured to be {alpha}{sub s}(M{sub W}{sup 2}) = 0.124 {plus_minus} 0.005(stat) {plus_minus} 0.006(MC) {plus_minus} 0.008(theory){sub {minus}0.022}{sup +0.026}(sys) or ({sub {minus}0.025}{sup +0.028} combined) with a jet minimum E{sub T} of 25 GeV. A quantitative test of perturbative QCD has been made by comparing the experimentally measured ratio with the theoretical predictions. The theoretical predictions of the ratio in both the leading order and next-to-leading order are in good agreement with the measured ratio.
Zou, Zhi-Tian; Lu, Cai-Dian
2012-01-01
In perturbative QCD approach, we investigate the $B(B_{s})\\rightarrow D_{(s)}(\\bar{D}_{(s)})\\,T$ and $D_{(s)}^{*}(\\bar{D}_{(s)}^{*})\\,T$ decays, which include the Cabibbo-Kobayashi-Maskawa (CKM) favored decays and the Cabibbo-Kobayashi-Maskawa-suppressed decays, where T denotes a light tensor meson. From our calculation, we find that the nonfactorizable emission diagrams and the annihilation type diagrams are important, especially for those color suppressed channels. For those decays with a tensor meson emitted, the factorizable emission diagrams vanish owing to the fact that a tensor meson can not be produced through the local (V-A) or tensor current. The numerical results show that the predictions for the branching ratios of considered charmed B decays are in the range of $10^{-4}$ to $10^{-6}$ for those CKM-favored decays (governed by $|V_{cb}|$) and in the range of $10^{-5}$ to $10^{-8}$ for those CKM-suppressed decays (governed by $|V_{ub}|$). We also predict large transverse polarization contributions i...
Non-leptonic decays of $B \\to ( f_1(1285),f_1(1420) ) V$ in the perturbative QCD approach
Liu, Xin; Zou, Zhi-Tian
2016-01-01
We investigate the branching ratios, the polarization fractions, the direct CP-violating asymmetries, and the relative phases in 20 non-leptonic decay modes of $B \\to f_1 V$ within the framework of perturbative QCD approach at leading order with $f_1$ including two $^3\\!P_1$-axial-vector states $f_1(1285)$ and $f_1(1420)$. Here, $B$ denotes $B^+$, $B^0$, and $B_s^0$ mesons and $V$ stands for the lightest vector mesons $\\rho$, $K^*$, $\\omega$, and $\\phi$ , respectively. The $B_s^0 \\to f_1 V$ decays are studied theoretically for the first time in the literature. Together with the angle $\\phi_{f_1} \\approx (24^{+3.2}_{-2.7})^\\circ$ extracted from the measurement through $B_{d/s} \\to J/\\psi f_1(1285)$ modes for the $f_1(1285)-f_1(1420)$ mixing system, it is of great interest to find phenomenologically that some modes such as the tree-dominated $B^+ \\to f_1 \\rho^+$ and the penguin-dominated $B^{+,0} \\to f_1 K^{*+,0}, B_s^0 \\to f_1 \\phi$ with large branching ratios around ${\\cal O}(10^{-6})$ or even ${\\cal O}(10^{-...
Quasi-two-body decays B(s )→P ρ →P π π in the perturbative QCD approach
Li, Ya; Ma, Ai-Jun; Wang, Wen-Fei; Xiao, Zhen-Jun
2017-03-01
In this work, we calculate the C P -averaged branching ratios and the direct C P -violating asymmetries of the quasi-two-body decays B(s )→P (ρ →)π π by employing the perturbative QCD (PQCD) approach (here P stands for a light pseudoscalar meson π , K , η or η'). The vector current timelike form factor Fπ, which contains the final-state interactions between the pion pair in the resonant region associated with the P -wave states ρ (770 ) along with the two-pion distribution amplitudes, is employed to describe the interactions between the ρ and the pion pair under the hypothesis of the conserved vector current. We found that (a) the PQCD predictions for the branching ratios and the direct C P -violating asymmetries for most considered B(s )→P (ρ →)π π decays agree with currently available data within errors, (b) for B (B →π0ρ0→π0(π+π-) , the PQCD prediction is much smaller than the measured one, and (c) for the B+→π+(ρ0→)π+π- decay mode, there is a negative C P asymmetry (-27.5-3.7+3.0)% , which agrees with other theoretical predictions but is different in sign from those reported by the BABAR and LHCb Collaborations.
Borel summability and the non perturbative $1/N$ expansion of arbitrary quartic tensor models
Delepouve, Thibault; Rivasseau, Vincent
2014-01-01
We extend the proof of Borel summability of melonic quartic tensor models to tensor models with arbitrary quartic interactions. This extension requires a new version of the loop vertex expansion using several species of intermediate fields and new bounds based on Cauchy-Schwarz inequalities. The Borel summability is proven to be uniform as the tensor size becomes large. Furthermore, we show that the $1/N$ expansion of any quartic tensor model can be performed at the constructive level, that is we show that every cumulant is a sum of explicit terms up to some order plus a rest term which is an analytic function in the coupling constant in a cardioid domain of the complex plane and which is suppressed in $1/N$.
Unified QCD picture of hard diffraction
Navelet, H
2001-01-01
Using a combination of S-Matrix and perturbative QCD properties in the small x_{Bjorken} regime, we propose a formulation of hard diffraction unifying the partonic (Ingelman-Schlein) Pomeron, Soft Colour Interaction and QCD dipole descriptions. In particular, we show that all three approaches give an unique and mutually compatible formula for the proton diffractive structure functions incorporating perturbative and non perturbative QCD features.
Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions
Bruno, Mattia; Engel, Georg P; Francis, Anthony; Herdoiza, Gregorio; Horch, Hanno; Korcyl, Piotr; Korzec, Tomasz; Papinutto, Mauro; Schaefer, Stefan; Scholz, Enno E; Simeth, Jakob; Simma, Hubert; Söldner, Wolfgang
2014-01-01
We describe a new set of gauge configurations generated within the CLS effort. These ensembles have N_f=2+1 flavors of non-perturbatively improved Wilson fermions in the sea with the Luescher-Weisz action used for the gluons. Open boundary conditions in time are used to address the problem of topological freezing at small lattice spacings and twisted-mass reweighting for improved stability of the simulations. We give the bare parameters at which the ensembles have been generated and how these parameters have been chosen. Details of the algorithmic setup and its performance are presented as well as measurements of the pion and kaon masses alongside the scale parameter t_0.
Non-perturbative renormalisation of Delta F=2 four-fermion operators in two-flavour QCD
Dimopoulos, P; Palombi, Filippo; Papinutto, Mauro; Peña, C; Vladikas, A; Wittig, H
2008-01-01
Using Schroedinger Functional methods, we compute the non-perturbative renormalisation and renormalisation group running of several four-fermion operators, in the framework of lattice simulations with two dynamical Wilson quarks. Two classes of operators have been targeted: (i) those with left-left current structure and four propagating quark fields/ (ii) all operators containing two static quarks. In both cases, only the parity-odd contributions have been considered, being the ones that renormalise multiplicatively. Our results, once combined with future simulations of the corresponding lattice hadronic matrix elements, may be used for the computation of phenomenological quantities of interest, such as B_K and B_B (the latter also in the static limit).
Non-perturbative renormalisation of {delta}F=2 four-fermion operators in two-flavour QCD
Energy Technology Data Exchange (ETDEWEB)
Dimopoulos, P.; Vladikas, A. [INFN, Sezione di Roma II (Italy)]|[Rome-3 Univ. (Italy). Dipt. di Fisica; Herdoiza, G. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Palombi, F.; Papinutto, M. [CERN, Geneva (Switzerland). Physics Dept., TH Division; Pena, C. [Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica C-XI]|[Univ. Autonoma de Madrid (Spain). Inst. de Fisica Teorica UAM/CSIC C-XVI; Wittig, H. [Mainz Univ. (Germany). Inst. fuer Kernphysik
2007-12-15
Using Schroedinger Functional methods, we compute the non-perturbative renormalisation and renormalisation group running of several four-fermion operators, in the framework of lattice simulations with two dynamical Wilson quarks. Two classes of operators have been targeted: (i) those with left-left current structure and four propagating quark fields; (ii) all operators containing two static quarks. In both cases, only the parity-odd contributions have been considered, being the ones that renormalise multiplicatively. Our results, once combined with future simulations of the corresponding lattice hadronic matrix elements, may be used for the computation of phenomenological quantities of interest, such as B{sub K} and B{sub B} (the latter also in the static limit). (orig.)
Korcyl, Piotr
2016-01-01
We determine quark mass dependent order $a$ improvement terms of the form $b_J am$ for non-singlet scalar, pseudoscalar, vector and axialvector currents, using correlators in coordinate space. We use a set of CLS ensembles comprising non-perturbatively improved Wilson Fermions and the tree-level Luescher-Weisz gauge action at $\\beta=3.4,3.46,3.55$ and $\\beta=3.7$, corresponding to lattice spacings $a$ ranging from $0.05$ fm to $0.09$ fm. We report the values of the $b_J$ improvement coefficients which are proportional to non-singlet quark mass combinations and also discuss the possibility of determining the $\\bar{b}_J$ coefficients which are proportional to the trace of the quark mass matrix.
QCD, conformal invariance and the two Pomerons
Munier, S
1998-01-01
Using the solution of the BFKL equation including the leading and subleading conformal spin components, we show how the conformal invariance underlying the leading log (1/x) expansion of perturbative QCD leads to elastic amplitudes described by two effective Pomeron singularities. One Pomeron is the well-known "hard" BFKL leading singularity while the new one appears from a shift of the higher conformal spin BFKL singularities from subleading to leading position. This new effective singularity is compatible with the "soft" Pomeron and thus, together with the "hard" Pomeron, meets at large $Q^{2}$ the "double Pomeron" solution which has been recently conjectured by Donnachie and Landshoff.
Lattice QCD spectroscopy for hadronic CP violation
Directory of Open Access Journals (Sweden)
Jordy de Vries
2017-03-01
In this work we propose a strategy to calculate these couplings by using spectroscopic lattice QCD techniques. Instead of directly calculating the pion–nucleon coupling constants, a challenging task, we use chiral symmetry relations that link the pion–nucleon couplings to nucleon sigma terms and mass splittings that are significantly easier to calculate. In this work, we show that these relations are reliable up to next-to-next-to-leading order in the chiral expansion in both SU(2 and SU(3 chiral perturbation theory. We conclude with a brief discussion about practical details regarding the required lattice QCD calculations and the phenomenological impact of an improved understanding of CP-violating matrix elements.
Baaquie, Belal E
2007-01-01
European options on coupon bonds are studied in a quantum field theory model of forward interest rates. Swaptions are briefly reviewed. An approximation scheme for the coupon bond option price is developed based on the fact that the volatility of the forward interest rates is a small quantity. The field theory for the forward interest rates is Gaussian, but when the payoff function for the coupon bond option is included it makes the field theory nonlocal and nonlinear. A perturbation expansion using Feynman diagrams gives a closed form approximation for the price of coupon bond option. A special case of the approximate bond option is shown to yield the industry standard one-factor HJM formula with exponential volatility.
Directory of Open Access Journals (Sweden)
Stefan Hollands
2009-09-01
Full Text Available In this paper, we propose a new framework for quantum field theory in terms of consistency conditions. The consistency conditions that we consider are ''associativity'' or ''factorization'' conditions on the operator product expansion (OPE of the theory, and are proposed to be the defining property of any quantum field theory. Our framework is presented in the Euclidean setting, and is applicable in principle to any quantum field theory, including non-conformal ones. In our framework, we obtain a characterization of perturbations of a given quantum field theory in terms of a certain cohomology ring of Hochschild-type. We illustrate our framework by the free field, but our constructions are general and apply also to interacting quantum field theories. For such theories, we propose a new scheme to construct the OPE which is based on the use of non-linear quantized field equations.
String effect and QCD coherence
Energy Technology Data Exchange (ETDEWEB)
Azimov, Ya.I.; Dokshitzer, Yu.L.; Khoze, V.A.; Troyan, S.I.
1985-12-19
In the framework of the idea of local parton-hadron duality we discuss the asymptotic predictions of QCD perturbation theory for angular distributions of hadron flows in the three-jet events, e/sup +/e/sup -/->qanti qg->hadrons. The coherence of soft gluon emission provides the QCD explanation of the string effect observed in experiments. (orig.).
Institute of Scientific and Technical Information of China (English)
张荣; 何雪明
2004-01-01
A numerical perturbation expansion method is developed, analysed and implemented for the numerical solution of a second-order initial-value problem. The differential equation in this problem exhibits cubic damping, a cubic restoring force and a decaying forcing-term which is periodic with constant frequency. The method is compared with the numerical method by Twizell [1]. In fact, the later is first perturbation approximate solution in the present paper.
Randall, Lisa
1994-01-01
We present a detailed analysis of the use of heavy quark fragmentation into heavy hadrons for testing the heavy quark effective theory through comparison of the measured fragmentation parameters of the c and b quarks. Our analysis is entirely model independent. We interpret the known perturbative evolution in a way useful for exploiting heavy quark symmetry at low energy. We first show consistency with perturbative QCD scaling for measurements done solely with c quarks. We then apply the perturbative analysis and the heavy quark expansion to relate measurements from ARGUS and LEP. We place bounds on a nonperturbative quark mass suppressed parameter, and compare the values for the b and c quarks. We find consistency with the heavy quark expansion but fairly sizable QCD uncertainties. We also suggest that one might reduce the systematic uncertainty in the result by not extrapolating to low z.
Energy Technology Data Exchange (ETDEWEB)
Lindenbaum, S.J.; Samuel, S.
1993-09-01
A critical investigation of non-perturbative QCD require investigating glueballs, search for a Quark Gluon Plasma (OGP), and search for strangelets. In the glueball area the data obtained (E- 881) at 8 GeV/c were analyzed for {pi}{sup {minus}} + p {yields} {phi}{phi}n (OZI forbidden), {phi}K{sup +}K{sup {minus}}n (OZI allowed), K{sup {minus}}p {yields} {phi}{phi}({Lambda}{Sigma}) (OZI allowed), and {bar p}p {yields} {phi}{phi} {yields} {phi}{phi}{pi}{sup 0} (OZI forbidden), {phi}K{sup +}K{sup {minus}}{pi}{sup 0} (OZI allowed). By comparing the OZI forbidden (glueball filter reactions) with the OZI allowed and previous 22 GeV/c {pi}{sup {minus}}p {yields} {phi}{phi}n or {phi}K{sup +}K{sup {minus}}n data a further critical test of the so far unsuccessfully challenged hypothesis that our g{sup T}(2010), g{sub T}{prime}(2300) and g{sub T}{double_prime}(2340) all with I{sup G}J{sup PC} = 0{sup +}2{sup ++} are produced by 1-3 2{sup ++} glueballs will be made. In the QGP search with a large-solid-angle TPC a good {Xi} signal was observed. The ratio of {Xi} to single strange quark particles such as {lambda} is a better indication of strangeness enhancement in QGP formation. The data indicate enhancement by a factor {approx} 2 over cascade model (corrected to observed strangeness) predictions, but it is definitely far from conclusive at this stage since the result is model dependent. Double {lambda} topologies of the type needed to discover light strangelets in the nanosecond lifetime region were found. In addition, research has been accomplished in three main areas: bosonic technicolor and strings, buckministerfullerene C{sub 60} and neutrino oscillations in a dense neutrino gas.
Deur, Alexandre; Brodsky, Stanley J.; de Téramond, Guy F.
2016-09-01
We review the present theoretical and empirical knowledge for αs, the fundamental coupling underlying the interactions of quarks and gluons in Quantum Chromodynamics (QCD). The dependence of αs(Q2) on momentum transfer Q encodes the underlying dynamics of hadron physics-from color confinement in the infrared domain to asymptotic freedom at short distances. We review constraints on αs(Q2) at high Q2, as predicted by perturbative QCD, and its analytic behavior at small Q2, based on models of nonperturbative dynamics. In the introductory part of this review, we explain the phenomenological meaning of the coupling, the reason for its running, and the challenges facing a complete understanding of its analytic behavior in the infrared domain. In the second, more technical, part of the review, we discuss the behavior of αs(Q2) in the high momentum transfer domain of QCD. We review how αs is defined, including its renormalization scheme dependence, the definition of its renormalization scale, the utility of effective charges, as well as "Commensurate Scale Relations" which connect the various definitions of the QCD coupling without renormalization-scale ambiguity. We also report recent significant measurements and advanced theoretical analyses which have led to precise QCD predictions at high energy. As an example of an important optimization procedure, we discuss the "Principle of Maximum Conformality", which enhances QCD's predictive power by removing the dependence of the predictions for physical observables on the choice of theoretical conventions such as the renormalization scheme. In the last part of the review, we discuss the challenge of understanding the analytic behavior αs(Q2) in the low momentum transfer domain. We survey various theoretical models for the nonperturbative strongly coupled regime, such as the light-front holographic approach to QCD. This new framework predicts the form of the quark-confinement potential underlying hadron spectroscopy and
van Westen, Thijs; Gross, Joachim
2017-07-01
The Helmholtz energy of a fluid interacting by a Lennard-Jones pair potential is expanded in a perturbation series. Both the methods of Barker-Henderson (BH) and of Weeks-Chandler-Andersen (WCA) are evaluated for the division of the intermolecular potential into reference and perturbation parts. The first four perturbation terms are evaluated for various densities and temperatures (in the ranges ρ*=0 -1.5 and T*=0.5 -12 ) using Monte Carlo simulations in the canonical ensemble. The simulation results are used to test several approximate theoretical methods for describing perturbation terms or for developing an approximate infinite order perturbation series. Additionally, the simulations serve as a basis for developing fully analytical third order BH and WCA perturbation theories. The development of analytical theories allows (1) a careful comparison between the BH and WCA formalisms, and (2) a systematic examination of the effect of higher-order perturbation terms on calculated thermodynamic properties of fluids. Properties included in the comparison are supercritical thermodynamic properties (pressure, internal energy, and chemical potential), vapor-liquid phase equilibria, second virial coefficients, and heat capacities. For all properties studied, we find a systematically improved description upon using a higher-order perturbation theory. A result of particular relevance is that a third order perturbation theory is capable of providing a quantitative description of second virial coefficients to temperatures as low as the triple-point of the Lennard-Jones fluid. We find no reason to prefer the WCA formalism over the BH formalism.
Eriksen, Janus J.; Matthews, Devin A.; Jørgensen, Poul; Gauss, Jürgen
2016-05-01
We extend our assessment of the potential of perturbative coupled cluster (CC) expansions for a test set of open-shell atoms and organic radicals to the description of quadruple excitations. Namely, the second- through sixth-order models of the recently proposed CCSDT(Q-n) quadruples series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)] are compared to the prominent CCSDT(Q) and ΛCCSDT(Q) models. From a comparison of the models in terms of their recovery of total CC singles, doubles, triples, and quadruples (CCSDTQ) energies, we find that the performance of the CCSDT(Q-n) models is independent of the reference used (unrestricted or restricted (open-shell) Hartree-Fock), in contrast to the CCSDT(Q) and ΛCCSDT(Q) models, for which the accuracy is strongly dependent on the spin of the molecular ground state. By further comparing the ability of the models to recover relative CCSDTQ total atomization energies, the discrepancy between them is found to be even more pronounced, stressing how a balanced description of both closed- and open-shell species—as found in the CCSDT(Q-n) models—is indeed of paramount importance if any perturbative CC model is to be of chemical relevance for high-accuracy applications. In particular, the third-order CCSDT(Q-3) model is found to offer an encouraging alternative to the existing choices of quadruples models used in modern computational thermochemistry, since the model is still only of moderate cost, albeit markedly more costly than, e.g., the CCSDT(Q) and ΛCCSDT(Q) models.
Eriksen, Janus J; Matthews, Devin A; Jørgensen, Poul; Gauss, Jürgen
2016-05-21
We extend our assessment of the potential of perturbative coupled cluster (CC) expansions for a test set of open-shell atoms and organic radicals to the description of quadruple excitations. Namely, the second- through sixth-order models of the recently proposed CCSDT(Q-n) quadruples series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)] are compared to the prominent CCSDT(Q) and ΛCCSDT(Q) models. From a comparison of the models in terms of their recovery of total CC singles, doubles, triples, and quadruples (CCSDTQ) energies, we find that the performance of the CCSDT(Q-n) models is independent of the reference used (unrestricted or restricted (open-shell) Hartree-Fock), in contrast to the CCSDT(Q) and ΛCCSDT(Q) models, for which the accuracy is strongly dependent on the spin of the molecular ground state. By further comparing the ability of the models to recover relative CCSDTQ total atomization energies, the discrepancy between them is found to be even more pronounced, stressing how a balanced description of both closed- and open-shell species-as found in the CCSDT(Q-n) models-is indeed of paramount importance if any perturbative CC model is to be of chemical relevance for high-accuracy applications. In particular, the third-order CCSDT(Q-3) model is found to offer an encouraging alternative to the existing choices of quadruples models used in modern computational thermochemistry, since the model is still only of moderate cost, albeit markedly more costly than, e.g., the CCSDT(Q) and ΛCCSDT(Q) models.
Introduction to non-perturbative heavy quark effective theory
Energy Technology Data Exchange (ETDEWEB)
Sommer, R. [DESY, Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2010-08-15
My lectures on the effective field theory for heavy quarks, an expansion around the static limit, concentrate on the motivation and formulation of HQET, its renormalization and discretization. This provides the basis for understanding that and how this effective theory can be formulated fully non-perturbatively in the QCD coupling, while by the very nature of an effective field theory, it is perturbative in the expansion parameter 1/m. After the couplings in the effective theory have been determined, the result at a certain order in 1/m is unique up to higher order terms in 1/m. In particular the continuum limit of the lattice regularized theory exists and leaves no trace of how it was regularized. In other words, the theory yields an asymptotic expansion of the QCD observables in 1/m - as usual in a quantum field theory modified by powers of logarithms. None of these properties has been shown rigorously (e.g. to all orders in perturbation theory) but perturbative computations and recently also non-perturbative lattice results give strong support to this ''standard wisdom''. A subtle issue is that a theoretically consistent formulation of the theory is only possible through a non-perturbative matching of its parameters with QCD at finite values of 1/m. As a consequence one finds immediately that the splitting of a result for a certain observable into, for example, lowest order and first order is ambiguous. Depending on how the matching between effective theory and QCD is done, a first order contribution may vanish and appear instead in the lowest order. For example, the often cited phenomenological HQET parameters anti {lambda} and {lambda}{sub 1} lack a unique non-perturbative definition. But this does not affect the precision of the asymptotic expansion in 1/m. The final result for an observable is correct up to order (1/m){sup n+1} if the theory was treated including (1/m){sup n} terms. Clearly, the weakest point of HQET is that it
Coluzzi, Barbara; Bersani, Enrico
2016-01-01
We recall the perturbation expansion for Michaelis-Menten kinetics, beyond the standard quasi-steady-state approximation (sQSSA). Against this background, we are able to appropriately apply the alternative approach to the study of singularly perturbed differential equations that is based on the renormalization group (SPDERG), by clarifying similarities and differences. In the present demanding situation, we directly renormalize the bare initial condition value for the substrate. Our main results are: i) the 2nd order SPDERG uniform approximations to the correct solutions contain, up to 1st order, the same outer components as the known perturbation expansion ones; ii) the differential equation to be solved for the derivation of the 1st order outer substrate component is simpler within the SPDERG approach; iii) the approximations better reproduce the numerical solutions of the original problem in a region encompassing the matching one, because of the 2nd order terms in the inner components, calculated here for ...
Eriksen, Janus Juul; Jørgensen, Poul; Gauss, Jürgen
2015-01-01
The accuracy with which total energies of open-shell species may be calculated using coupled cluster perturbative triples expansions is investigated. In particular, the acclaimed CCSD(T) model, in which a non-iterative correction for the effect of triple excitations is added to the coupled cluster singles and doubles (CCSD) energy, is compared to the second- through sixth-order models of the recently proposed CCSD(T-n) triples series for both unrestricted as well as restricted open-shell Hartree-Fock (UHF/ROHF) reference determinants. By comparing UHF- and ROHF-based statistical results for a test set of 18 atoms and small radicals with comparable RHF-based results, it is found that not only the numerical consistency of the CCSD(T) model, but also its fortuitous cancellation of errors for closed-shell systems break down in the transition from closed- to open-shell systems. For the higher-order models of the CCSD(T-n) series, however, no behavioral differences are found between the correlated descriptions of c...
Eriksen, Janus J; Jørgensen, Poul; Gauss, Jürgen
2016-01-01
We extend our assessment of the potential of perturbative coupled cluster (CC) expansions for a test set of open-shell species to the description of quadruple excitations. In doing so, we compare the prominent CCSDT(Q) and lambda-CCSDT(Q) (a-CCSDT(Q)) models, in which the CC singles, doubles, and triples (CCSDT) energy is augmented by similar corrections for quadruple excitations, to the second- through sixth-order models of the CCSDT(Q-n) quadruples series, which is based on a CCSDT rather than an HF zeroth-order state. By comparing the models in terms of the size-intensive recovery of as well as the total deviation from the quadruples contribution to CC singles, doubles, triples, and quadruples (CCSDTQ) energies, we find (i) that the accuracy offered by the CCSDT(Q) and a-CCSDT(Q) models is strongly dependent on the spin of the molecular ground state - like for the CCSD(T) model in the first part of the present series [arXiv:1512.02846] - and (ii) that the performance of the CCSDT(Q-n) models is practically...
19th High-Energy Physics International Conference in Quantum Chromodynamics (QCD)
2016-01-01
Experimental and Theoretical Issues on: Perturbative and Non-Perturbative QCD QCD at colliders Tau, Kaon and B decays, CP-violation Exotic Hadrons Spectroscopy Precision Tests of the Standard Model Physics Beyond the Standard Model.
Cerci, Salim
2016-01-01
Jets which are the signatures of quarks and gluons in the detector can be described by Quantum Chromodynamics (QCD) in terms of parton-parton scattering. Jets are abundantly produced at the LHC's high energy scales. Measurements of inclusive jets, dijets and multijets can be used to test perturbative QCD predictions and to constrain parton distribution functions (PDF), as well as to measure the strong coupling constant $\\alpha_{S}$. The measurements use the samples of proton-proton collisions collected with the CMS detector at the LHC at various center-of-mass energies of 7, 8 and 13 TeV.
Eriksen, Janus J; Matthews, Devin A; Jørgensen, Poul; Gauss, Jürgen
2016-05-21
The accuracy at which total energies of open-shell atoms and organic radicals may be calculated is assessed for selected coupled cluster perturbative triples expansions, all of which augment the coupled cluster singles and doubles (CCSD) energy by a non-iterative correction for the effect of triple excitations. Namely, the second- through sixth-order models of the recently proposed CCSD(T-n) triples series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)] are compared to the acclaimed CCSD(T) model for both unrestricted as well as restricted open-shell Hartree-Fock (UHF/ROHF) reference determinants. By comparing UHF- and ROHF-based statistical results for a test set of 18 modest-sized open-shell species with comparable RHF-based results, no behavioral differences are observed for the higher-order models of the CCSD(T-n) series in their correlated descriptions of closed- and open-shell species. In particular, we find that the convergence rate throughout the series towards the coupled cluster singles, doubles, and triples (CCSDT) solution is identical for the two cases. For the CCSD(T) model, on the other hand, not only its numerical consistency, but also its established, yet fortuitous cancellation of errors breaks down in the transition from closed- to open-shell systems. The higher-order CCSD(T-n) models (orders n > 3) thus offer a consistent and significant improvement in accuracy relative to CCSDT over the CCSD(T) model, equally for RHF, UHF, and ROHF reference determinants, albeit at an increased computational cost.
QCD corrections in a class of spontaneous CP-violating models
Energy Technology Data Exchange (ETDEWEB)
Tracas, N.D.; Vlachos, N.D.; Zoupanos, G.
1985-10-31
We present a study of QCD corrections in a class of spontaneous CP-violating models. We find that the Higgs fields which are responsible for the CP-violating transitions should be one order of magnitude heavier than what is expected fom tree order estimates. This implies so large a self-coupling of the Higgs fields that it makes the use of perturbation expansion questionable. (orig.).
On the relation between QCD potentials in momentum and position space
Jezabek, M.; Peter, M.; Sumino, Y.
1998-01-01
We derive a formula which relates the QCD potentials in momentum space and in position space in terms of the beta-function of the renormalization-group equation for the potential. This formula is used to study the theoretical uncertainties in the potential and in particular in its application to the determination of the pole mass m_b when we use perturbative expansions. We demonstrate the existence of these uncertainties for the Richardson potential explicitly and then discuss the limited the...
Indian Academy of Sciences (India)
Zaiyun Zhang; Jianhua Huang; Juan Zhong; Sha-Sha Dou; Jiao Liu; Dan Peng; Ting Gao
2014-06-01
In this paper, we construct the travelling wave solutions to the perturbed nonlinear Schrödinger’s equation (NLSE) with Kerr law non-linearity by the extended (′/)-expansion method. Based on this method, we obtain abundant exact travelling wave solutions of NLSE with Kerr law nonlinearity with arbitrary parameters. The travelling wave solutions are expressed by the hyperbolic functions, trigonometric functions and rational functions.
Cvetič, Gorazd
2016-01-01
We consider a new form of analytical perturbation theory expansion in the massless $SU(N_c)$ theory, for the $e^+e^-$-annihilation to hadrons Adler function, and the Bjorken sum rule of the polarized lepton-hadron deep-inelastic scattering, and demonstrate its validity at the $O(\\alpha_s^4)$-level at least. It is expressed through a two-fold series in terms of powers of the conformal anomaly and the coupling constant $\\alpha_s$ of the $SU(N_c)$ gauge model. Subsequently, explicit expressions are obtained for the $\\{\\beta\\}$-expanded perturbation coefficients at $O(\\alpha_s^4)$ level in $\\overline{\\rm MS}$ scheme, for the nonsinglet contribution to the Adler function and the Bjorken polarized sum rule. Comparisons of the obtained terms in the $\\{\\beta\\}$-expanded perturbation coefficients are made with the corresponding terms obtained by using extra gluino degrees of freedom, or skeleton-motivated expansion, or $R_{\\delta}$-scheme motivated expansion in the Principle of Maximal Conformality. Relations are pres...
2015-01-01
These are the proceedings of the QCD Evolution 2015 Workshop which was held 26–30 May, 2015 at Jefferson Lab, Newport News, Virginia, USA. The workshop is a continuation of a series of workshops held during four consecutive years 2011, 2012, 2013 at Jefferson Lab, and in 2014 in Santa Fe, NM. With the rapid developments in our understanding of the evolution of parton distributions including low-x, TMDs, GPDs, higher-twist correlation functions, and the associated progress in perturbative QCD, lattice QCD and effective field theory techniques we look forward with great enthusiasm to the 2015 meeting. A special attention was also paid to participation of experimentalists as the topics discussed are of immediate importance for the JLab 12 experimental program and a future Electron Ion Collider.
Excited Baryons in Holographic QCD
Energy Technology Data Exchange (ETDEWEB)
de Teramond, Guy F.; /Costa Rica U.; Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins
2011-11-08
The light-front holographic QCD approach is used to describe baryon spectroscopy and the systematics of nucleon transition form factors. Baryon spectroscopy and the excitation dynamics of nucleon resonances encoded in the nucleon transition form factors can provide fundamental insight into the strong-coupling dynamics of QCD. The transition from the hard-scattering perturbative domain to the non-perturbative region is sensitive to the detailed dynamics of confined quarks and gluons. Computations of such phenomena from first principles in QCD are clearly very challenging. The most successful theoretical approach thus far has been to quantize QCD on discrete lattices in Euclidean space-time; however, dynamical observables in Minkowski space-time, such as the time-like hadronic form factors are not amenable to Euclidean numerical lattice computations.
QCD Factorization and PDFs from Lattice QCD Calculation
Ma, Yan-Qing
2014-01-01
In this talk, we review a QCD factorization based approach to extract parton distribution and correlation functions from lattice QCD calculation of single hadron matrix elements of quark-gluon operators. We argue that although the lattice QCD calculations are done in the Euclidean space, the nonperturbative collinear behavior of the matrix elements are the same as that in the Minkowski space, and could be systematically factorized into parton distribution functions with infrared safe matching coefficients. The matching coefficients can be calculated perturbatively by applying the factorization formalism on to asymptotic partonic states.
Cvetič, Gorazd; Kataev, A. L.
2016-07-01
We consider a new form of analytical perturbation theory expansion in the massless S U (Nc) theory, for the nonsinglet part of the e+e--annihilation to hadrons Adler function Dn s and of the Bjorken sum rule of the polarized lepton-hadron deep-inelastic scattering Cns B j p, and demonstrate its validity at the O (αs4)-level at least. It is a two-fold series in powers of the conformal anomaly and of S U (Nc) coupling αs. Explicit expressions are obtained for the {β }-expanded perturbation coefficients at O (αs4) level in MS ¯ scheme, for both considered physical quantities. Comparisons of the terms in the {β }-expanded coefficients are made with the corresponding terms obtained by using extra gluino degrees of freedom, or skeleton-motivated expansion, or Rδ-scheme motivated expansion in the Principle of Maximal Conformality. Relations between terms of the {β }-expansion for the Dn s- and Cns B j p-functions, which follow from the conformal symmetry limit and its violation, are presented. The relevance to the possible new analyses of the experimental data for the Adler function and Bjorken sum rule is discussed.
Introduction to QCD - a bound state perspective
Hoyer, Paul
2011-01-01
These lecture notes focus on the bound state sector of QCD. Motivated by data which suggests that the strong coupling \\alpha_s(Q) freezes at low Q, and by similarities between the spectra of hadrons and atoms, I discuss if and how QCD bound states may be treated perturbatively. I recall the basic principles of perturbative gauge theory bound states at lowest order in the \\hbar expansion. Born level amplitudes are insensitive to the i\\epsilon prescription of propagators, which allows to eliminate the Z-diagrams of relativistic, time-ordered Coulomb interactions. The Dirac wave function thus describes a single electron which propagates forward in time only, even though the bound state has any number of pair constituents when Feynman propagators are used. In the absence of an external potential, states that are bound by the Coulomb attraction of their constituents can be analogously described using only their valence degrees of freedom. The instantaneous A^0 field is determined by Gauss' law for each wave functi...
Cross section of e(+)e(-) annihilation into hadrons of order alpha(4)(s)n(2)(f) in perturbative QCD.
Baikov, P A; Chetyrkin, K G; Kühn, J H
2002-01-07
We present the first genuine QCD five-loop calculation of the vacuum polarization functions: analytical terms of order alpha(4)(s)n(2)(f) to the absorptive parts of vector and scalar correlators. These corrections form an important gauge-invariant subset of the full omicron(alpha(4)(s)) correction to e(+)e(-) annihilation into hadrons and the Higgs decay rate into hadrons, respectively. They discriminate between different widely used estimates of the full result.
Some Applications of Hard Thermal Loop Perturbation Theory in Quark Gluon Plasma
Haque, Najmul
2014-01-01
This thesis is mainly devoted to the study of thermodynamics for quantum Chromodynamics. In this thesis I apply hard-thermal-loop perturbation theory, which is a gauge-invariant reorganization of the conventional perturbative expansion for quantum gauge theories to study the thermodynamics of QCD in leading-order, next-to-leading-order and next-to-next-to-leading order at finite temperature and finite chemical potential. I also discuss about various order diagonal and off-diagonale quark number susceptibilities in leading order as well as beyond leading order. For all the observables, I compare our results with available lattice QCD data and we find good agreement. Along-with the computation of thermodynamic quantities of hot and dense matter, I also discuss about low mass dilepton rate from hot and dense medium using both perturbative and non-perturbative models and compare them with those from lattice gauge theory and in-medium hadron gas.
Energy Technology Data Exchange (ETDEWEB)
Bietenholz, W. [Universidad Nacional Autonoma de Mexico, Mexico City (Mexico). Inst. de Ciencias Nucleares; Cundy, N. [Seoul National Univ. (Korea, Republic of). Lattice Gauge Theory Research Center; Goeckeler, M. [Regensburg Univ. (Germany). Inst. fuer Theoretische Physik; Horsley, R.; Zanotti, J.M. [Edinburgh Univ. (United Kingdom). School of Physics; Nakamura, Y. [Tsukuba Univ., Ibaraki (Japan). Center for Computational Sciences; Pleiter, D. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Theoretical Physics Div.; Schierholz, G. [Regensburg Univ. (Germany). Inst. fuer Theoretische Physik; Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2011-03-15
The {delta}-regime of QCD is characterised by light quarks in a small spatial box, but a large extent in (Euclidean) time. In this setting a specific variant of chiral perturbation theory - the {delta}-expansion - applies, based on a quantum mechanical treatment of the quasi onedimensional system. In particular, for vanishing quark masses one obtains a residual pion mass M{sup R}{sub {pi}}, which has been computed to the third order in the {delta}-expansion. A comparison with numerical measurements of this residual mass allows for a new determination of some Low Energy Constants, which appear in the chiral Lagrangian. We first review the attempts to simulate 2-flavour QCD directly in the {delta}-regime. This is very tedious, but results compatible with the predictions for M{sup R}{sub {pi}} have been obtained. Then we show that an extrapolation of pion masses measured in a larger volume towards the {delta}-regime leads to good agreement with the theoretical predictions. From those results, we also extract a value for the (controversial) sub-leading Low Energy Constant anti l{sub 3}. (orig.)
Higher order QCD corrections in exclusive charmless B decays
Energy Technology Data Exchange (ETDEWEB)
Bell, G.
2006-10-15
We discuss exclusive charmless B decays within the Standard Model of particle physics. These decays play a central role in the on-going process to constrain the parameters of the CKM matrix and to clarify the nature of CP violation. In order to exploit the rich source of data that is currently being collected at the experiments, a systematic theoretical treatment of the complicated hadronic dynamics is strongly desired. QCD Factorization represents a model-independent framework to compute hadronic matrix elements from first principles. It is based on a power expansion in {lambda}{sub QCD}/m{sub b} and allows for the systematic implementation of perturbative corrections. In particular, we consider hadronic two-body decays as B {yields} {pi}{pi} and perform a conceptual analysis of heavy-to-light form factors which encode the strong interaction effects in semi-leptonic decays as B {yields} {pi}l{nu}. Concerning the hadronic decays we compute NNLO QCD corrections which are particularly important with respect to strong interaction phases and hence direct CP asymmetries. On the technical level, we perform a 2-loop calculation which is based on an automatized reduction algorithm and apply sophisticated techniques for the calculation of loop-integrals. We indeed find that the considered quantities are well-defined as predicted by QCD Factorization, which is the result of a highly complicated subtraction procedure. We present results for the imaginary part of the topological tree amplitudes and observe that the considered corrections are substantial. The calculation of the real part of the amplitudes is far more complicated and we present a preliminary result which is based on certain simplifications. Our calculation is one part of the full NNLO analysis of nonleptonic B decays within QCD Factorization which is currently pursued by various groups. In our conceptual analysis of the QCD dynamics in heavy-to-light transitions we consider form factors between non
Analysis of the scalar nonet mesons with QCD sum rules
Energy Technology Data Exchange (ETDEWEB)
Wang, Zhi-Gang [North China Electric Power University, Department of Physics, Baoding (China)
2016-08-15
In this article, we assume that the nonet scalar mesons below 1 GeV are the two-quark-tetraquark mixed states and study their masses and pole residues using the QCD sum rules. In the calculation, we take into account the vacuum condensates up to dimension 10 and the O(α{sub s}) corrections to the perturbative terms in the operator product expansion. We determine the mixing angles, which indicate the two-quark components are much larger than 50 %, then we obtain the masses and pole residues of the nonet scalar mesons. (orig.)
Can mass-less QCD dynamically generate heavy quarks?
Cabo-Montes de Oca, Alejandro; Oca, Alejandro Cabo Montes de; Martinez-Pedrera, Danny
2005-01-01
As it was suggested by previous works on a modified perturbation expansion for QCD, the possibility for the generation of large quark condensates in the mass-less version of the theory is explored. For this purpose, it is firstly presented a way of well define the Feynman diagrams at any number of loops by just employing dimensional regularization. After that, the calculated zero and one loop corrections to the effective potential indicate a strong instability of the system under the generation of quark condensates. The also evaluated quark condensate dependence of particular two loop terms does not modify the instability picture arising at one loop. The results suggest a possible mechanism for a sort of Top Condensate Model to be a dynamically fixed effective action for mass-less QCD. The inability of lattice calculations in detecting this possibility could be related with the limitations in treating the fermion determinants.
Hard-Thermal-Loop QCD thermodynamics and quark number susceptibility
Directory of Open Access Journals (Sweden)
Mogliacci Sylvain
2014-04-01
Full Text Available The weak-coupling expansion of the QCD pressure is known up to the order g6 log g. However, at experimentally relevant temperatures, the corresponding series is poorly convergent. In this proceedings, we discuss at which extent the gauge-invariant resummation scheme, Hard-Thermal-Loop perturbation theory (HTLpt, improves the apparent convergence. We first present HTLpt results for QCD thermodynamic functions up to three-loop order at vanishing chemical potential. Then, we report a preliminary HTLpt result of one-loop quark number susceptibility, probing the finite density equation of state. Our results are consistent with lattice data down to 2 − 3Tc, reinforcing the weakly-coupled quasiparticle picture in the intermediate coupling regime.
Towards Quantum Simulating QCD
Wiese, Uwe-Jens
2014-01-01
Quantum link models provide an alternative non-perturbative formulation of Abelian and non-Abelian lattice gauge theories. They are ideally suited for quantum simulation, for example, using ultracold atoms in an optical lattice. This holds the promise to address currently unsolvable problems, such as the real-time and high-density dynamics of strongly interacting matter, first in toy-model gauge theories, and ultimately in QCD.
Towards quantum simulating QCD
Energy Technology Data Exchange (ETDEWEB)
Wiese, Uwe-Jens
2014-11-15
Quantum link models provide an alternative non-perturbative formulation of Abelian and non-Abelian lattice gauge theories. They are ideally suited for quantum simulation, for example, using ultracold atoms in an optical lattice. This holds the promise to address currently unsolvable problems, such as the real-time and high-density dynamics of strongly interacting matter, first in toy-model gauge theories, and ultimately in QCD.
Scalar correlator, Higgs decay into quarks, and scheme variations of the QCD coupling
Energy Technology Data Exchange (ETDEWEB)
Jamin, Matthias [IFAE, BIST,Campus UAB, 08193 Bellaterra (Barcelona) (Spain); ICREA,Pg. Lluís Companys 23, 08010 Barcelona (Spain); Miravitllas, Ramon [IFAE, BIST,Campus UAB, 08193 Bellaterra (Barcelona) (Spain)
2016-10-12
In this work, the perturbative QCD series of the scalar correlation function Ψ(s) is investigated. Besides /rm ImΨ(s), which is relevant for Higgs decay into quarks, two other physical correlators, Ψ{sup ″}(s) and D{sup L}(s), have been employed in QCD applications like quark mass determinations or hadronic τ decays. D{sup L}(s) suffers from large higher-order corrections and, by resorting to the large-β{sub 0} approximation, it is shown that this is related to a spurious renormalon ambiguity at u=1. Hence, this correlator should be avoided in phenomenological analyses. Moreover, it turns out advantageous to express the quark mass factor, introduced to make the scalar current renormalisation group invariant, in terms of the renormalisation invariant quark mass m̂{sub q}. To further study the behaviour of the perturbative expansion, we introduce a QCD coupling α̂{sub s}, whose running is explicitly renormalisation scheme independent. The scheme dependence of α̂{sub s} is parametrised by a single parameter C, being related to transformations of the QCD scale parameter Λ. It is demonstrated that appropriate choices of C lead to a substantial improvement in the behaviour of the perturbative series for Ψ{sup ″}(s) and /rm ImΨ(s).
Short-distance repulsion in three-nucleon forces from perturbative quantum chromodynamics
Aoki, Sinya; Balog, Janos; Weisz, Peter
2012-01-01
We investigate the short-distance behavior of three-nucleon forces (3NF) defined through the Nambu–Bethe–Salpeter (NBS) wave functions using the operator product expansion and calculating anomalous dimensions of nine-quark operators in perturbative quantum chromodynamics (QCD). As in the case of NN forces considered previously, we show that 3NF have repulsions at short distance at one-loop, which becomes exact in the short-distance limit thanks to the asymptotic freedom of QCD. Moreover, thes...
Heavy Quarks, QCD, and Effective Field Theory
Energy Technology Data Exchange (ETDEWEB)
Thomas Mehen
2012-10-09
The research supported by this OJI award is in the area of heavy quark and quarkonium production, especially the application Soft-Collinear E ective Theory (SCET) to the hadronic production of quarkonia. SCET is an e ffective theory which allows one to derive factorization theorems and perform all order resummations for QCD processes. Factorization theorems allow one to separate the various scales entering a QCD process, and in particular, separate perturbative scales from nonperturbative scales. The perturbative physics can then be calculated using QCD perturbation theory. Universal functions with precise fi eld theoretic de nitions describe the nonperturbative physics. In addition, higher order perturbative QCD corrections that are enhanced by large logarithms can be resummed using the renormalization group equations of SCET. The applies SCET to the physics of heavy quarks, heavy quarkonium, and similar particles.
Perturbative quantum chromodynamics
1989-01-01
This book will be of great interest to advanced students and researchers in the area of high energy theoretical physics. Being the most complete and updated review volume on Perturbative QCD, it serves as an extremely useful textbook or reference book. Some of the reviews in this volume are the best that have been written on the subject anywhere. Contents: Factorization of Hard Processes in QCD (J C Collins, D E Soper & G Sterman); Exclusive Processes in Quantum Chromodynamics (S J Brodsky & G P Lepage); Coherence and Physics of QCD Jets (Yu L Dokshitzer, V A Khoze & S I Troyan); Pomeron in Qu
Bilocal expansion of Borel amplitude and hadronic tau decay width
Cvetic, G; Cvetic, Gorazd; Lee, Taekoon
2001-01-01
The singular part of Borel transform of a QCD amplitude near the infrared renormalon can be expanded in terms of higher order Wilson coefficients of the operators associated with the renormalon. In this paper we observe that this expansion gives nontrivial constraints on the Borel amplitude that can be used to improve the accuracy of the ordinary perturbative expansion of the Borel amplitude. In particular, we consider the Borel transform of the Adler function and its expansion around the first infrared renormalon due to the gluon condensate. Using the next-to-leading order Wilson coefficient of the gluon condensate operator, we obtain an exact constraint on the Borel amplitude at the first IR renormalon. We then extrapolate, using judiciously chosen conformal transformations and Pade approximants, the ordinary perturbative expansion of the Borel amplitude in such a way that this constraint is satisfied. This procedure allows us to predict the four-loop Adler function, which gives a result consistent with the...
Higgs boson gluon-fusion production beyond threshold in N$^3$LO QCD
Anastasiou, Charalampos; Dulat, Falko; Furlan, Elisabetta; Gehrmann, Thomas; Herzog, Franz; Mistlberger, Bernhard
2015-01-01
In this article, we compute the gluon fusion Higgs boson cross-section at N3LO through the second term in the threshold expansion. This calculation constitutes a major milestone towards the full N3LO cross section. Our result has the best formal accuracy in the threshold expansion currently available, and includes contributions from collinear regions besides subleading corrections from soft and hard regions, as well as certain logarithmically enhanced contributions for general kinematics. We use our results to perform a critical appraisal of the validity of the threshold approximation at N3LO in perturbative QCD.
Trottier, H D; Lepage, G P; MacKenzie, P B
2002-01-01
Perturbative coefficients for Wilson loops and the static-quark self-energy are extracted from Monte Carlo simulations at weak coupling. The lattice volumes and couplings are chosen to ensure that the lattice momenta are all perturbative. Twisted boundary conditions are used to eliminate the effects of lattice zero modes and to suppress nonperturbative finite-volume effects due to Z(3) phases. Simulations of the Wilson gluon action are done with both periodic and twisted boundary conditions, and over a wide range of lattice volumes (from $3^4$ to $16^4$) and couplings (from $\\beta \\approx 9$ to $\\beta \\approx 60$). A high precision comparison is made between the simulation data and results from finite-volume lattice perturbation theory. The Monte Carlo results are shown to be in excellent agreement with perturbation theory through second order. New results for third-order coefficients for a number of Wilson loops and the static-quark self-energy are reported.
Holographic QCD: Past, Present, and Future
Kim, Youngman; Tsukioka, Takuya
2012-01-01
At the dawn of a new theoretical tool based on AdS/CFT for non-perturbative aspects of quantum chromodynamics, we give an interim review on the the new tool, holographic QCD, with some of its accomplishment. We try to give an A-to-Z picture of the holographic QCD, from string theory to a few selected top-down holographic QCD models with one or two physical applications in each model. We may not attempt to collect diverse results from various holographic QCD model studies.
Nizic, Bene
1985-12-01
This thesis consists of two unrelated topics in perturbative quantum field theory: eighth order QED contribution to the anomalous magnetic moment of the muon and next to leading order perturbative QCD correction to (gamma)(gamma) ( --->) M('+)M('-)(M = (pi),K). In Part I we present the evaluation of the complete eighth order QED contribution to the difference of the anomalous magnetic moments of the muon and the electron, (a(,(mu)) - a(,e))('(8)), arising from 469 Feynman diagrams. Our result is 140.7(4.5)((alpha)/(pi))('4). The theoretical error represents the estimated accuracy of the required numerical integration. We have also improved the light -by-light QED contribution to (a(,(mu)) - a(,e))('(6)). With these results the difference a(,(mu)) - a(,e) through eighth order in QED is (a(,(mu)) - a(,e))('QED) = 619 551(21) x 10('-11). Adding to the present theoretical value of the electron anomaly a(,e)('QED) = 115 965 246(5) x 10(' -11), we find that the pure QED contribution to the muon anomaly is given by a(,(mu))('QED) = 116 584 797(22) x 10('-11). In Part II we present the results of our calculation of the next to leading order perturbative QCD correction to the two-photon exclusive channels (gamma)(gamma)(-- ->)M('+)M('-)(M = (pi),K) at large momentum transfer. Calculation is performed in the Feynman gauge. Dimensional regularization is used to treat both UV and (//R) divergences. The meson distribution amplitude is taken to be (PHI)(,M)(PROPORTIONAL)('(delta))(x - 1/2). In order to reduce the dependence on the particular choice of (PHI)(,M), similarity of (gamma)(gamma)(--->)M('+)M(' -) and meson electromagnetic form-factor is employed. One loop correction to the (gamma)(gamma)(--->)M('+)M('-) cross section is obtained. In the MS renormalization scheme this correction is found not to be large.
Shuryak, E V
1996-01-01
In the recent years we have learned that light quarks play a crucial role in QCD-like theories, transforming it to many different phases. We review what is known about them, both from lattice and non-lattice approaches. A particularly simple mechanism of the QCD chiral restoration phase transition is discussed first: it suggests that it is a transition from randomly placed tunneling events (instantons) at low T to strongly localized tunneling-anti-tunneling pairs at high T. Many features of the transition found on the lattice can be explained in this simple picture. Very relevant for RHIC, this approach predicts a strong non-perturbative interaction between quarks $above$ the phase transition. It also predicts that QGP-like phase sets in at $zero$ temperature, provided few more light quark flavors are added to QCD. Finally, we also discuss possible experimental signatures of the QCD phase transition. One issue is CERN dilepton data, possibly related with ``dropping'' masses of $\\rho, A_1$ mesons. Another is d...
Setting the Renormalization Scale in QCD: The Principle of Maximum Conformality
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins; Di Giustino, Leonardo; /SLAC
2011-08-19
A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale {mu} of the running coupling {alpha}{sub s}({mu}{sup 2}): The purpose of the running coupling in any gauge theory is to sum all terms involving the {beta} function; in fact, when the renormalization scale is set properly, all non-conformal {beta} {ne} 0 terms in a perturbative expansion arising from renormalization are summed into the running coupling. The remaining terms in the perturbative series are then identical to that of a conformal theory; i.e., the corresponding theory with {beta} = 0. The resulting scale-fixed predictions using the 'principle of maximum conformality' (PMC) are independent of the choice of renormalization scheme - a key requirement of renormalization group invariance. The results avoid renormalon resummation and agree with QED scale-setting in the Abelian limit. The PMC is also the theoretical principle underlying the BLM procedure, commensurate scale relations between observables, and the scale-setting method used in lattice gauge theory. The number of active flavors nf in the QCD {beta} function is also correctly determined. We discuss several methods for determining the PMC/BLM scale for QCD processes. We show that a single global PMC scale, valid at leading order, can be derived from basic properties of the perturbative QCD cross section. The elimination of the renormalization scheme ambiguity using the PMC will not only increase the precision of QCD tests, but it will also increase the sensitivity of collider experiments to new physics beyond the Standard Model.
Polyakov loop modeling for hot QCD
Fukushima, Kenji; Skokov, Vladimir
2017-09-01
We review theoretical aspects of quantum chromodynamics (QCD) at finite temperature. The most important physical variable to characterize hot QCD is the Polyakov loop, which is an approximate order parameter for quark deconfinement in a hot gluonic medium. Additionally to its role as an order parameter, the Polyakov loop has rich physical contents in both perturbative and non-perturbative sectors. This review covers a wide range of subjects associated with the Polyakov loop from topological defects in hot QCD to model building with coupling to the Polyakov loop.
Higgs boson gluon-fusion production in QCD at three loops.
Anastasiou, Charalampos; Duhr, Claude; Dulat, Falko; Herzog, Franz; Mistlberger, Bernhard
2015-05-29
We present the cross section for the production of a Higgs boson at hadron colliders at next-to-next-to-next-to-leading order (N^{3}LO) in perturbative QCD. The calculation is based on a method to perform a series expansion of the partonic cross section around the threshold limit to an arbitrary order. We perform this expansion to sufficiently high order to obtain the value of the hadronic cross at N^{3}LO in the large top-mass limit. For renormalization and factorization scales equal to half the Higgs boson mass, the N^{3}LO corrections are of the order of +2.2%. The total scale variation at N^{3}LO is 3%, reducing the uncertainty due to missing higher order QCD corrections by a factor of 3.
Hadron Physics from Lattice QCD
2016-01-01
We sketch the basic ideas of the lattice regularization in Quantum Field Theory, the corresponding Monte Carlo simulations, and applications to Quantum Chromodynamics (QCD). This approach enables the numerical measurement of observables at the non-perturbative level. We comment on selected results, with a focus on hadron masses and the link to Chiral Perturbation Theory. At last we address two outstanding issues: topological freezing and the sign problem.
Energy Technology Data Exchange (ETDEWEB)
Pelaez, J. R. [Univ. Complutense Madrid (Spain); Pennington, Michael R. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); de Elvira, J. Ruiz [Univ. Complutense Madrid (Spain); Wilson, D. J. [Argonne National Lab. (ANL), Argonne, IL (United States)
2011-11-01
The leading 1/N{sub c} behavior of Unitarized Chiral Perturbation Theory distinguishes the nature of the {rho} and the {sigma}. At one loop order the {rho} is a {bar q}q meson, while the {sigma} is not. However, semi-local duality between resonances and Regge behaviour cannot be satisfied for larger N{sub c}, if such a distinction holds. While the {sigma} at N{sub c}= 3 is inevitably dominated by its di-pion component, Unitarised Chiral Perturbation Theory beyond one loop order reveals that as N{sub c} increases above 6-8, the {sigma} has a sub-dominant {bar q}q fraction up at 1.2 GeV. Remarkably this ensures semi-local duality is fulfilled for the range of N{sub c} {approx}< 15-30, where the unitarization procedure adopted applies.
Energy Technology Data Exchange (ETDEWEB)
Pietrafesa, L.J.; Struble, R.A.; Klinck, J.M.
1974-01-01
Consideration of geophysical vertical plane flows in estuaries and on continental shelves results in nonlinearly coupled partial differential equations for flow and density variables. For the case of steady flow, the equations are reduced to ordinary differential equations by the use of similarity transformations. The remaining nonlinearly coupled ordinary differential equations are solved using a revised Euler-Shohat perturbation technique. An existence theorem for this application of the technique is stated and proved.
QCD Phase Transitions, Volume 15
Energy Technology Data Exchange (ETDEWEB)
Schaefer, T.; Shuryak, E.
1999-03-20
The title of the workshop, ''The QCD Phase Transitions'', in fact happened to be too narrow for its real contents. It would be more accurate to say that it was devoted to different phases of QCD and QCD-related gauge theories, with strong emphasis on discussion of the underlying non-perturbative mechanisms which manifest themselves as all those phases. Before we go to specifics, let us emphasize one important aspect of the present status of non-perturbative Quantum Field Theory in general. It remains true that its studies do not get attention proportional to the intellectual challenge they deserve, and that the theorists working on it remain very fragmented. The efforts to create Theory of Everything including Quantum Gravity have attracted the lion share of attention and young talent. Nevertheless, in the last few years there was also a tremendous progress and even some shift of attention toward emphasis on the unity of non-perturbative phenomena. For example, we have seen some efforts to connect the lessons from recent progress in Supersymmetric theories with that in QCD, as derived from phenomenology and lattice. Another example is Maldacena conjecture and related development, which connect three things together, string theory, super-gravity and the (N=4) supersymmetric gauge theory. Although the progress mentioned is remarkable by itself, if we would listen to each other more we may have chance to strengthen the field and reach better understanding of the spectacular non-perturbative physics.
Lattice QCD spectroscopy for hadronic CP violation
de Vries, Jordy; Mereghetti, Emanuele; Seng, Chien-Yeah; Walker-Loud, André
2017-03-01
The interpretation of nuclear electric dipole moment (EDM) experiments is clouded by large theoretical uncertainties associated with nonperturbative matrix elements. In various beyond-the-Standard Model scenarios nuclear and diamagnetic atomic EDMs are expected to be dominated by CP-violating pion-nucleon interactions that arise from quark chromo-electric dipole moments. The corresponding CP-violating pion-nucleon coupling strengths are, however, poorly known. In this work we propose a strategy to calculate these couplings by using spectroscopic lattice QCD techniques. Instead of directly calculating the pion-nucleon coupling constants, a challenging task, we use chiral symmetry relations that link the pion-nucleon couplings to nucleon sigma terms and mass splittings that are significantly easier to calculate. In this work, we show that these relations are reliable up to next-to-next-to-leading order in the chiral expansion in both SU (2) and SU (3) chiral perturbation theory. We conclude with a brief discussion about practical details regarding the required lattice QCD calculations and the phenomenological impact of an improved understanding of CP-violating matrix elements.
QCD at nonzero chemical potential: recent progress on the lattice
Aarts, Gert; Jäger, Benjamin; Seiler, Erhard; Sexty, Denes; Stamatescu, Ion-Olimpiu
2014-01-01
We summarise recent progress in simulating QCD at nonzero baryon density using complex Langevin dynamics. After a brief outline of the main idea, we discuss gauge cooling as a means to control the evolution. Subsequently we present a status report for heavy dense QCD and its phase structure, full QCD with staggered quarks, and full QCD with Wilson quarks, both directly and using the hopping parameter expansion to all orders.
QCD at nonzero chemical potential: Recent progress on the lattice
Energy Technology Data Exchange (ETDEWEB)
Aarts, Gert; Jäger, Benjamin [Department of Physics, College of Science, Swansea University, Swansea SA2 8PP (United Kingdom); Attanasio, Felipe [Department of Physics, College of Science, Swansea University, Swansea SA2 8PP (United Kingdom); CAPES Foundation, Ministry of Education of Brazil, Brasília - DF 70040-020 (Brazil); Seiler, Erhard [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), 80805 München (Germany); Sexty, Dénes [Department of Physics, University of Wuppertal, 42119 Wuppertal (Germany); Stamatescu, Ion-Olimpiu [Institut für Theoretische Physik, Universität Heidelberg, 69120 Heidelberg (Germany)
2016-01-22
We summarise recent progress in simulating QCD at nonzero baryon density using complex Langevin dynamics. After a brief outline of the main idea, we discuss gauge cooling as a means to control the evolution. Subsequently we present a status report for heavy dense QCD and its phase structure, full QCD with staggered quarks, and full QCD with Wilson quarks, both directly and using the hopping parameter expansion to all orders.
Determining the QCD coupling from lattice vacuum polarization
Hudspith, Renwick J; Maltman, Kim; Shintani, Eigo
2015-01-01
The QCD coupling appears in the perturbative expansion of the current-current two-point (vacuum polarization) function. Any lattice calculation of vacuum polarization is plagued by several competing non-perturbative effects at small momenta and by discretization errors at large momenta. We work in an intermediate region, computing the vacuum polarization for many off-axis momentum directions on the lattice. Having many momentum directions provides a way to monitor and account for lattice artifacts. Our results are competitive with, and have certain systematic advantages over, the alternate phenomenological determination of the strong coupling from the same light quark vacuum polarization produced by sum rule analyses of hadronic tau decay data.
Contreras, Carlos; Meneses, Rodrigo; Potashnikova, Irina
2016-01-01
This paper is the first attempt to build CGC/saturation model based on the next-to-leading order corrections to linear and non-linear evolution in QCD. We assume that the renormalization scale is the saturation momentum and found that the scattering amplitude has geometric scaling behaviour deep in the saturation domain with the explicit formula of this behaviour at large $\\tau = r^2 Q^2_s$. We built a model that include this behaviour, as well as the ingredients that has been known: (i) the behaviour of the scattering amplitude in the vicinity of the saturation momentum, using the NLO BFKL kernel, (ii) the pre-asymptotic behaviour of $\\ln\\Lb Q^2_s\\Lb Y \\Rb\\Rb$, as function of $Y$ and (iii) the impact parameter behaviour of the saturation momentum, which has exponential behaviour $\\propto \\exp\\Lb -\\, m\\, b\\Rb$ at large $b$.We demonstrated that the model is able to describe the experimental data for the deep inelastic structure function. Despite this, our model has difficulties that are related to the small va...
QCD as a theory of hadrons from partons to confinement, [preface, outline and TOC
Narison, Stéphan
2004-01-01
Introduction to QCD and reviews its modern developments. Perturbative (from partons) and nonperturbative (to confinement) aspects of QCD are discussed. Preface, outline and contents of the book are presented here.
Analytic structure of QCD propagators in Minkowski space
Siringo, Fabio
2016-01-01
Analytical functions for the propagators of QCD, including a set of chiral quarks, are derived by a one-loop massive expansion in the Landau gauge, deep in the infrared. By analytic continuation, the spectral functions are studied in Minkowski space, yielding a direct proof of positivity violation and confinement from first principles.The dynamical breaking of chiral symmetry is described on the same footing of gluon mass generation, providing a unified picture. While dealing with the exact Lagrangian, the expansion is based on massive free-particle propagators, is safe in the infrared and is equivalent to the standard perturbation theory in the UV. By dimensional regularization, all diverging mass terms cancel exactly without including mass counterterms that would spoil the gauge and chiral symmetry of the Lagrangian. Universal scaling properties are predicted for the inverse dressing functions and shown to be satisfied by the lattice data. Complex conjugated poles are found for the gluon propagator, in agre...
Neutron star structure from QCD
Fraga, Eduardo S.; Kurkela, Aleksi; Vuorinen, Aleksi
2016-03-01
In this review article, we argue that our current understanding of the thermodynamic properties of cold QCD matter, originating from first principles calculations at high and low densities, can be used to efficiently constrain the macroscopic properties of neutron stars. In particular, we demonstrate that combining state-of-the-art results from Chiral Effective Theory and perturbative QCD with the current bounds on neutron star masses, the Equation of State of neutron star matter can be obtained to an accuracy better than 30% at all densities.
Neutron star structure from QCD
Fraga, Eduardo S; Vuorinen, Aleksi
2016-01-01
In this review article, we argue that our current understanding of the thermodynamic properties of cold QCD matter, originating from first principles calculations at high and low densities, can be used to efficiently constrain the macroscopic properties of neutron stars. In particular, we demonstrate that combining state-of-the-art results from Chiral Effective Theory and perturbative QCD with the current bounds on neutron star masses, the Equation of State of neutron star matter can be obtained to an accuracy better than 30% at all densities.
Hadron scattering, resonances, and QCD
Energy Technology Data Exchange (ETDEWEB)
Briceno, Raul [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
2016-12-01
The non-perturbative nature of quantum chromodynamics (QCD) has historically left a gap in our understanding of the connection between the fundamental theory of the strong interactions and the rich structure of experimentally observed phenomena. For the simplest properties of stable hadrons, this is now circumvented with the use of lattice QCD (LQCD). In this talk I discuss a path towards a rigorous determination of few-hadron observables from LQCD. I illustrate the power of the methodology by presenting recently determined scattering amplitudes in the light-meson sector and their resonance content.
Neutron star structure from QCD
Energy Technology Data Exchange (ETDEWEB)
Fraga, Eduardo S. [Universidade Federal do Rio de Janeiro, Instituto de Fisica, Rio de Janeiro, RJ (Brazil); Kurkela, Aleksi [PH-TH, Case C01600, CERN, Theory Division, Geneva (Switzerland); University of Stavanger, Faculty of Science Technology, Stavanger (Norway); Vuorinen, Aleksi [University of Helsinki, Helsinki Institute of Physics and Department of Physics (Finland)
2016-03-15
In this review article, we argue that our current understanding of the thermodynamic properties of cold QCD matter, originating from first principles calculations at high and low densities, can be used to efficiently constrain the macroscopic properties of neutron stars. In particular, we demonstrate that combining state-of-the-art results from Chiral Effective Theory and perturbative QCD with the current bounds on neutron star masses, the Equation of State of neutron star matter can be obtained to an accuracy better than 30% at all densities. (orig.)
Ma, Ai-Jun; Wang, Wen-Fei; Xiao, Zhen-Jun
2016-01-01
In this paper, we study the $B_{(s)} \\to (D_{(s)},\\bar{D}_{(s)}) \\rho \\to (D_{(s)}, \\bar{D}_{(s)})\\pi \\pi$ decays by employing a framework for the quasi-two-body decays in the perturbative QCD(PQCD) factorization approach. We use the two-pion distribution amplitudes $\\Phi_{\\pi\\pi}$, which contains both resonant and nonresonant contributions from the pion pair to explain the final-state interactions between the pions in the resonant regions. We found that (a) for the four $B\\to (\\bar{D}^0,D^-) \\rho \\to (\\bar{D}^0,D^-) \\pi\\pi$ and $B_s \\to D_s^- \\rho^+ \\to D_s^- \\pi^+\\pi^0$ decays, the PQCD predictions for their branching ratios can be as large as $10^{-4}-10^{-2}$; (b) for other ten considered decays, the PQCD predictions for their decay rates are around $10^{-8}$ to $10^{-5}$ mainly due to strong CKM suppressions; and (c) the PQCD predictions based on the quasi-two-body and the two-body framework agree well with each other, and also be consistent with currently available experimental measurements.
Brumby, Paul E.; Haslam, Andrew J.; de Miguel, Enrique; Jackson, George
2011-01-01
An efficient and versatile method to calculate the components of the pressure tensor for hard-body fluids of generic shape from the perspective of molecular simulation is presented. After due consideration of all the possible repulsive contributions exerted by molecules upon their surroundings during an anisotropic system expansion, it is observed that such a volume change can, for non-spherical molecules, give rise to configurations where overlaps occur. This feature of anisotropic molecules has to be taken into account rigorously as it can lead to discrepancies in the calculation of tensorial contributions to the pressure. Using the condition of detailed balance as a basis, a perturbation method developed for spherical molecules has been extended so that it is applicable to non-spherical and non-convex molecules. From a series of 'ghost' anisotropic volume perturbations the residual contribution to the components of the pressure tensor may be accurately calculated. Comparisons are made with prior methods and, where relevant, results are evaluated against existing data. For inhomogeneous systems this method provides a particularly convenient route to the calculation of the interfacial tension (surface free energy) from molecular simulations.
Two-body non-leptonic heavy-to-heavy decays at NNLO in QCD factorization
Huber, Tobias; Li, Xin-Qiang
2016-01-01
We evaluate in the framework of QCD factorization the two-loop vertex corrections to the decays $\\bar{B}_{(s)}\\to D_{(s)}^{(\\ast)+} \\, L^-$ and $\\Lambda_b \\to \\Lambda_c^+ \\, L^-$, where $L$ is a light meson from the set $\\{\\pi,\\rho,K^{(\\ast)},a_1\\}$. These decays are paradigms of the QCD factorization approach since only the colour-allowed tree amplitude contributes at leading power. Hence they are sensitive to the size of power corrections once their leading-power perturbative expansion is under control. Here we compute the two-loop ${\\cal O}(\\alpha_s^2)$ correction to the leading-power hard scattering kernels, and give the results for the convoluted kernels almost completely analytically. Our newly computed contribution amounts to a positive shift of the magnitude of the tree amplitude by $\\sim 2$\\%. We then perform an extensive phenomenological analysis to NNLO in QCD factorization, using the most recent values for non-perturbative input parameters. Given the fact that the NNLO perturbative correction and ...
Deur, A; de Teramond, G F
2016-01-01
We review the present knowledge for $\\alpha_s$, the fundamental coupling underlying the interactions of quarks and gluons in QCD. The dependence of $\\alpha_s(Q^2)$ on momentum transfer $Q$ encodes the underlying dynamics of hadron physics -from color confinement in the infrared domain to asymptotic freedom at short distances. We review constraints on $\\alpha_s(Q^2)$ at high $Q^2$, as predicted by perturbative QCD, and its analytic behavior at small $Q^2$, based on models of nonperturbative dynamics. In the introductory part of this review, we explain the phenomenological meaning of $\\alpha_s$, the reason for its running, and the challenges facing a complete understanding of its analytic behavior in the infrared domain. In the second, more technical, part of the review, we discuss the behavior of $\\alpha_s(Q^2)$ in the high $Q^2$ domain of QCD. We review how $\\alpha_s$ is defined, including its renormalization scheme dependence, the definition of its renormalization scale, the utility of effective charges, as ...
Perturbative $O(\\alpha_s)$ corrections to the correlation functions of light tetraquark currents
Groote, S; Niinepuu, D
2014-01-01
We calculate the next-to-leading order QCD corrections to the perturbative term in the operator product expansion of the spectral functions of light tetraquark currents. By using also configuration space methods we keep the momentum space four-loop calculation to a manageable level. We find that the next-to-leading order corrections to the perturbative term are large and can amount to $O(100\\%)$. The corrections to the corresponding Borel sum rules, however, are small since the nonperturbative condensate contributions dominate the Borel sum rules.
Ducati, M B G
2001-01-01
The dynamics of high partonic density QCD is presented considering, in the double logarithm approximation, the parton recombination mechanism built in the AGL formalism, developed including unitarity corrections for the nucleon as well for nucleus. It is shown that these corrections are under theoretical control. The resulting non linear evolution equation is solved in the asymptotic regime, and a comprehensive phenomenology concerning Deep Inelastic Scattering like $F_2$, $F_L$, $F_2^c$. $\\partial F_2/ \\partial \\ln Q^2$, $\\partial F^A_2/ \\partial \\ln Q^2$, etc, is presented. The connection of our formalism with the DGLAP and BFKL dynamics, and with other perturbative (K) and non-perturbative (MV-JKLW) approaches is analised in detail. The phenomena of saturation due to shadowing corrections and the relevance of this effect in ion physics and heavy quark production is emphasized. The implications to e-RHIC, HERA-A, and LHC physics and some open questions are mentioned.
Brodsky, S J
2004-01-01
In these lectures, I survey a number of applications of light-front methods to hadron and nuclear physics phenomenology and dynamics, Light-front Fock-state wavefunctions provide a frame-independent representation of hadrons in terms of their fundamental quark and gluon degrees of freedom. Nonperturbative methods for computing LFWFs in QCD are discussed, including string/gauge duality which predicts the power-law fall-off at high momentum transfer of light-front Fock-state hadronic wavefunctions with an arbitrary number of constituents and orbital angular momentum. The AdS/CFT correspondence has important implications for hadron phenomenology in the conformal limit, including an all-orders derivation of counting rules for exclusive processes. One can also compute the hadronic spectrum of near-conformal QCD assuming a truncated AdS/CFT space. The quantum fluctuations represented by the light-front Fock expansion leads to novel QCD phenomena such as color transparency, intrinsic heavy quark distributions, diffr...
The $\\hbar$ Expansion in Quantum Field Theory
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins; Hoyer, Paul; /Southern Denmark U., CP3-Origins /Helsinki U. /Helsinki Inst. of Phys.
2010-10-27
We show how expansions in powers of Planck's constant {h_bar} = h = 2{pi} can give new insights into perturbative and nonperturbative properties of quantum field theories. Since {h_bar} is a fundamental parameter, exact Lorentz invariance and gauge invariance are maintained at each order of the expansion. The physics of the {h_bar} expansion depends on the scheme; i.e., different expansions are obtained depending on which quantities (momenta, couplings and masses) are assumed to be independent of {h_bar}. We show that if the coupling and mass parameters appearing in the Lagrangian density are taken to be independent of {h_bar}, then each loop in perturbation theory brings a factor of {h_bar}. In the case of quantum electrodynamics, this scheme implies that the classical charge e, as well as the fine structure constant are linear in {h_bar}. The connection between the number of loops and factors of {h_bar} is more subtle for bound states since the binding energies and bound-state momenta themselves scale with {h_bar}. The {h_bar} expansion allows one to identify equal-time relativistic bound states in QED and QCD which are of lowest order in {h_bar} and transform dynamically under Lorentz boosts. The possibility to use retarded propagators at the Born level gives valence-like wave-functions which implicitly describe the sea constituents of the bound states normally present in its Fock state representation.
Effective Field Theories and Lattice QCD
Bernard, C
2015-01-01
I describe some of the many connections between lattice QCD and effective field theories, focusing in particular on chiral effective theory, and, to a lesser extent, Symanzik effective theory. I first discuss the ways in which effective theories have enabled and supported lattice QCD calculations. Particular attention is paid to the inclusion of discretization errors, for a variety of lattice QCD actions, into chiral effective theory. Several other examples of the usefulness of chiral perturbation theory, including the encoding of partial quenching and of twisted boundary conditions, are also described. In the second part of the talk, I turn to results from lattice QCD for the low energy constants of the two- and three-flavor chiral theories. I concentrate here on mesonic quantities, but the dependence of the nucleon mass on the pion mass is also discussed. Finally I describe some recent preliminary lattice QCD calculations by the MILC Collaboration relating to the three-flavor chiral limit.
Energy Technology Data Exchange (ETDEWEB)
Constantinou, M. [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Dimopoulos, P. [Roma ' ' La Sapienza' ' Univ. (Italy). Dipt. di Fisica; INFN, Rome (Italy); Frezzotti, R. [Roma ' ' Tor Vergata' ' Univ. (Italy). Dipt. di Fisica; INFN, Roma (IT)] (and others)
2010-06-15
We present results for the renormalization constants of bilinear quark operators obtained b4>UNL<426>UNL using the tree-level Symanzik improved gauge action and the N{sub f}=2 twisted mass fermion action at maximal twist, which guarantees automatic O(a)- improvement. Our results are also relevant for the corresponding standard (untwisted) Wilson fermionic action since the two actions only differ, in the massless limit, by a chiral rotation of the quark fields. The scale-independent renormalization constants Z{sub V}, Z{sub A} and the ratio Z{sub P}/Z{sub S} have been computed using the RI-MOM approach, as well as other alternative methods. For Z{sub A} and Z{sub P}/Z{sub S}, the latter are based on both standard twisted mass and Osterwalder-Seiler fermions, while for Z{sub V} a Ward Identity has been used. The quark field renormalization constant Z{sub q} and the scale dependent renormalization constants Z{sub S}, Z{sub P} and Z{sub T} are determined in the RI-MOM scheme. Leading discretization effects of O(g{sup 2}a{sup 2}), evaluated in one-loop perturbation theory, are explicitly subtracted from the RI-MOM estimates. (orig.)
Abelof, Gabriel; Liu, Xiaohui; Petriello, Frank
2016-01-01
We compute the ${\\cal O}(\\alpha^2\\alpha_s^2)$ perturbative corrections to inclusive jet production in electron-nucleon collisions. This process is of particular interest to the physics program of a future Electron Ion Collider (EIC). We include all relevant partonic processes, including deep-inelastic scattering contributions, photon-initiated corrections, and parton-parton scattering terms that first appear at this order. Upon integration over the final-state hadronic phase space we validate our results for the deep-inelastic corrections against the known next-to-next-to-leading order (NNLO) structure functions. Our calculation uses the $N$-jettiness subtraction scheme for performing higher-order computations, and allows for a completely differential description of the deep-inelastic scattering process. We describe the application of this method to inclusive jet production in detail, and present phenomenological results for the proposed EIC. The NNLO corrections have a non-trivial dependence on the jet kinem...
Yacoob, Sahal; The ATLAS collaboration
2016-01-01
The talk will summarise measurements of the total inelastic proton-proton cross-section and charged particle distributions by ATLAS and CMS at 13 TeV. These measurements provide necessary inputs to non-perturbative models of soft QCD, and the transition region between non-perturbative and perturbative calculations. The results are compared to popular Monte-Carlo generators in collider, and cosmic shower physics.
Sommer, Rainer
1997-01-01
We review the O(a) improvement of lattice QCD with special emphasis on the motivation for performing the improvement programme non-perturbatively and the general concepts of on-shell improvement. The present status of the calculations of various improvement coefficients (perturbative and non-perturbative) is reviewed, as well as the computation of the isospin current normalization constants $Z_A$ and $Z_V$. We comment on recent results for hadronic observables obtained in the improved theory.
QCD resummation in the framework of supersymmetry
Fuks, Benjamin; Lamprea, David R; Rothering, Marcel
2013-01-01
Motivated by current searches for electroweak superpartners at the Large Hadron Collider, we present precision predictions for pair production of such particles in the framework of the Minimal Supersymmetric Standard Model. We make use of various QCD resummation formalisms and match the results to pure perturbative QCD computations. We study the impact of scale variations and compare our results to predictions obtained by means of traditionally used Monte Carlo event generators.
Lattice QCD and the Jefferson Laboratory Program
Energy Technology Data Exchange (ETDEWEB)
Jozef Dudek, Robert Edwards, David Richards, Konstantinos Orginos
2011-06-01
Lattice gauge theory provides our only means of performing \\textit{ab initio} calculations in the non-perturbative regime. It has thus become an increasing important component of the Jefferson Laboratory physics program. In this paper, we describe the contributions of lattice QCD to our understanding of hadronic and nuclear physics, focusing on the structure of hadrons, the calculation of the spectrum and properties of resonances, and finally on deriving an understanding of the QCD origin of nuclear forces.
Parametric form of QCD travelling waves
Peschanski, R.
2005-01-01
We derive parametric travelling-wave solutions of non-linear QCD equations. They describe the evolution towards saturation in the geometric scaling region. The method, based on an expansion in the inverse of the wave velocity, leads to a solvable hierarchy of differential equations. A universal parametric form of travelling waves emerges from the first two orders of the expansion.
Parametric form of QCD travelling waves
Peschanski, R.
2005-01-01
We derive parametric travelling-wave solutions of non-linear QCD equations. They describe the evolution towards saturation in the geometric scaling region. The method, based on an expansion in the inverse of the wave velocity, leads to a solvable hierarchy of differential equations. A universal parametric form of travelling waves emerges from the first two orders of the expansion.
Energy Technology Data Exchange (ETDEWEB)
Nizic, B.
1985-01-01
In Part I the evaluation of the complete eighth order QED contribution to the difference of the anomalous magnetic moments of the muon and the electron, (a/sub ..mu../ - a/sub e/, arising from 469 Feynman diagrams is presented. The result is 140.7(4.5)(..cap alpha../..pi..). The theoretical error represents the estimated accuracy of the required numerical integration. The light-by-light QED contribution to (a/sub ..mu../ - a/sub e/) has also been improved. With these results the difference a/sub ..mu../ - a/sub e/ through eighth order in QED is (a/sub ..mu../ - a/sub e/)/sup QED/ = 619,551(21) x 10/sup -11/. Adding to the present theoretical value of the electron anomaly a/sub e//sup QED/ = 115,965,246(5) x 10/sup -11/, it was found that the pure QED contribution to the muon anomaly is given by a/sub ..mu..//sup QED/ = 116,584,797(22) x 10/sup -11/. In Part II the results of the calculation of the next to leading order perturbative QCD correction to the two-photon exclusive channels ..gamma gamma -->..M/sup +/M/sup -/(M = ..pi..,K) at large momentum transfer is presented. Calculation is performed in the Feynman gauge. Dimensional regularization is used to treat both UV and the set of reals divergences. One loop correction to the ..gamma gamma -->..M/sup +/M/sup -/ cross section is obtained. In the mean MS renormalization scheme this correction is found not to be large.
Hadronic Interactions In Large N_c Qcd: Studies Of Excited Baryon Decays And Scattering Relations
Dakin, D C
2005-01-01
Decays and scattering events are two of the principal ways to learn about particle physics. Decays, in which a particle spontaneously disintegrates and we examine the debris, are quantified by a decay width. The decay of a resonance state provides information about the structure of the state and the interaction between its components. In particular, we can learn about the dynamics of quarks and gluons by studying the decay of hadrons. Scattering, in which particles are directed towards each other and interact, are quantified by partial-wave amplitudes. These amplitudes give us information about the interaction between the scattered particles. In principle, all of hadronic physics follows from quantum chromodynamics (QCD), which describes the interactions of quarks and gluons. However, the techniques of perturbation theory are not applicable to QCD at low energy because the strong coupling constant (the natural choice for the expansion parameter) is large at the energy scale of hadronic physics. A powerful mod...
The Nc dependencies of baryon masses: Analysis with Lattice QCD and Effective Theory
Energy Technology Data Exchange (ETDEWEB)
Calle Cordon, Alvaro C. [JLAB; DeGrand, Thomas A. [University of Colorado; Goity, Jose L. [JLAB
2014-07-01
Baryon masses at varying values of Nc and light quark masses are studied with Lattice QCD and the results are analyzed in a low energy effective theory based on a combined framework of the 1/Nc and Heavy Baryon Chiral Perturbation Theory expansions. Lattice QCD results for Nc=3, 5 and 7 obtained in quenched calculations, as well as results for unquenched calculations for Nc=3, are used for the analysis. The results are consistent with a previous analysis of Nc=3 LQCD results, and in addition permit the determination of sub-leading in 1/Nc effects in the spin-flavor singlet component of the baryon masses as well as in the hyperfine splittings.
QCD factorization for hadronic B decays: Proofs and higher-order corrections
Pecjak, Benjamin Dale
Several issues related to the QCD factorization approach to exclusive hadronic B decays are discussed. This includes a proof of factorization in B → K*gamma using the soft-collinear effective theory, and an examination of higher-order corrections to QCD factorization for two-body decays into heavy-light states, such as B → Dpi, and light-light final states, such as B → Kpi,pipi. The proof of factorization in B → K*gamma is arguably the most complicated QCD factorization formula proven so far. It is shown that reparameterization invariance in the intermediate effective theory restricts the appearance of transverse momentum components and 3-particle Fock states to operators that can be absorbed into the QCD from factor. This proof also includes an extension of SCET to deal with two collinear directions. The examination of higher-order corrections to QCD factorization has implications for using this technique to extract CP violating weal; phases from data taken at the B factories. The renormalon calculus is used to calculate the b0a2s contributions to the hard scattering kernels, and also to analyze the strength of power corrections due to soft gluon exchange. It is shown that while power corrections are generally small, the higher-order perturbative contributions to the hard scattering kernels have much larger imaginary parts than those at next-to-leading order (NLO). This significantly enhances some CP asymmetries compared to the NLO results, which is an effect that would survive a two-loop calculation unless there were large multi-loop corrections not related to the b0a2s terms of the perturbative expansion.
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins
2011-08-12
I review a number of topics where conventional wisdom in hadron physics has been challenged. For example, hadrons can be produced at large transverse momentum directly within a hard higher-twist QCD subprocess, rather than from jet fragmentation. Such 'direct' processes can explain the deviations from perturbative QCD predictions in measurements of inclusive hadron cross sections at fixed x{sub T} = 2p{sub T}/{radical}s, as well as the 'baryon anomaly', the anomalously large proton-to-pion ratio seen in high centrality heavy ion collisions. Initial-state and final-state interactions of the struck quark, the soft-gluon rescattering associated with its Wilson line, lead to Bjorken-scaling single-spin asymmetries, diffractive deep inelastic scattering, the breakdown of the Lam-Tung relation in Drell-Yan reactions, as well as nuclear shadowing and antishadowing. The Gribov-Glauber theory predicts that antishadowing of nuclear structure functions is not universal, but instead depends on the flavor quantum numbers of each quark and antiquark, thus explaining the anomalous nuclear dependence measured in deep-inelastic neutrino scattering. Since shadowing and antishadowing arise from the physics of leading-twist diffractive deep inelastic scattering, one cannot attribute such phenomena to the structure of the nucleus itself. It is thus important to distinguish 'static' structure functions, the probability distributions computed from the square of the target light-front wavefunctions, versus 'dynamical' structure functions which include the effects of the final-state rescattering of the struck quark. The importance of the J = 0 photon-quark QCD contact interaction in deeply virtual Compton scattering is also emphasized. The scheme-independent BLM method for setting the renormalization scale is discussed. Eliminating the renormalization scale ambiguity greatly improves the precision of QCD predictions and increases the sensitivity of
The running coupling of QCD with four flavors
Energy Technology Data Exchange (ETDEWEB)
Tekin, Fatih; Wolff, Ulli [Berlin Univ. (Germany). Inst. fuer Physik; Sommer, Rainer [DESY, Zeuthen (Germany). NIC
2010-06-15
We have calculated the step scaling function and the running coupling of QCD in the Schroedinger functional scheme with four flavors of O(a) improved Wilson quarks. Comparisons of our non-perturbative results with 2-loop and 3-loop perturbation theory as well as with non-perturbative data for only two flavors are made. (orig.)
Extrapolation of lattice QCD results beyond the power-counting regime
Leinweber, D B; Young, R D
2005-01-01
Resummation of the chiral expansion is necessary to make accurate contact with current lattice simulation results of full QCD. Resummation techniques including relativistic formulations of chiral effective field theory and finite-range regularization (FRR) techniques are reviewed, with an emphasis on using lattice simulation results to constrain the parameters of the chiral expansion. We illustrate how the chiral extrapolation problem has been solved and use FRR techniques to identify the power-counting regime (PCR) of chiral perturbation theory. To fourth-order in the expansion at the 1% tolerance level, we find $0 \\le m_\\pi \\le 0.18$ GeV for the PCR, extending only a small distance beyond the physical pion mass.
QCD with jets and photons at ATLAS and CMS
Barnovska-Blenessy, Zuzana; The ATLAS collaboration
2017-01-01
A selection of recent QCD measurements by the ATLAS and CMS collaborations in final states with photons and jets is presented. New results with improved precision provide a probe of perturbative QCD, allowing to perform PDF fits and extracting the strong coupling constant $\\alpha_{S}$.
A New Effect in the QCD Fusion of Nuclear Partons
Institute of Scientific and Technical Information of China (English)
RUAN Jian-Hong; ZHU Wei; LI Guang-Lie
2001-01-01
The parton fusion in nucleus at the leading order of recombination is investigated based on perturbative QCD. We compute various cut diagrams including the nuclear parton fusion, and find that the parton-fusion effects depend on the nuclear QCD structure.``
Scalar correlator, Higgs decay into quarks, and scheme variations of the QCD coupling
Jamin, Matthias
2016-01-01
In this work, the perturbative QCD series of the scalar correlation function $\\Psi(s)$ is investigated. Besides ${\\rm Im}\\Psi(s)$, which is relevant for Higgs decay into quarks, two other physical correlators, $\\Psi^{''}(s)$ and $D^L(s)$, have been employed in QCD applications like quark mass determinations or hadronic $\\tau$ decays. $D^L(s)$ suffers from large higher-order corrections and, by resorting to the large-$\\beta_0$ approximation, it is shown that this is related to a spurious renormalon ambiguity at $u=1$. Hence, this correlator should be avoided in phenomenological analyses. Moreover, it turns out advantageous to express the quark mass factor, introduced to make the scalar current renormalisation group invariant, in terms of the renormalisation invariant quark mass $\\widehat m_q$. To further study the behaviour of the perturbative expansion, we introduce a QCD coupling $\\widehat\\alpha_s$, whose running is explicitly renormalisation scheme independent. The scheme dependence of $\\widehat\\alpha_s$ is...
Hump-backed QCD plateau in hadron spectra
Energy Technology Data Exchange (ETDEWEB)
Azimov, Ya.I.; Dokshitzer, Yu.L.; Khoze, V.A.; Troyan, S.I.
1986-06-01
New data on inclusive energy distribution of hadrons from quark jets in e/sup +/e/sup -/ annihilation are shown to agree with the quantitative predictions of perturbative QCD, supporting the hypothesis of local parton-hadron duality.
Energy Technology Data Exchange (ETDEWEB)
Kaneko, T.; Hashimoto, S. [High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki (Japan)]|[Graduate Univ. for Advanced Studies, Tsukuba, Ibaraki (Japan); Aoki, S. [Tsukuba Univ., Ibaraki (Japan). Graduate School of Pure and Applied Sciences]|[Brookhaven National Laboratory, Upton, NY (United States). Riken BNL Research Center; Della Morte, M. [CERN, Physics Dept., Geneva (Switzerland); Hoffmann, R. [Colorado Univ., Boulder, CO (United States). Dept. of Physics; Sommer, R. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2007-03-15
We perform a non-perturbative determination of the improvement coefficient c{sub A} to remove O(a) discretization errors in the axial vector current in three-flavor lattice QCD with the Iwasaki gauge action and the standard O(a)-improved Wilson quark action. An improvement condition with a good sensitivity to c{sub A} is imposed at constant physics. Combining our results with the perturbative expansion, c{sub A} is now known rather precisely for a{sup -1}>or similar 1.6 GeV. (orig.)
Density matrix perturbation theory.
Niklasson, Anders M N; Challacombe, Matt
2004-05-14
An orbital-free quantum perturbation theory is proposed. It gives the response of the density matrix upon variation of the Hamiltonian by quadratically convergent recursions based on perturbed projections. The technique allows treatment of embedded quantum subsystems with a computational cost scaling linearly with the size of the perturbed region, O(N(pert.)), and as O(1) with the total system size. The method allows efficient high order perturbation expansions, as demonstrated with an example involving a 10th order expansion. Density matrix analogs of Wigner's 2n+1 rule are also presented.
Incomplete Modal Expansion Method Using Perturbed Force%一种基于摄动力的不完备模态扩充方法
Institute of Scientific and Technical Information of China (English)
刘金玉; 姜建华
2012-01-01
The measured modals are incomplete in practice because of the limited number of sensors,and the rotational degrees of freedom are usually difficult to measure. To deal with the incompleteness of measured modal data for the damage identification of structure, a new mode shape expansion methods is presented. The approach adopts a perturbed force vector which can be obtained from measured modal data and only consider the influence of stiffness perturbation. Modelling-difference between the finite element analysis model and the actual tested model were also considered by introducing a set of model correction factors. And modal assurance criterion(MAC) was used to evaluate the performance of the existing methods and proposed method. Finally,the proposed method was numerically illustrated by a spatial truss model. Results indicated that the unmeasured components in the modal shapes were properly estimated by implementing the proposed method.%通常,应用损伤标识量进行损伤识别时都需要用到结构的完备模态,而实际振动试验难以测得结构的全部自由度信息.已有的模态扩充方法大都没有考虑有限元模型与试验模型之间的模型误差.基于摄动力矢量的模态扩充方法,考虑了刚度摄动对摄动力的影响.同时,考虑到有限元模型与试验模型之间的误差,引入模态修正因子.然后,通过模态置信准则对该方法进行评估.最后,以空间桁架结构模型进行数值分析,表明该方法扩充后的模态相关性较好,各阶模态误差较小.
QCD Sum Rule Studies of Heavy Quarkonium-like States
Kleiv, Robin
2014-01-01
The research presented here uses QCD sum rules (QSR) to study exotic hadrons. There are several themes in this work. First is the use of QSR to predict the masses of exotic hadrons that may exist among the heavy quarkonium-like states. The second theme is the application of sophisticated loop integration methods in order to obtain more complete theoretical results. These in turn can be extended to higher orders in the perturbative expansion in order to predict the properties of exotic hadrons more accurately. The third theme involves developing a renormalization methodology for these higher order calculations. This research has implications for the $Y(3940)$, $X(3872)$, $Z_c^\\pm\\left(3895\\right)$, $Y_b\\left(10890\\right)$, $Z_b^{\\pm}(10610)$ and $Z_b^{\\pm}(10650)$ particles, thereby contributing to the ongoing effort to understand these and other heavy quarkonium-like states.
Olsen, Stephen Lars
2014-01-01
QCD-motivated models for hadrons predict an assortment of "exotic" hadrons that have structures that are more complex then the quark-antiquark mesons and three-quark baryons of the original quark-parton model. These include pentaquark baryons, the six-quark H-dibaryon, and tetra-quark, hybrid, and glueball mesons. Despite extensive experimental searches, no unambiguous candidates for any of these exotic configurations have yet to be identified. On the other hand, a number of meson states, one that seems to be a proton-antiproton bound state, and others that contain either charmed-anticharmed quark pairs or bottom-antibottom quark pairs, have been recently discovered that neither fit into the quark-antiquark meson picture nor match the expected properties of the QCD-inspired exotics. Here I briefly review results from a recent search for the H-dibaryon, and discuss some properties of the newly discovered states --the so-called XYZ mesons-- and compare them with expectations for conventional quark-antiquark mes...
Building a non-perturbative quark-gluon vertex from a perturbative one
Bermudez, Rocio
2016-10-01
The quark-gluon vertex describes the electromagnetic and the strong interaction among these particles. The description of this interaction at high precision in both regimes, perturbative and non-perturbative, continues being a matter of interest in the context of QCD and Hadron Physics. There exist very helpful models in the literature that explain perturbative aspects of the theory but they fail describing non-perturbative phenomena, as confinement and dynamic chiral symmetry breaking. In this work we study the structure of the quark-gluon vertex in a non-perturbative regime examining QCD, checking results with QED, and working in the Schwinger-Dyson formalism.
Non-Perturbative Aspects of Thermal QCD
Energy Technology Data Exchange (ETDEWEB)
Greensite, Jeff [San Francisco State Univ., CA (United States); Golterman, Maarten F. l. [San Francisco State Univ., CA (United States)
2015-09-30
This report summarizes research in theoretical high energy physics carried out under grant support by Mithat Unsal, Jeff Greensite and Maarten Golterman, together with a list of publications generated under this grant.
Nucleon and Delta structure in continuum QCD
Cloet, Ian
2014-03-01
Quantum Chromodynamics (QCD) is the only known example in nature of a fundamental quantum field theory that is innately non-perturbative. Solving QCD will have profound implications for our understanding of the natural world, for example, it will explain how light quarks and massless gluons bind together to form the observed mesons and baryons; hence explaining the origin of more than 98% of the mass in the visible universe. Given the challenges posed by QCD, it is insufficient to study hadron ground-states alone if one seeks a solution; in this regard the delta plays a special role as the lightest baryon resonance. I will discuss recent progress using continuum QCD approaches to the study of nucleon and delta properties, with a focus on insights gained by the calculation (and measurement) of their electromagnetic form factors.
Compact Variables and Singular Fields in QCD
Lenz, F; Lenz, Frieder; Woerlen, Stefan
2000-01-01
Subject of our investigations is QCD formulated in terms of physical degrees of freedom. Starting from the Faddeev-Popov procedure, the canonical formulation of QCD is derived for static gauges. Particular emphasis is put on obstructions occurring when implementing gauge conditions and on the concomitant emergence of compact variables and singular fields. A detailed analysis of non-perturbative dynamics associated with such exceptional field configurations within Coulomb- and axial gauge is described. We present evidence that compact variables generate confinement-like phenomena in both gauges and point out the deficiencies in achieving a satisfactory non-perturbative treatment concerning all variables. Gauge fixed formulations are shown to constitute also a useful framework for phenomenological studies. Phenomenological insights into the dynamics of Polyakov loops and monopoles in confined and deconfined phases are presented within axial gauge QCD
Eigenspectrum Noise Subtraction Methods in Lattice QCD
Guerrero, Victor; Wilcox, Walter
2010-01-01
We propose a new noise subtraction method, which we call "eigenspectrum subtraction", which uses low eigenmode information to suppress statistical noise at low quark mass. This is useful for lattice calculations involving disconnected loops or all-to-all propagators. It has significant advantages over perturbative subtraction methods. We compare unsubtracted, eigenspectrum and perturbative error bar results for the scalar operator on a small Wilson QCD matrix.
The Feynman-Schwinger representation in QCD /
Simonov, Yu A.; Tjon, J. A.
2002-01-01
Published in: Ann. Phys. 300 (2002) 54-87 citations recorded in [Science Citation Index] Abstract: The proper time path integral representation is derived explicitly for Green's functions in QCD. After an introductory analysis of perturbative properties, the total gluonic field is separated in a rig
Status Report of NNLO QCD Calculations
Klasen, M
2005-01-01
We review recent progress in next-to-next-to-leading order (NNLO) perturbative QCD calculations with special emphasis on results ready for phenomenological applications. Important examples are new results on structure functions and jet or Higgs boson production. In addition, we describe new calculational techniques based on twistors and their potential for efficient calculations of multiparticle amplitudes.
Infrared Scales and Factorization in QCD
Manohar, A V
2006-01-01
Effective field theory methods are used to study factorization of the deep inelastic scattering cross-section. The cross-section is shown to factor in QCD, even though it does not factor in perturbation theory for some choices of the infrared regulator. Messenger modes are not required in soft-collinear effective theory for deep inelastic scattering as x -> 1.
Renormalized Wick expansion for a modified PQCD
de Oca, Alejandro Cabo Montes
2007-01-01
The renormalization scheme for the Wick expansion of a modified version of the perturbative QCD introduced in previous works is discussed. Massless QCD is considered, by implementing the usual multiplicative scaling of the gluon and quark wave functions and vertices. However, also massive quark and gluon counter-terms are allowed in this mass less theory since the condensates are expected to generate masses. A natural set of expansion parameters of the physical quantities is introduced: the coupling itself and to masses $m_q$ and $m_g$ associated to quarks and gluons respectively. This procedure allows to implement a dimensional transmutation effect through these new mass scales. A general expression for the new generating functional in terms of the mass parameters $m_q$ and $m_g$ is obtained in terms of integrals over arbitrary but constant gluon or quark fields in each case. Further, the one loop potential, is evaluated in more detail in the case when only the quark condensate is retained. This lowest order...
Renormalized Wick expansion for a modified PQCD
Energy Technology Data Exchange (ETDEWEB)
Cabo Montes de Oca, Alejandro [Instituto de Cibernetica, Matematica y Fisica, Group of Theoretical Physics, Vedado, La Habana (Cuba); Abdus Salam International Centre for Theoretical Physics, Trieste (Italy)
2008-05-15
The renormalization scheme for the Wick expansion of a modified version of the perturbative QCD introduced in previous works is discussed. Massless QCD is considered by implementing the usual multiplicative scaling of the gluon and quark wave functions and vertices. However, also massive quark and gluon counterterms are allowed in this massless theory since the condensates are expected to generate masses. A natural set of expansion parameters of the physical quantities is introduced: the coupling itself and the two masses m{sub q} and m{sub g} associated to quarks and gluons, respectively. This procedure allows one to implement a dimensional transmutation effect through these new mass scales. A general expression for the new generating functional in terms of the mass parameters m{sub q} and m{sub g} is obtained in terms of integrals over arbitrary but constant gluon or quark fields in each case. Further, the one loop potential is evaluated in more detail in the case when only the quark condensate is retained. This lowest order result again indicates the dynamical generation of quark condensates in the vacuum. (orig.)
Precision QCD measurements at HERA
Directory of Open Access Journals (Sweden)
Pirumov Hayk
2014-01-01
Full Text Available A review of recent experimental results on perturbative QCD from the HERA experiments H1 and ZEUS is presented. All inclusive deep inelastic cross sections measured by the H1 and ZEUS collaborations in neutral and charged current unpolarised ep scattering are combined. They span six orders of magnitude in negative four-momentum-transfer squared, Q2, and in Bjorken x. This data set is used as the sole input to NLO and NNLO QCD analyses to determine new sets of parton distributions, HERAPDF2.0, with small experimental uncertainties and an estimate of model and parametrisation uncertainties. Also shown are new results on inclusive jet, dijet and trijet differential cross sections measured in neutral current deep inelastic scattering. The precision jet data is used to extract the strong coupling αs at NLO with small experimental errors.
DEFF Research Database (Denmark)
Bechi, Jacopo
2009-01-01
This paper focuses on some issues about condensates and renormalization in AdS/QCD models. In particular we consider the consistency of the AdS/QCD approach for scale dependent quantities as the chiral condensate questioned in some recent papers and the 4D meaning of the 5D cosmological constant...... in a model in which the QCD is dual to a 5D gravity theory. We will be able to give some arguments that the cosmological constant is related to the QCD gluon condensate....
Finite Density QCD in the Chiral Limit
Aloisio, R; Di Carlo, G; Galante, A; Grillo, A F
1998-01-01
We present the first results of an exact simulation of full QCD at finite density in the chiral limit. We have used a MFA (Microcanonical Fermionic Average) inspired approach for the reconstruction of the Grand Canonical Partition Function of the theory; using the fugacity expansion of the fermionic determinant we are able to move continuously in the ($\\beta -\\mu$) plane with $m=0$.
OPE in planar QCD from integrability
Ahn, Changrim; Nepomechie, Rafael I
2012-01-01
We consider the operator product expansion of local single-trace operators composed of the self-dual components of the field strength tensor in planar QCD. Using the integrability of the one-loop matrix of anomalous dimensions of such operators, we obtain a determinant expression for certain tree-level structure constants in the OPE.
Decay constants of B-mesons from non-perturbative HQET with two light dynamical quarks
DEFF Research Database (Denmark)
Bernardoni, F.; Blossier, B.; Bulava, J.;
2014-01-01
We present a computation of B-meson decay constants from lattice QCD simulations within the framework of Heavy Quark Effective Theory for the b-quark. The next-to-leading order corrections in the HQET expansion are included non-perturbatively. Based on Nf=2 gauge field ensembles, covering three...... limits. Our final results read fB=186(13)MeV, fBs=224(14)MeV and fBs/fB=1.203(65). A comparison with other results in the literature does not reveal a dependence on the number of dynamical quarks, and effects from truncating HQET appear to be negligible....
Alexander, Stephon; Yang, Zhi
2016-01-01
We account for the late time acceleration of the Universe by extending the QCD color to a $SU(3)$ invisible sector (IQCD). If the Invisible Chiral symmetry is broken in the early universe, a condensate of dark pions (dpions) and dark gluons (dgluons) forms. The condensate naturally forms due to strong dynamics similar to the Nambu--Jona-Lasinio mechanism. As the Universe evolves from early times to present times the interaction energy between the dgluon and dpion condensate dominates with a negative pressure equation of state and causes late time acceleration. We conclude with a stability analysis of the coupled perturbations of the dark pions and dark gluons.
The impact of quark masses on pQCD thermodynamics
Graf, Thorben; Fraga, Eduardo S
2015-01-01
We present results for several thermodynamic quantities within the next-to-leading order calculation of the thermodynamic potential in perturbative QCD at finite temperature and chemical potential including non-vanishing quark masses. These results are compared to lattice data and to higher-order optimized perturbative calculations to investigate the trend brought about by mass corrections.
The impact of quark masses on pQCD thermodynamics
Energy Technology Data Exchange (ETDEWEB)
Graf, Thorben; Schaffner-Bielich, Juergen [Goethe University, Institute for Theoretical Physics, Frankfurt am Main (Germany); Fraga, Eduardo S. [Universidade Federal do Rio de Janeiro, Instituto de Fisica, Rio de Janeiro (Brazil)
2016-07-15
We present results for several thermodynamic quantities within the next-to-leading order calculation of the thermodynamic potential in perturbative QCD at finite temperature and chemical potential including non-vanishing quark masses. These results are compared to lattice data and to higher-order optimized perturbative calculations to investigate the trend brought about by mass corrections. (orig.)
Recent QCD Results from the Tevatron
Energy Technology Data Exchange (ETDEWEB)
Vellidis, Costas [Fermilab
2015-10-10
Four years after the shutdown of the Tevatron proton-antiproton collider, the two Tevatron experiments, CDF and DZero, continue producing important results that test the theory of the strong interaction, Quantum Chromodynamics (QCD). The experiments exploit the advantages of the data sample acquired during the Tevatron Run II, stemming from the unique pp initial state, the clean environment at the relatively low Tevatron instantaneous luminosities, and the good understanding of the data sample after many years of calibrations and optimizations. A summary of results using the full integrated luminosity is presented, focusing on measurements of prompt photon production, weak boson production associated with jets, and non-perturbative QCD processes.
Playing with QCD I: effective field theories
Energy Technology Data Exchange (ETDEWEB)
Fraga, Eduardo S. [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Inst. de Fisica
2009-07-01
The building blocks of hadrons are quarks and gluons, although color is confined into singlet states. QCD is believed to be the fundamental theory of strong interactions. Its asymptotically free nature puts the vacuum out of reach for perturbation theory. The Lagrangian of QCD and the Feynman rules associated were built by using the Gauge Principle, starting from the quark matter fields and obtaining gluons as connections. A simpler, and sometimes necessary or complementary, approach is provided by effective field theories or effective models, especially when one has to deal with the nonperturbative sector of the theory. (author)
Perturbative corrections to zero recoil inclusive B decay sum rules
Kapustin, A A; Wise, M B; Grinstein, B; Kapustin, Anton; Ligeti, Zoltan; Wise, Mark B; Grinstein, Benjamin
1996-01-01
Comparing the result of inserting a complete set of physical states in a time ordered product of b decay currents with the operator product expansion gives a class of zero recoil sum rules. They sum over physical states with excitation energies less than \\Delta, where \\Delta is much greater than the QCD scale and much less than the heavy charm and bottom quark masses. These sum rules have been used to derive an upper bound on the zero recoil limit of the B\\to D^* form-factor, and on the matrix element of the kinetic energy operator between B meson states. Perturbative corrections to the sum rules of order \\alpha_s(\\Delta) \\Delta^2/m_{c,b}^2 have previously been computed. We calculate the corrections of order \\alpha_s(\\Delta) and \\alpha_s^2(\\Delta) \\beta_0 keeping all orders in \\Delta/m_{c,b}, and show that these perturbative QCD corrections suppressed by powers of \\Delta/m_{c,b} significantly weaken the upper bound on the zero recoil B\\to D^* form-factor, and also on the kinetic energy operator's matrix eleme...
Energy Technology Data Exchange (ETDEWEB)
Mannel, T. [Siegen Univ. (Germany). FB 7, Theoretische Physik; Pecjak, B.D. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Pivovarov, A.A. [Siegen Univ. (Germany). FB 7, Theoretische Physik]|[Russian Academy of Sciecnes, Moscow (Russian Federation). Inst. for Nuclear Research
2007-03-15
We use QCD sum rules to compute matrix elements of the {delta}B=2 operators appearing in the heavy-quark expansion of the width difference of the B{sub s} mass eigenstates. Our analysis includes the leading-order operators Q and Q{sub S}, as well as the subleading operators R{sub 2} and R{sub 3}, which appear at next-to-leading order in the 1/m{sub b} expansion. We conclude that the violation of the factorization approximation for these matrix elements due to non-perturbative vacuum condensates is as low as 1-2%. (orig.)
The generalized BLM approach to fix scale-dependence in QCD: the current status of investigations
Kataev, A L
2014-01-01
I present a brief review of the generalized Brodsky-Lepage-McKenzie (BLM) approaches to fix the scale-dependence of the renormalization group (RG) invariant quantities in QCD. At first, these approaches are based on the expansions of the coefficients of the perturbative series for the RG-invariant quantities in the products of the coefficients $\\beta_i$ of the QCD $\\beta$-function, which are evaluated in the MS-like schemes. As a next step all $\\beta_i$-dependent terms are absorbed into the BLM-type scale(s) of the powers of the QCD couplings. The difference between two existing formulations of the above mentioned generalizations based on the seBLM approach and the Principle of Maximal Conformality (PMC) are clarified in the case of the Bjorken polarized deep-inelastic scattering sum rule. Using the conformal symmetry-based relations for the non-singlet coefficient functions of the Adler D-function and of Bjorken polarized deep-inelastic scattering sum rules $C^{\\rm Bjp}_{\\rm NS}(a_s)$ the $\\beta_i$-dependent...
Pleskot, Vojtech; The ATLAS collaboration
2016-01-01
ATLAS has has performed several measurements of phenomena connected to QCD at soft scales or at the transition to the hard regime. These include the measurements at different centre-of-mass energies in Run-1 and Run-2 of the elastic, inelastic and total cross sections in pp collisions, the properties of minimum bias and the underlying event interactions, particle production and their correlations, as well as of diffractive and exclusive events. These results are sensitive to non-perturbative models of soft QCD. Jet and photon production cross sections have been measured differentially for inclusive and multi-object final states at 7, 8 and 13 TeV pp collisions with the ATLAS detector and are compared to expectations based on next-to-leading order QCD calculations as well as Monte Carlo simulations. Further studies of jet production properties include the measurements of jet properties, and the determination of the strong coupling constant alpha_s. These measurements provide direct probes of short-distance phy...
Voutilainen, Mikko
2012-01-01
We review recent experimental work on probing QCD at high $p_{T}$ at the Tevatron and at the LHC. The Tevatron has just finished a long and illustrious career at the forefront of high energy physics, while the LHC now has its physics program in full swing and is producing results at a quick rate in a new energy regime. Many of the LHC measurements extend well into the TeV range, with potential sensitivity to new physics. The experimental systematics at the LHC are also becoming competitive with the Tevatron, making precision measurements of QCD possible. Measurements of inclusive jet, dijet and isolated prompt photon production can be used to test perturbative QCD predictions and to constrain parton distribution functions, as well as to measure the strong coupling constant. More exclusive topologies are used to constrain aspects of parton shower modeling, initial and final state radiation. Interest in boosted heavy resonances has resulted in novel studies of jet mass and subjet structure that also test pertu...
Zhou, Shiqi; Solana, J. R.
2013-06-01
The first four perturbation coefficients in the expansion of the Helmholtz free energy in power series of the inverse of the reduced temperature for a number of potential models with hard-sphere cores plus core-softened and discontinuous tails are obtained from Monte Carlo simulations. The potential models considered include square-well, double square-well, and square-shoulder plus square-well, with different potential parameters. These simulation data are used to evaluate the performance of a traditional macroscopic compressibility approximation (MCA) for the second order coefficient and a recent coupling parameter series expansion (CPSE) for the first four coefficients. Comprehensive comparison indicates the incapability of the MCA for the second order coefficient in most non-stringent situations, and significance of the CPSE in accurately calculating these four coefficients.
Nucleon structure from lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Dinter, Simon
2012-11-13
In this thesis we compute within lattice QCD observables related to the structure of the nucleon. One part of this thesis is concerned with moments of parton distribution functions (PDFs). Those moments are essential elements for the understanding of nucleon structure and can be extracted from a global analysis of deep inelastic scattering experiments. On the theoretical side they can be computed non-perturbatively by means of lattice QCD. However, since the time lattice calculations of moments of PDFs are available, there is a tension between these lattice calculations and the results from a global analysis of experimental data. We examine whether systematic effects are responsible for this tension, and study particularly intensively the effects of excited states by a dedicated high precision computation. Moreover, we carry out a first computation with four dynamical flavors. Another aspect of this thesis is a feasibility study of a lattice QCD computation of the scalar quark content of the nucleon, which is an important element in the cross-section of a heavy particle with the nucleon mediated by a scalar particle (e.g. Higgs particle) and can therefore have an impact on Dark Matter searches. Existing lattice QCD calculations of this quantity usually have a large error and thus a low significance for phenomenological applications. We use a variance-reduction technique for quark-disconnected diagrams to obtain a precise result. Furthermore, we introduce a new stochastic method for the calculation of connected 3-point correlation functions, which are needed to compute nucleon structure observables, as an alternative to the usual sequential propagator method. In an explorative study we check whether this new method is competitive to the standard one. We use Wilson twisted mass fermions at maximal twist in all our calculations, such that all observables considered here have only O(a{sup 2}) discretization effects.
Academic Training: QCD: are we ready for the LHC
2006-01-01
2006-2007 ACADEMIC TRAINING PROGRAMME LECTURE SERIES 4, 5, 6, 7 December, from 11:00 to 12:00 4, 5, 6 December - Main Auditorium, bldg. 500, 7 December - TH Auditorium, bldg. 4 - 3-006 QCD: are we ready for the LHC S. FRIXIONE / INFN, Genoa, Italy The LHC energy regime poses a serious challenge to our capability of predicting QCD reactions to the level of accuracy necessary for a successful programme of searches for physics beyond the Standard Model. In these lectures, I'll introduce basic concepts in QCD, and present techniques based on perturbation theory, such as fixed-order and resummed computations, and Monte Carlo simulations. I'll discuss applications of these techniques to hadron-hadron processes, concentrating on recent trends in perturbative QCD aimed at improving our understanding of LHC phenomenology.
Non-perturbative quark mass renormalization
Capitani, S.; Luescher, M.; Sint, S.; Sommer, R.; Weisz, P.; Wittig, H.
1998-01-01
We show that the renormalization factor relating the renormalization group invariant quark masses to the bare quark masses computed in lattice QCD can be determined non-perturbatively. The calculation is based on an extension of a finite-size technique previously employed to compute the running coupling in quenched QCD. As a by-product we obtain the $\\Lambda$--parameter in this theory with completely controlled errors.
Energy Technology Data Exchange (ETDEWEB)
Brandt, Bastian B. [Institute for Theoretical Physics, Goethe-University of Frankfurt,60438 Frankfurt (Germany); Institute for Theoretical Physics, University of Regensburg,93040 Regensburg (Germany); Lohmayer, Robert; Wettig, Tilo [Institute for Theoretical Physics, University of Regensburg,93040 Regensburg (Germany)
2016-11-14
We explore an alternative discretization of continuum SU(N{sub c}) Yang-Mills theory on a Euclidean spacetime lattice, originally introduced by Budzcies and Zirnbauer. In this discretization the self-interactions of the gauge field are induced by a path integral over N{sub b} auxiliary boson fields, which are coupled linearly to the gauge field. The main progress compared to earlier approaches is that N{sub b} can be as small as N{sub c}. In the present paper we (i) extend the proof that the continuum limit of the new discretization reproduces Yang-Mills theory in two dimensions from gauge group U(N{sub c}) to SU(N{sub c}), (ii) derive refined bounds on N{sub b} for non-integer values, and (iii) perform a perturbative calculation to match the bare parameter of the induced gauge theory to the standard lattice coupling. In follow-up papers we will present numerical evidence in support of the conjecture that the induced gauge theory reproduces Yang-Mills theory also in three and four dimensions, and explore the possibility to integrate out the gauge fields to arrive at a dual formulation of lattice QCD.
SOLVABILITY FOR NONLINEAR ELLIPTIC EQUATION WITH BOUNDARY PERTURBATION
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The solvability of nonlinear elliptic equation with boundary perturbation is considered. The perturbed solution of original problem is obtained and the uniformly valid expansion of solution is proved.
Matrix Theory for Baryons: An Overview of Holographic QCD for Nuclear Physics
Aoki, Sinya; Iizuka, Norihiro
2013-01-01
We provide, for non-experts, a brief overview of holographic QCD and a review of a recent proposal of matrix-description of multi-baryon systems in holographic QCD. Based on the matrix model, we derive the baryon interaction at short distances in multi-flavor holographic QCD. We show that there is a very universal repulsive core of inter-baryon forces for generic number of flavors. This is consistent with a recent lattice QCD analysis for N_f = 2, 3 where repulsive core looks universal. We also provide a comparison of our results with the lattice QCD and the operator product expansion (OPE) analysis.
Properties of the quark gluon plasma from lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Mages, Simon Wolfgang
2015-03-02
Quantum Chromodynamics (QCD) is the theory of the strong interaction, the theory of the interaction between the constituents of composite elementary particles (hadrons). In the low energy regime of the theory, standard methods of theoretical physics like perturbative approaches break down due to a large value of the coupling constant. However, this is the region of most interest, where the degrees of freedom of QCD, the color charges, form color-neutral composite elementary particles, like protons and neutrons. Also the transition to more energetic states of matter like the quark gluon plasma (QGP), is difficult to investigate with perturbative approaches. A QGP is a state of strongly interacting matter, which existed shortly after the Big Bang and can be created with heavy ion collisions for example at the LHC at CERN. In a QGP the color charges of QCD are deconfined. This thesis explores ways how to use the non-perturbative approach of lattice QCD to determine properties of the QGP. It focuses mostly on observables which are derived from the energy momentum tensor, like two point correlation functions. In principle these contain information on low energy properties of the QGP like the shear and bulk viscosity and other transport coefficients. The thesis describes the lattice QCD simulations which are necessary to measure the correlation functions and proposes new methods to extract these low energy properties. The thesis also tries to make contact to another non-perturbative approach which is Improved Holographic QCD. The aim of this approach is to use the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence to make statements about QCD with calculations of a five dimensional theory of gravity. This thesis contributes to that work by constraining the parameters of the model action by comparing the predictions with those of measurements with lattice QCD.
QCD Sum Rules and Models for Generalized Parton Distributions
Energy Technology Data Exchange (ETDEWEB)
Anatoly Radyushkin
2004-10-01
I use QCD sum rule ideas to construct models for generalized parton distributions. To this end, the perturbative parts of QCD sum rules for the pion and nucleon electromagnetic form factors are interpreted in terms of GPDs and two models are discussed. One of them takes the double Borel transform at adjusted value of the Borel parameter as a model for nonforward parton densities, and another is based on the local duality relation. Possible ways of improving these Ansaetze are briefly discussed.
Summary: Working Group on QCD and Strong Interactions
Energy Technology Data Exchange (ETDEWEB)
Edmond L. Berger et al.
2002-12-23
In this summary of the considerations of the QCD working group at Snowmass 2001, the roles of quantum chromodynamics in the Standard Model and in the search for new physics are reviewed, with empahsis on frontier areas in the field. We discuss the importance of, and prospects for, precision QCD in perturbative and lattice calculations. We describe new ideas in the analysis of parton distribution functions and jet structure, and review progress in small-x and in polarization experiments.
Model of the Stochastic Vacuum and QCD Parameters
Ferreira, E; Ferreira, Erasmo; Pereira, Flávio
1997-01-01
Accounting for the two independent correlation functions of the QCD vacuum, we improve the simple and consistent description given by the model of the stochastic vacuum to the high-energy pp and pbar-p data, with a new determination of parameters of non-perturbative QCD. The increase of the hadronic radii with the energy accounts for the energy dependence of the observables.
Renormalized quark-antiquark Hamiltonian induced by a gluon mass ansatz in heavy-flavor QCD
Głazek, Stanisław D.; Gómez-Rocha, María; More, Jai; Serafin, Kamil
2017-10-01
In response to the growing need for theoretical tools that can be used in QCD to describe and understand the dynamics of gluons in hadrons in the Minkowski space-time, the renormalization group procedure for effective particles (RGPEP) is shown in the simplest available context of heavy quarkonia to exhibit a welcome degree of universality in the first approximation it yields once one assumes that beyond perturbation theory gluons obtain effective mass. Namely, in the second-order terms, the Coulomb potential with Breit-Fermi spin couplings in the effective quark-antiquark component of a heavy quarkonium, is corrected in one-flavor QCD by a spin-independent harmonic oscillator term that does not depend on the assumed effective gluon mass or the choice of the RGPEP generator. The new generator we use here is much simpler than the ones used before and has the advantage of being suitable for studies of the effective gluon dynamics at higher orders than the second and beyond the perturbative expansion.
Hadronic Light-Front Wavefunctions and QCD Phenomenology
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.
2001-02-02
A fundamental goal in QCD is to understand the non-perturbative structure of hadrons at the amplitude level--not just the single-particle flavor, momentum, and helicity distributions of the quark constituents, but also the multi-quark, gluonic, and hidden-color correlations intrinsic to hadronic and nuclear wavefunctions. A natural calculus for describing the bound-state structure of relativistic composite systems in quantum field theory is the light-front Fock expansion which encodes the properties of a hadrons in terms of a set of frame-independent n-particle wavefunctions. Light-front quantization in the doubly-transverse light-cone gauge has a number of remarkable advantages, including explicit unitarity, a physical Fock expansion, the absence of ghost degrees of freedom, and the decoupling properties needed to prove factorization theorems in high momentum transfer inclusive and exclusive reactions. A number of applications are discussed in these lectures, including semileptonic B decays, two-photon exclusive reactions, and deeply virtual Compton scattering. The relation of the intrinsic sea to the light-front wavefunctions is discussed. A new type of jet production reaction, ''self-resolving diffractive interactions'' can provide direct information on the light-front wavefunctions of hadrons in terms of their quark and gluon degrees of freedom as well as the composition of nuclei in terms of their nucleon and mesonic degrees of freedom.
Analytic structure of QCD propagators in Minkowski space
Siringo, Fabio
2016-12-01
Analytical functions for the propagators of QCD, including a set of chiral quarks, are derived by a one-loop massive expansion in the Landau gauge, deep in the infrared. By analytic continuation, the spectral functions are studied in Minkowski space, yielding a direct proof of positivity violation and confinement from first principles. The dynamical breaking of chiral symmetry is described on the same footing of gluon mass generation, providing a unified picture. While dealing with the exact Lagrangian, the expansion is based on massive free-particle propagators, is safe in the infrared and is equivalent to the standard perturbation theory in the UV. By dimensional regularization, all diverging mass terms cancel exactly without including mass counterterms that would spoil the gauge and chiral symmetry of the Lagrangian. Universal scaling properties are predicted for the inverse dressing functions and shown to be satisfied by the lattice data. Complex conjugated poles are found for the gluon propagator, in agreement with the i-particle scenario.
Nonperturbative QCD and elastic processes at CEBAF energies
Energy Technology Data Exchange (ETDEWEB)
Radyushkin, A.V. [Old Dominion Univ., Norfolk, VA (United States)]|[Continuous Electron Beam Accelerator Facility, Newport News, VA (United States)
1994-04-01
The author outlines how one can approach nonperturbative aspects of the QCD dynamics studying elastic processes at energies accessible at upgraded CEBAF. The author`s point is that, in the absence of a complete theory of the nonperturbative effects, a possible way out is based on a systematic use of the QCD factorization procedure which separates theoretically understood ({open_quotes}known{close_quotes}) short-distance effects and nonperturbative ({open_quotes}unknown{close_quotes}) long-distance ones. The latter include hadronic distribution amplitudes, soft components of hadronic form factors etc. Incorporating the QCD sum rule version of the QCD factorization approach, one can relate these nonperturbative functions to more fundamental objects, vacuum condensates, which accumulate information about the nonperturbative structure of the QCD vacuum. The emerging QCD sum rule picture of hadronic form factors is characterized by a dominant role of essentially nonperturbative effects in the few GeV region, with perturbative mechanisms starting to show up for momentum transfers Q{sup 2} closer to 10 GeV{sup 2} and higher. Thus, increasing CEBAF energy provides a unique opportunity for a precision study of interplay between the perturbative and nonperturbative phenomena in the QCD description of elastic processes.
Charm-quark mass from weighted finite energy QCD sum rules
Bodenstein, S; Dominguez, C A; Peñarrocha, J; Schilcher, K
2010-01-01
The running charm-quark mass in the $\\bar{MS}$ scheme is determined from weighted finite energy QCD sum rules (FESR) involving the vector current correlator. Only the short distance expansion of this correlator is used, together with integration kernels (weights) involving positive powers of $s$, the squared energy. The optimal kernels are found to be a simple {\\it pinched} kernel, and polynomials of the Legendre type. The former kernel reduces potential duality violations near the real axis in the complex s-plane, and the latter allows to extend the analysis to energy regions beyond the end point of the data. These kernels, together with the high energy expansion of the correlator, weigh the experimental and theoretical information differently from e.g. inverse moments FESR. Current, state of the art results for the vector correlator up to four-loop order in perturbative QCD are used in the FESR, together with the latest experimental data. The integration in the complex s-plane is performed using three diffe...
Exclusive radiative decays of W and Z bosons in QCD factorization
Grossman, Yuval; König, Matthias; Neubert, Matthias
2015-04-01
We present a detailed theoretical analysis of very rare, exclusive hadronic decays of the electroweak gauge bosons V = W, Z from first principles of QCD. Our main focus is on the radiative decays V → Mγ, in which M is a pseudoscalar or vector meson. At leading order in an expansion in powers of ΛQCD /m V the decay amplitudes can be factorized into convolutions of calculable hard-scattering coefficients with the leading-twist light-cone distribution amplitude of the meson M. Power corrections to the decay rates arise first at order (ΛQCD /m V ) 2 . They can be estimated in terms of higher-twist distribution amplitudes and are predicted to be tiny. We include one-loop radiative corrections to the hard-scattering coefficients and perform the resummation of large logarithms ( α s ln( m {/v 2}/ μ {0/2})) n (with μ 0 ˜ 1 GeV a typical hadronic scale) to all orders in perturbation theory. Evolution effects have an important impact both numerically and conceptually, since they reduce the sensitivity to poorly determined hadronic parameters. We present detailed numerical predictions and error estimates, which can serve as benchmarks for future precision measurements. We also present an exploratory study of the weak radiative decays Z → MW. Some of the decay modes studied here have branching ratios large enough to be accessible in the high-luminosity run of the LHC. Many of them can be measured with high accuracy at a future lepton collider. This will provide stringent tests of the QCD factorization formalism and enable novel searches for new physics.
Exclusive radiative decays of W and Z bosons in QCD factorization
Energy Technology Data Exchange (ETDEWEB)
Grossman, Yuval [Department of Physics, LEPP, Cornell University,Ithaca, NY 14853 (United States); König, Matthias [PRISMA Cluster of Excellence & Mainz Institute for Theoretical Physics,Johannes Gutenberg University,55099 Mainz (Germany); Neubert, Matthias [Department of Physics, LEPP, Cornell University,Ithaca, NY 14853 (United States); PRISMA Cluster of Excellence & Mainz Institute for Theoretical Physics,Johannes Gutenberg University,55099 Mainz (Germany)
2015-04-20
We present a detailed theoretical analysis of very rare, exclusive hadronic decays of the electroweak gauge bosons V=W,Z from first principles of QCD. Our main focus is on the radiative decays V→Mγ, in which M is a pseudoscalar or vector meson. At leading order in an expansion in powers of Λ{sub QCD}/m{sub V} the decay amplitudes can be factorized into convolutions of calculable hard-scattering coefficients with the leading-twist light-cone distribution amplitude of the meson M. Power corrections to the decay rates arise first at order (Λ{sub QCD}/m{sub V}){sup 2}. They can be estimated in terms of higher-twist distribution amplitudes and are predicted to be tiny. We include one-loop O(α{sub s}) radiative corrections to the hard-scattering coefficients and perform the resummation of large logarithms (α{sub s}ln (m{sub V}{sup 2}/μ{sub 0}{sup 2})){sup n} (with μ{sub 0}∼1 GeV a typical hadronic scale) to all orders in perturbation theory. Evolution effects have an important impact both numerically and conceptually, since they reduce the sensitivity to poorly determined hadronic parameters. We present detailed numerical predictions and error estimates, which can serve as benchmarks for future precision measurements. We also present an exploratory study of the weak radiative decays Z→MW. Some of the decay modes studied here have branching ratios large enough to be accessible in the high-luminosity run of the LHC. Many of them can be measured with high accuracy at a future lepton collider. This will provide stringent tests of the QCD factorization formalism and enable novel searches for new physics.
Basics of thermal field theory a tutorial on perturbative computations
Laine, Mikko
2016-01-01
This book presents thermal field theory techniques, which can be applied in both cosmology and the theoretical description of the QCD plasma generated in heavy-ion collision experiments. It focuses on gauge interactions (whether weak or strong), which are essential in both contexts. As well as the many differences in the physics questions posed and in the microscopic forces playing a central role, the authors also explain the similarities and the techniques, such as the resummations, that are needed for developing a formally consistent perturbative expansion. The formalism is developed step by step, starting from quantum mechanics; introducing scalar, fermionic and gauge fields; describing the issues of infrared divergences; resummations and effective field theories; and incorporating systems with finite chemical potentials. With this machinery in place, the important class of real-time (dynamic) observables is treated in some detail. This is followed by an overview of a number of applications, ranging from t...
Mass and chemical asymmetry in QCD matter
Palhares, L F; Villavicencio, C
2008-01-01
We consider two-flavor asymmetric QCD combined with a low-energy effective model inspired by chiral perturbation theory and lattice data to investigate the effects of masses, isospin and baryon number on the pressure and the deconfinement phase transition. Remarkable agreement with lattice results is found for the critical temperature behavior. Further analyses of the cold, dense case and the influence of quark mass asymmetry are also presented.
Diffractive Leptoproduction of Vector Mesons in QCD
Brodsky, Stanley J.; Frankfurt, L.; Gunion, J. F.; Mueller, A.H.; Strikman, M.
1994-01-01
We demonstrate that the distinctive features of the forward differential cross section of diffractive leptoproduction of a vector meson can be legitimately calculated in perturbative QCD in terms of the light-cone $q \\bar q$ wave function of the vector meson and the gluon distribution of the target. In particular, we calculate the $Q^2$ and nuclear dependence of the diffractive leptoproduction of vector mesons and estimate the cross section. The production of longitudinally polarized vector m...
Studying QCD factorizations in exclusive gamma* gamma* -> rho^0_L rho^0_L
Wallon, S; Segond, M; Szymanowski, L
2007-01-01
The exclusive process e+ e- -> e+ e- rho^0_L rho^0_L allows to study various dynamics and factorization properties of perturbative QCD. At moderate energy, we demonstrate how collinear QCD factorization emerges, involving generalized distribution amplitudes (GDA) and transition distribution amplitudes (TDA). At higher energies, in the Regge limit of QCD, we show that it offers a promising probe of the BFKL resummation effects to be studied at the International Linear Collider (ILC).
QCD Factorizations in Exclusive gamma* gamma* -> rho0_L rho0_L
Pire, B; Szymanowski, L; Wallon, S
2008-01-01
The exclusive process e+ e- -> e+ e-rho0_L rho0_L allows to study various dynamics and factorization properties of perturbative QCD. At moderate energy, we demonstrate how collinear QCD factorization emerges, involving either generalized distribution amplitudes (GDA) or transition distribution amplitudes (TDA). At higher energies, in the Regge limit of QCD, we show that it offers a promising probe of the BFKL resummation effects to be studied at ILC.
The low-energy effective theory of QCD at small quark masses in a finite volume
Energy Technology Data Exchange (ETDEWEB)
Lehner, Christoph
2010-01-15
At low energies the theory of quantum chromodynamics (QCD) can be described effectively in terms of the lightest particles of the theory, the pions. This approximation is valid for temperatures well below the mass difference of the pions to the next heavier particles. We study the low-energy effective theory at very small quark masses in a finite volume V. The corresponding perturbative expansion in 1/{radical}(V) is called {epsilon} expansion. At each order of this expansion a finite number of low-energy constants completely determine the effective theory. These low-energy constants are of great phenomenological importance. In the leading order of the {epsilon} expansion, called {epsilon} regime, the theory becomes zero-dimensional and is therefore described by random matrix theory (RMT). The dimensionless quantities of RMT are mapped to dimensionful quantities of the low-energy effective theory using the leading-order lowenergy constants {sigma} and F. In this way {sigma} and F can be obtained from lattice QCD simulations in the '' regime by a fit to RMT predictions. For typical volumes of state-of-the-art lattice QCD simulations, finite-volume corrections to the RMT prediction cannot be neglected. These corrections can be calculated in higher orders of the {epsilon} expansion. We calculate the finite-volume corrections to {sigma} and F at next-to-next-to-leading order in the {epsilon} expansion. We also discuss non-universal modifications of the theory due to the finite volume. These results are then applied to lattice QCD simulations, and we extract {sigma} and F from eigenvalue correlation functions of the Dirac operator. As a side result, we provide a proof of equivalence between the parametrization of the partially quenched low-energy effective theory without singlet particle and that of the super-Riemannian manifold used earlier in the literature. Furthermore, we calculate a special version of the massless sunset diagram at finite volume without
QCD factorization for high $p_T$ heavy quarkonium production
Ma, Yan-Qing; Sterman, George; Zhang, Hong
2015-01-01
In this talk, we present the QCD factorization formula for heavy quarkonium production at large $p_T$ with factorized leading-power and next-to-leading power contributions in the $1/p_T$ expansion. We show that the leading order analytical calculations in this QCD factorization approach can reproduce effectively the full next-to-leading order numerical results derived using non-relativistic QCD (NRQCD) factorization formalism. We demonstrate that the next-to-leading power contributions are crucial to the description of the channels that are the most relevant for the rate as well as polarization of $J/\\psi$ production at current collider energies.
Phase structure of finite density QCD with a histogram method
Nakagawa, Yoshiyuki; Ejiri, Shinji; Hatsuda, Tetsuo; Kanaya, Kazuyuki; Ohno, Hiroshi; Saito, Hana; Umeda, Takashi
2012-01-01
We study the phase structure of QCD in the $T-\\mu$ plane using a histogram method and the reweighting technique by performing phase quenched simulations of two-flavor QCD with RG-improved gauge action and O($a$) improved Wilson quark action. Taking the effects of the complex phase of the quark determinant using the cumulant expansion method, we calculate the probability distribution function of plaquette and phase-quenched determinant as a function of $T$ and $\\mu$. We discuss the order of the QCD phase transition consulting the shape of the probability distribution function.
Quark masses in two-flavor QCD
Creutz, Michael
2011-01-01
Considered as a function of the quark mases, two-flavor QCD depends on three parameters, including one that is CP violating. As the masses vary to unphysical values, regions of both first- and second-order phase transitions are expected. For non-degenerate quarks, non-perturbative effects leave individual quark mass ratios with a renormalization scheme dependence. This complicates matching lattice results with perturbative schemes and clarifies the tautology with attacking the strong CP problem via a vanishing up quark mass.
Solving QCD via multi-Regge theory.
Energy Technology Data Exchange (ETDEWEB)
White, A. R.
1998-11-04
To solve QCD at high-energy the authors must simultaneously find the hadronic states and the exchanged pomeron (IP) giving UNITARY scattering amplitudes. Experimentally, the IP {approximately} a Regge pole at small Q{sup 2} and a single gluon at larger Q{sup 2}. (F{sub 2}{sup D}-H1, dijets-ZEUS). In the solution which the author describes, these non-perturbative properties of the IP are directly related to the non-perturbative confinement and chiral symmetry breaking properties of hadrons.
Perturbation theory and renormalisation group equations
Litim, Daniel F; Litim, Daniel F.; Pawlowski, Jan M.
2002-01-01
We discuss the perturbative expansion of several one-loop improved renormalisation group equations. It is shown that in general the integrated renormalisation group flows fail to reproduce perturbation theory beyond one loop.
Energy Technology Data Exchange (ETDEWEB)
Norniella, Olga; /Barcelona, IFAE
2005-01-01
Recent QCD measurements from the CDF collaboration at the Tevatron are presented, together with future prospects as the luminosity increases. The measured inclusive jet cross section is compared to pQCD NLO predictions. Precise measurements on jet shapes and hadronic energy flows are compared to different phenomenological models that describe gluon emissions and the underlying event in hadron-hadron interactions.
Energy Technology Data Exchange (ETDEWEB)
Ma, Hong -Hao [Chongqing Univ., Chongqing (People' s Republic of China); Wu, Xing -Gang [Chongqing Univ., Chongqing (People' s Republic of China); Ma, Yang [Chongqing Univ., Chongqing (People' s Republic of China); Brodsky, Stanley J. [Stanford Univ., Stanford, CA (United States); Mojaza, Matin [KTH Royal Inst. of Technology and Stockholm Univ., Stockholm (Sweden)
2015-05-26
A key problem in making precise perturbative QCD (pQCD) predictions is how to set the renormalization scale of the running coupling unambiguously at each finite order. The elimination of the uncertainty in setting the renormalization scale in pQCD will greatly increase the precision of collider tests of the Standard Model and the sensitivity to new phenomena. Renormalization group invariance requires that predictions for observables must also be independent on the choice of the renormalization scheme. The well-known Brodsky-Lepage-Mackenzie (BLM) approach cannot be easily extended beyond next-to-next-to-leading order of pQCD. Several suggestions have been proposed to extend the BLM approach to all orders. In this paper we discuss two distinct methods. One is based on the “Principle of Maximum Conformality” (PMC), which provides a systematic all-orders method to eliminate the scale and scheme ambiguities of pQCD. The PMC extends the BLM procedure to all orders using renormalization group methods; as an outcome, it significantly improves the pQCD convergence by eliminating renormalon divergences. An alternative method is the “sequential extended BLM” (seBLM) approach, which has been primarily designed to improve the convergence of pQCD series. The seBLM, as originally proposed, introduces auxiliary fields and follows the pattern of the β0-expansion to fix the renormalization scale. However, the seBLM requires a recomputation of pQCD amplitudes including the auxiliary fields; due to the limited availability of calculations using these auxiliary fields, the seBLM has only been applied to a few processes at low orders. In order to avoid the complications of adding extra fields, we propose a modified version of seBLM which allows us to apply this method to higher orders. As a result, we then perform detailed numerical comparisons of the two alternative scale-setting approaches by investigating their predictions for the annihilation cross section ratio R
Beane, Silas R; Vuorinen, Aleksi
2009-01-01
We present a new formulation of effective field theory for nucleon-nucleon (NN) interactions which treats pion interactions perturbatively, and we offer evidence that the expansion converges satisfactorily to third order in the expansion, which we have computed analytically for s and d wave NN scattering. Starting with the Kaplan-Savage-Wise (KSW) expansion about the nontrivial fixed point corresponding to infinite NN scattering length, we cure the convergence problems with that theory by summing to all orders the singular short distance part of the pion tensor interaction. This method makes possible a host of high precision analytic few-body calculations in nuclear physics.
On scale dependence of QCD string operators
Kivel, N A
1999-01-01
We have obtained a general solution of evolution equations for QCD twist-2 string operators in form of expansion over complete set of orthogonal eigenfunctions of evolution kernels in coordinate-space representation. In the leading logarithmic approximation the eigenfunctions can be determined using constraints imposed by conformal symmetry. Explicit formulae for the LO scale-dependence of quark and gluon twist-2 string operators are given.
Two-flavor lattice QCD simulation in the epsilon-regime with exact chiral symmetry
Fukaya, H; Chiu, T W; Hashimoto, S; Kaneko, T; Matsufuru, H; Noaki, J; Ogawa, K; Okamoto, M; Onogi, T; Yamada, N
2007-01-01
We perform lattice simulations of two-flavor QCD using Neuberger's overlap fermion, with which the exact chiral symmetry is realized at finite lattice spacings. The epsilon-regime is reached by decreasing the light quark mass down to 3 MeV on a 16^3 32 lattice with a lattice spacing \\sim 0.11 fm. We find a good agreement of the low-lying Dirac eigenvalue spectrum with the analytical predictions of the chiral random matrix theory, which reduces to the chiral perturbation theory in the epsilon-regime. The chiral condensate is extracted as \\Sigma(2 GeV) = (251(7)(11) MeV)^3, where the errors are statistical and an estimate of the higher order effects in the epsilon-expansion.
Heavy Quark Thermalization in Classical Lattice Gauge Theory Lessons for Strongly-Coupled QCD
Laine, Mikko; Philipsen, Owe; Tassler, Marcus
2009-01-01
Thermalization of a heavy quark near rest is controlled by the correlator of two electric fields along a temporal Wilson line. We address this correlator within real-time, classical lattice Yang-Mills theory, and elaborate on the analogies that exist with the dynamics of hot QCD. In the weak-coupling limit, it can be shown analytically that the dynamics on the two sides are closely related to each other. For intermediate couplings, we carry out non-perturbative simulations within the classical theory, showing that the leading term in the weak-coupling expansion significantly underestimates the heavy quark thermalization rate. Our analytic and numerical results also yield a general understanding concerning the overall shape of the spectral function corresponding to the electric field correlator, which may be helpful in subsequent efforts to reconstruct it from Euclidean lattice Monte Carlo simulations.
Energy Technology Data Exchange (ETDEWEB)
Smith, W.H. [Univ. of Wisconsin, Madison, WI (United States). Physics Dept.
1997-06-01
These lectures describe QCD physics studies over the period 1992--1996 from data taken with collisions of 27 GeV electrons and positrons with 820 GeV protons at the HERA collider at DESY by the two general-purpose detectors H1 and ZEUS. The focus of these lectures is on structure functions and jet production in deep inelastic scattering, photoproduction, and diffraction. The topics covered start with a general introduction to HERA and ep scattering. Structure functions are discussed. This includes the parton model, scaling violation, and the extraction of F{sub 2}, which is used to determine the gluon momentum distribution. Both low and high Q{sup 2} regimes are discussed. The low Q{sup 2} transition from perturbative QCD to soft hadronic physics is examined. Jet production in deep inelastic scattering to measure {alpha}{sub s}, and in photoproduction to study resolved and direct photoproduction, is also presented. This is followed by a discussion of diffraction that begins with a general introduction to diffraction in hadronic collisions and its relation to ep collisions, and moves on to deep inelastic scattering, where the structure of diffractive exchange is studied, and in photoproduction, where dijet production provides insights into the structure of the Pomeron. 95 refs., 39 figs.
B→πη('), η(')η(') decays and NLO contributions in the pQCD approach
Institute of Scientific and Technical Information of China (English)
ZHANG Zhi-Qing; LIU Xin; XIAO Zhen-Jun
2009-01-01
By employing the perturbative QCD (pQCD) factorization approach, we calculate the full leading and the partial next-to-leading order (NLO) contributions to the seven B→πη(') and η(')η(') decays. For B+B→π+η(') decays, the pQCD predictions for their decay rates agree very well with the data after the inclusion of the small NLO contributions. For neutral decays, the pQCD predictions are also consistent with the experimental upper limits and can be tested by the LHC experiments. The measured value of ACPdir(π±η)=-19±7% can also be accommodated by the pQCD approach.
Electroweak symmetry breaking via QCD.
Kubo, Jisuke; Lim, Kher Sham; Lindner, Manfred
2014-08-29
We propose a new mechanism to generate the electroweak scale within the framework of QCD, which is extended to include conformally invariant scalar degrees of freedom belonging to a larger irreducible representation of SU(3)c. The electroweak symmetry breaking is triggered dynamically via the Higgs portal by the condensation of the colored scalar field around 1 TeV. The mass of the colored boson is restricted to be 350 GeV≲mS≲3 TeV, with the upper bound obtained from perturbative renormalization group evolution. This implies that the colored boson can be produced at the LHC. If the colored boson is electrically charged, the branching fraction of the Higgs boson decaying into two photons can slightly increase, and moreover, it can be produced at future linear colliders. Our idea of nonperturbative electroweak scale generation can serve as a new starting point for more realistic model building in solving the hierarchy problem.
Shear Viscosity from Lattice QCD
Mages, Simon W; Fodor, Zoltán; Schäfer, Andreas; Szabó, Kálmán
2015-01-01
Understanding of the transport properties of the the quark-gluon plasma is becoming increasingly important to describe current measurements at heavy ion collisions. This work reports on recent efforts to determine the shear viscosity h in the deconfined phase from lattice QCD. The main focus is on the integration of the Wilson flow in the analysis to get a better handle on the infrared behaviour of the spectral function which is relevant for transport. It is carried out at finite Wilson flow time, which eliminates the dependence on the lattice spacing. Eventually, a new continuum limit has to be carried out which sends the new regulator introduced by finite flow time to zero. Also the non-perturbative renormalization strategy applied for the energy momentum tensor is discussed. At the end some quenched results for temperatures up to 4 : 5 T c are presented
Pion structure from lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Javadi Motaghi, Narjes
2015-05-12
In this thesis we use lattice QCD to compute the second Mellin moments of pion generalized parton distributions and pion electromagnetic form factors. For our calculations we are able to analyze a large set of gauge configurations with 2 dynamical flavours using non-perturbatively the improved Wilson-Sheikholeslami-Wohlert fermionic action pion masses ranging down to 151 MeV. By employing improved smearing we were able to suppress excited state contamination. However, our data in the physical quark mass limit show that some excited state contamination remains. We show the non-zero sink momentum is optimal for the computation of the electromagnetic form factors and generalized form factors at finite momenta.
From QCD to Physical Resonances
Bolton, Daniel R; Wilson, David J
2016-01-01
In this talk, we present the first chiral extrapolation of a resonant scattering amplitude obtained from lattice QCD. Finite-volume spectra, determined by the Hadron Spectrum Collaboration at $m_\\pi = 236$ MeV, for the isotriplet $\\pi\\pi$ channel are analyzed using the L\\"uscher method to determine the infinite-volume scattering amplitude. Unitarized Chiral Perturbation Theory is then used to extrapolate the scattering amplitude to the physical light quark masses. The viability of this procedure is demonstrated by its agreement with the experimentally determined scattering phase shift up to center-of-mass energies of 1.2 GeV. Finally, we analytically continue the amplitude to the complex plane to obtain the $\\rho$-pole at $\\left[755(2)(1)\\left({}^{20}_{02}\\right) - \\frac{i}{2} 129(3)(1)\\left({}^7_1\\right)\\right]$ MeV.
Chiral-scale perturbation theory about an infrared fixed point
Directory of Open Access Journals (Sweden)
Crewther R.J.
2014-06-01
Full Text Available We review the failure of lowest order chiral SU(3L ×SU(3R perturbation theory χPT3 to account for amplitudes involving the f0(500 resonance and O(mK extrapolations in momenta. We summarize our proposal to replace χPT3 with a new effective theory χPTσ based on a low-energy expansion about an infrared fixed point in 3-flavour QCD. At the fixed point, the quark condensate ⟨q̅q⟩vac ≠ 0 induces nine Nambu-Goldstone bosons: π,K,η and a QCD dilaton σ which we identify with the f0(500 resonance. We discuss the construction of the χPTσ Lagrangian and its implications for meson phenomenology at low-energies. Our main results include a simple explanation for the ΔI = 1/2 rule in K-decays and an estimate for the Drell-Yan ratio in the infrared limit.
Unconstrained Hamiltonian formulation of low energy QCD
Directory of Open Access Journals (Sweden)
Pavel Hans-Peter
2014-04-01
Full Text Available Using a generalized polar decomposition of the gauge fields into gaugerotation and gauge-invariant parts, which Abelianises the Non-Abelian Gauss-law constraints to be implemented, a Hamiltonian formulation of QCD in terms of gauge invariant dynamical variables can be achieved. The exact implementation of the Gauss laws reduces the colored spin-1 gluons and spin-1/2 quarks to unconstrained colorless spin-0, spin-1, spin-2 and spin-3 glueball fields and colorless Rarita-Schwinger fields respectively. The obtained physical Hamiltonian naturally admits a systematic strongcoupling expansion in powers of λ = g−2/3, equivalent to an expansion in the number of spatial derivatives. The leading-order term corresponds to non-interacting hybridglueballs, whose low-lying spectrum can be calculated with high accuracy by solving the Schrödinger-equation of the Dirac-Yang-Mills quantum mechanics of spatially constant fields (at the moment only for the 2-color case. The discrete glueball excitation spectrum shows a universal string-like behaviour with practically all excitation energy going in to the increase of the strengths of merely two fields, the “constant Abelian fields” corresponding to the zero-energy valleys of the chromomagnetic potential. Inclusion of the fermionic degrees of freedom significantly lowers the spectrum and allows for the study of the sigma meson. Higher-order terms in λ lead to interactions between the hybridglueballs and can be taken into account systematically using perturbation theory in λ, allowing for the study of IR-renormalisation and Lorentz invarianz. The existence of the generalized polar decomposition used, the position of the zeros of the corresponding Jacobian (Gribov horizons, and the ranges of the physical variables can be investigated by solving a system of algebraic equations. Its exact solution for the case of one spatial dimension and first numerical solutions for two and three spatial dimensions indicate
Quark Gluon Condensate,Virtuality and Susceptibility of QCD Vacuum
Institute of Scientific and Technical Information of China (English)
ZHOU Li-Juan; WU Qing; MA Wei-Xing
2008-01-01
We study vacuum of QCD in this work.The structure of non-local quark vacuum condensate,values of various local quark and gluon vacuum condensates,quark-gluon mixed vacuum condensate,quark and gluon virtuality in QCD vacuum state,quark dynamical mass and susceptibility of QCD vacuum state to external field are predicted by use of the solutions of Dyson-Schwinger equations in "rainbow" approximation with a modeling gluon propagator and three different sets of quark-quark interaction parameters.Our theoretical predictions are in good agreement with the correspondent empirical values used widely in literature,and many other theoretical calculations.The quark propagator and self-energy functions are also obtained from the numerical solutions of Dyson-Schwinger equations.This work is centrally important for studying non-perturbative QCD,and has many important applications both in particle and nuclear physics.
Virtualities of quark and gluon in QCD vacuum
Institute of Scientific and Technical Information of China (English)
2008-01-01
The non-local vacuum condensates of quantum chromodynamics (QCD) describe the distributions of quarks and gluons in the non-perturbative QCD vacuum state. Physically, this means that vacuum quarks and gluons have a nonzero mean-squared momentum in the vacuum, called virtuality. The quark virtuality is given by the ratio of the local quark-gluon mixed vacuum condensate to the quark local vacuum condensate. The gluon virtuality is expressed by gluon vacuum condensates and four-quark vacuum condensates. We study the two virtualities by solving Dyson-Schwinger Equations and calculating quark and gluon vacuum condensates. Our theoretical results for quark virtuality are in good agreement with many other theoretical model predictions such as QCD sum rules and lattice QCD calculations. Our calculation on gluon virtuality is initial and the results are quite interesting.
Early Run 2 Hard QCD Results from the ATLAS Collaboration
Directory of Open Access Journals (Sweden)
Orlando Nicola
2016-01-01
Full Text Available We provide an overview of hard QCD results based on data collected with the ATLAS detector in proton-proton collision at √s = 13 TeV at the Large Hadron Collider. The production of high transverse momentum jets, photons and photon-pairs were studied; the inclusive jet cross section is found to agree well with the prediction of perturbative QCD calculations performed at next-to-leading accuracy. The production cross sections for W and Z bosons in their e and μ decays was measured; in general, agreement is found with the expectation of next-to-next-to leading order QCD calculations and interesting sensitivities to the proton structure functions are already observed. The top production cross sections were measured in different top decay channels and found to agree with the state of the art QCD predictions.
Scheme variations of the QCD coupling and hadronic $\\tau$ decays
Boito, Diogo; Miravitllas, Ramon
2016-01-01
The Quantum Chromodynamics (QCD) coupling, $\\alpha_s$, is not a physical observable of the theory since it depends on conventions related to the renormalization procedure. We introduce a definition of the QCD coupling, denoted by $\\widehat\\alpha_s$, whose running is explicitly renormalization scheme invariant. The scheme dependence of the new coupling $\\widehat\\alpha_s$ is parameterized by a single parameter $C$, related to transformations of the QCD scale $\\Lambda$. It is demonstrated that appropriate choices of $C$ can lead to substantial improvements in the perturbative prediction of physical observables. As phenomenological applications, we study $e^+e^-$ scattering and decays of the $\\tau$ lepton into hadrons, both being governed by the QCD Adler function.
The Top Quark, QCD, And New Physics.
Dawson, S.
2002-06-01
The role of the top quark in completing the Standard Model quark sector is reviewed, along with a discussion of production, decay, and theoretical restrictions on the top quark properties. Particular attention is paid to the top quark as a laboratory for perturbative QCD. As examples of the relevance of QCD corrections in the top quark sector, the calculation of e{sup+}e{sup -}+ t{bar t} at next-to-leading-order QCD using the phase space slicing algorithm and the implications of a precision measurement of the top quark mass are discussed in detail. The associated production of a t{bar t} pair and a Higgs boson in either e{sup+}e{sup -} or hadronic collisions is presented at next-to-leading-order QCD and its importance for a measurement of the top quark Yulrawa coupling emphasized. Implications of the heavy top quark mass for model builders are briefly examined, with the minimal supersymmetric Standard Model and topcolor discussed as specific examples.
Lattice QCD with overlap fermions on GPUs
Walk, B.; Wittig, H.; Schömer, E.
2012-08-01
Lattice QCD is widely considered the correct theory of the strong force and is able to make quantitative statements in the low energy regime where perturbation theory is not applicable. The partition function of lattice QCD can be mapped onto a statistical mechanics system which then allows for the use of calculational methods such as Monte Carlo simulations. In recent years, the enormous success of GPU programming has also arrived at the lattice community. In this article, we give a short overview of Lattice QCD and motivate this need for large computing power. In our simulations we concentrate on a specific fermionic discretization, so-called Neuberger-Dirac fermions, which respect an exact chiral symmetry. We will discuss the algorithms we use in our GPU implementation which turns out to be an order of magnitude faster then the conventional CPU-equivalent. As an application we present results on the eigenvalue spectra in QCD and compare them to analytical calculations from Random Matrix Theory.
Hard And Soft QCD Physics In ATLAS
Directory of Open Access Journals (Sweden)
Adomeit Stefanie
2014-04-01
Full Text Available Hard and soft QCD results using proton-proton collisions recorded with the ATLAS detector at the LHC are reported. Charged-particle distributions and forward-backward correlations have been studied in low-luminosity minimum bias data taken at centre-of-mass energies of √s = 0.9, 2.36 and 7 TeV. Recent measurements on underlying event characteristics using charged-particle jets are also presented. The results are tested against various phenomenological soft QCD models implemented in Monte-Carlo generators. A summary of hard QCD measurements involving high transverse momentum jets is also given. Inclusive jet and dijet cross-sections have been measured at a centre-of-mass energy of 7 TeV and are compared to expectations based on NLO pQCD calculations corrected for non-perturbative effects as well as to NLO Monte Carlo predictions. Recent studies exploiting jet substructure techniques to identify hadronic decays of boosted massive particles are reported.
Chiral perturbation theory analysis of baryon temperature mass shifts
Bedaque, P F
1995-01-01
We compute the finite temperature pole mass shifts of the octet and decuplet baryons using heavy baryon chiral perturbation theory and the 1/N_c expansion, where N_c is the number of QCD colors. We consider the temperatures of the order of the pion mass m_\\pi, and expand truncate the chiral and 1/N_c expansions assuming that m_\\pi \\sim 1/N_c. There are three scales in the problem: the temperature T, the pion mass m_\\pi, and the octet--decuplet mass difference. Therefore, the result is not simply a power series in T. We find that the nucleon and \\Delta temperature mass shifts are opposite in sign, and that their mass difference changes by 20% in the temperature range 90 MeV < T < 130 MeV, that is the range where the freeze out in relativistic heavy ion collisions is expected to occur. We argue that our results are insensitive to the neglect of 1/N_c- supressed effects; the main purpose of the 1/N_c expansion in this work is to justify our treatment of the decuplet states.
The strong coupling constant of QCD with four flavors
Energy Technology Data Exchange (ETDEWEB)
Tekin, Fatih
2010-11-01
In this thesis we study the theory of strong interaction Quantum Chromodynamics on a space-time lattice (lattice QCD) with four flavors of dynamical fermions by numerical simulations. In the early days of lattice QCD, only pure gauge field simulations were accessible to the computational facilities and the effects of quark polarization were neglected. The so-called fermion determinant in the path integral was set to one (quenched approximation). The reason for this approximation was mainly the limitation of computational power because the inclusion of the fermion determinant required an enormous numerical effort. However, for full QCD simulations the virtual quark loops had to be taken into account and the development of new machines and new algorithmic techniques made the so-called dynamical simulations with at least two flavors possible. In recent years, different collaborations studied lattice QCD with dynamical fermions. In our project we study lattice QCD with four degenerated flavors of O(a) improved Wilson quarks in the Schroedinger functional scheme and calculate the energy dependence of the strong coupling constant. For this purpose, we determine the O(a) improvement coefficient c{sub sw} with four flavors and use this result to calculate the step scaling function of QCD with four flavors which describes the scale evolution of the running coupling. Using a recursive finite-size technique, the {lambda} parameter is determined in units of a technical scale L{sub max} which is an unambiguously defined length in the hadronic regime. The coupling {alpha}{sub SF} of QCD in the so-called Schroedinger functional scheme is calculated over a wide range of energies non-perturbatively and compared with 2-loop and 3-loop perturbation theory as well as with the non-perturbative result for only two flavors. (orig.)
AUTHOR|(INSPIRE)INSPIRE-00337682; Dasgupta, Mrinal
This thesis presents phenomenological studies of a state-of-the-art NNLL+NLO theoretical calculation of a novel collider observable known as 'phi star'. In these studies the 'phi star' observable, a measure of azimuthal decorrelation, is applied directly to the leptons in the production of massive lepton pairs in hadron collisions (the Drell-Yan process). This provides an alternate measure of the recoil of the massive vector boson (Z/gamma) against initial state QCD radiation, but with distinct experimental advantages over the traditional boson transverse momentum. Attention is focused on the small-'phi star' regime (the quasi-back-to-back regime) where the infrared dynamics of soft/collinear gluon emissions become important. These phenomenological studies are followed up with the presentation of a measurement of 'phi star' in 'Z to mu mu' events using 20.3 fb^-1 of collision data collected by the ATLAS experiment in 2012. Finally, studies directly related to the ATLAS absolute luminosity calibration by the v...
Hubble Parameter in QCD Universe for finite Bulk Viscosity
Tawfik, A; Mansour, H; Harko, T
2010-01-01
The influence of perturbative bulk viscosity on the evolution of Hubble parameter in the QCD era of the early Universe has been analyzed, where Friedmann-Robertson-Walker metric and Einstein field equations are utilized. Homogeneous and isotropic background matter is assumed to be characterized by barotropic equations of state deduced from recent lattice QCD simulations and heavy--ion collisions. Taking into account perturbative bulk viscosity coefficient, an estimation for the evolution of the Hubble parameter has been introduced and compared with its evolution in a non--viscous matter. A numerical solution for finite viscous Israel-Stewart background matter is also worked out. Both methods qualitatively agree in reproducing viscous Hubble parameter that turns to be slightly different from the non--viscous one. This treatment is strictly limited within a very narrow temperature-- or time--interval in QCD era, where the QGP matter is likely dominant.
Evidence for hard chiral logarithms in quenched lattice QCD
Kim, S; Kim, Seyong; Sinclair, D K
1995-01-01
We present the first direct evidence that quenched QCD differs from full QCD in the chiral (m_q \\rightarrow 0) limit, as predicted by chiral perturbation theory, from our quenched lattice QCD simulations at \\beta = 6/g^2 = 6.0. We measured the spectrum of light hadrons on 16^3 \\times 64, 24^3 \\times 64 and 32^3 \\times 64, using staggered quarks of masses m_q=0.01, m_q=0.005 and m_q=0.0025. The pion masses showed clear evidence for logarithmic violations of the PCAC relation m_{\\pi}^2 \\propto m_q, as predicted by quenched chiral perturbation theory. The dependence on spatial lattice volume precludes this being a finite size effect. No evidence was seen for such chiral logarithms in the behaviour of the chiral condensate \\langle\\bar{\\psi}\\psi\\rangle.
The Generalized Scheme-Independent Crewther Relation in QCD
Shen, Jian-Ming; Ma, Yang; Brodsky, Stanley J
2016-01-01
The Principle of Maximal Conformality (PMC) provides a systematic way to set the renormalization scales order-by-order for any perturbative QCD process. The resulting predictions are independent of the choice of renormalization scheme, a requirement of renormalization group invariance. The Crewther relation, which was originally derived for conformal theory, provides a remarkable connection between two observables when the $\\beta$ function vanishes. The "Generalized Crewther Relation" relates these two observables for physical QCD with nonzero $\\beta$ function; specifically, it connects the non-singlet Adler function ($D^{\\rm ns}$) to the Bjorken sum rule coefficient for polarized deep-inelastic electron scattering ($C_{\\rm Bjp}$) at leading twist. A scheme-dependent $\\Delta_{\\rm CSB}$-term appears in the analysis in order to compensate for the conformal symmetry breaking (CSB) terms from perturbative QCD. In conventional analyses, this normally leads to unphysical dependence in both the choice of the renorma...
Damping rates for moving particles in hot QCD
Pisarski, R D
1993-01-01
Using a program of perturbative resummation I compute the damping rates for fields at nonzero spatial momentum to leading order in weak coupling in hot $QCD$. Sum rules for spectral densities are used to simplify the calculations. For massless fields the damping rate has an apparent logarithmic divergence in the infrared limit, which is cut off by the screening of static magnetic fields (``magnetic mass''). This demonstrates how at high temperature even perturbative quantities are sensitive to nonperturbative phenomenon.
Perturbative Odderon in the Dipole Model
Kovchegov, Yu V; Wallon, S; Kovchegov, Yuri V.; Szymanowski, Lech; Wallon, Samuel
2003-01-01
We show that, in the framework of Mueller's dipole model, the perturbative QCD odderon is described by the dipole model equivalent of the BFKL equation with a $C$-odd initial condition. The eigenfunctions and eigenvalues of the odderon solution are the same as for the dipole BFKL equation and are given by the functions $E^{n,\
Energy Technology Data Exchange (ETDEWEB)
Lutz, Matthias F. M.; Lange, Jens Sören; Pennington, Michael; Bettoni, Diego; Brambilla, Nora; Crede, Volker; Eidelman, Simon; Gillitzer, Albrecht; Gradl, Wolfgang; Lang, Christian B.; Metag, Volker; Nakano, Takashi; Nieves, Juan; Neubert, Sebastian; Oka, Makoto; Olsen, Stephen L.; Pappagallo, Marco; Paul, Stephan; Pelizäus, Marc; Pilloni, Alessandro; Prencipe, Elisabetta; Ritman, Jim; Ryan, Sinead; Thoma, Ulrike; Uwer, Ulrich; Weise, Wolfram
2016-04-01
We report on the EMMI Rapid Reaction Task Force meeting 'Resonances in QCD', which took place at GSI October 12-14, 2015 (Fig.~1). A group of 26 people met to discuss the physics of resonances in QCD. The aim of the meeting was defined by the following three key questions; what is needed to understand the physics of resonances in QCD?; where does QCD lead us to expect resonances with exotic quantum numbers?; and what experimental efforts are required to arrive at a coherent picture? For light mesons and baryons only those with up, down and strange quark content were considered. For heavy-light and heavy-heavy meson systems, those with charm quarks were the focus.This document summarizes the discussions by the participants, which in turn led to the coherent conclusions we present here.
Energy Technology Data Exchange (ETDEWEB)
Kampf, Karol [Department of Astronomy and Theoretical Physics, Lund University, Soelvegatan 14A, SE 223-62 Lund (Sweden); Charles University, Faculty of Mathematics and Physics, V Holesovickach 2, Prague (Czech Republic)
2011-10-15
A systematic study of the odd-intrinsic parity sector of QCD is presented. We briefly describe different applications including {pi}{sup 0}{yields}{gamma}{gamma} decay, muonic g-2 factor and test of new holographic conjectures.
Lutz, Matthias F. M.; Lange, Jens Sören; Pennington, Michael; Bettoni, Diego; Brambilla, Nora; Crede, Volker; Eidelman, Simon; Gillitzer, Albrecht; Gradl, Wolfgang; Lang, Christian B.; Metag, Volker; Nakano, Takashi; Nieves, Juan; Neubert, Sebastian; Oka, Makoto; Olsen, Stephen L.; Pappagallo, Marco; Paul, Stephan; Pelizäus, Marc; Pilloni, Alessandro; Prencipe, Elisabetta; Ritman, Jim; Ryan, Sinead; Thoma, Ulrike; Uwer, Ulrich; Weise, Wolfram
2016-04-01
We report on the EMMI Rapid Reaction Task Force meeting 'Resonances in QCD', which took place at GSI October 12-14, 2015. A group of 26 people met to discuss the physics of resonances in QCD. The aim of the meeting was defined by the following three key questions: What is needed to understand the physics of resonances in QCD? Where does QCD lead us to expect resonances with exotic quantum numbers? What experimental efforts are required to arrive at a coherent picture? For light mesons and baryons only those with up, down and strange quark content were considered. For heavy-light and heavy-heavy meson systems, those with charm quarks were the focus. This document summarizes the discussions by the participants, which in turn led to the coherent conclusions we present here.
Lutz, Matthias F M; Pennington, Michael; Bettoni, Diego; Brambilla, Nora; Crede, Volker; Eidelman, Simon; Gillitzer, Albrecht; Gradl, Wolfgang; Lang, Christian B; Metag, Volker; Nieves, Juan; Neubert, Sebastian; Oka, Makoto; Olsen, Steve L; Pappagallo, Marco; Paul, Stephan; Pelizäus, Marc; Pilloni, Alessandro; Prencipe, Elisabetta; Ritman, Jim; Ryan, Sinead; Thoma, Ulrike; Uwer, Ulrich; Weise, Wolfram
2015-01-01
We report on the EMMI Rapid Reaction Task Force meeting 'Resonances in QCD', which took place at GSI October 12-14, 2015. A group of 26 people met to discuss the physics of resonances in QCD. The aim of the meeting was defined by the following three key questions: What is needed to understand the physics of resonances in QCD? Where does QCD lead us to expect resonances with exotic quantum numbers? What experimental efforts are required to arrive at a coherent picture? For light mesons and baryons only those with ${\\it up}$, ${\\it down}$ and ${\\it strange}$ quark content were considered. For heavy-light and heavy-heavy meson systems, those with ${\\it charm}$ quarks were the focus. This document summarizes the discussions by the participants, which in turn led to the coherent conclusions we present here.
From pQCD to neutron stars: matching equations of state to constrain global star properties
Gorda, Tyler
2016-01-01
The equation of state (EoS) of quantum chromodynamics (QCD) at zero temperature can be calculated in two different perturbative regimes: for small values of the baryon chemical potential $\\mu$, one may use chiral perturbation theory (ChEFT); and for large values of $\\mu$, one may use perturbative QCD (pQCD). There is, however, a gap for $\\mu \\in (0.97\\text{ GeV},\\, 2.6\\text{ GeV})$, where these theories becomes non-perturbative, and where there is currently no known microscopic description of QCD matter. Unfortunately, this interval obscures the values of $\\mu$ found within the cores of neutron stars (NSs). In this thesis, we argue that thermodynamic matching of the ChEFT and pQCD EoSs is a legitimate way to obtain quantitative constraints on the non-pertubative QCD EoS. Moreover, we argue that this method is effective, verifiable, and systematically improvable. First, we carry out a simplified matching procedure in QCD-like theories that can be simulated on the lattice without a sign problem. Our calculated ...
Cosmological perturbations beyond linear order
CERN. Geneva
2013-01-01
Cosmological perturbation theory is the standard tool to understand the formation of the large scale structure in the Universe. However, its degree of applicability is limited by the growth of the amplitude of the matter perturbations with time. This problem can be tackled with by using N-body simulations or analytical techniques that go beyond the linear calculation. In my talk, I'll summarise some recent efforts in the latter that ameliorate the bad convergence of the standard perturbative expansion. The new techniques allow better analytical control on observables (as the matter power spectrum) over scales very relevant to understand the expansion history and formation of structure in the Universe.
SUSY QCD effective action in the large N/sub c/ limit
Energy Technology Data Exchange (ETDEWEB)
Slavnov, A.A.; Chekhov, L.O.; Krivoshchekov, V.K.
1987-08-06
A low energy effective action for supersymmetric quantum chromodynamics (SUSY QCD) including anomalous terms is constructed in the leading order of the 1/N expansion. The absence of dynamical supersymmetry breaking is explicitly demonstrated.
Phase of the Fermion Determinant for QCD at Finite Chemical Potential
Splittorff, K
2008-01-01
In this lecture we discuss various properties of the phase factor of the fermion determinant for QCD at nonzero chemical potential. Its effect on physical observables is elucidated by comparing the phase diagram of QCD and phase quenched QCD and by illustrating the failure of the Banks-Casher formula with the example of one-dimensional QCD. The average phase factor and the distribution of the phase are calculated to one-loop order in chiral perturbation theory. In quantitative agreement with lattice QCD results, we find that the distribution is Gaussian with a width $\\sim \\mu T \\sqrt V$ (for $m_\\pi \\ll T \\ll \\Lambda_{\\rm QCD}$). Finally, we introduce, so-called teflon plated observables which can be calculated accurately by Monte Carlo even though the sign problem is severe.
Glue spin and helicity in proton from lattice QCD
Yang, Yi-Bo; Alexandru, Andrei; Draper, Terrence; Glatzmaier, Michael J; Liu, Keh-Fei; Zhao, Yong
2016-01-01
We report the first lattice QCD calculation of the glue spin $S_G$ in the nucleon. The lattice calculation is carried out with valence overlap fermions on 2+1 flavor DWF gauge configurations on four lattice spacings and four volumes including an ensemble with physical values for the quark masses. The glue spin $S_G$ in the $\\overline{\\text{MS}}$ scheme is obtained with the 1-loop perturbative matching. We find the results to be fairly insensitive to lattice spacing and quark masses. Since the frame dependence in the kinematic range $0\\leq \\vec{p} \\leq 1.5$ GeV is very mild, we take the first order large momentum expansion correction and determine the glue spin at the large momentum limit to be $S_G$=0.287(55)(16) at the physical pion mass in the $\\overline{\\text{MS}}$ scheme at $\\mu^2=10$ GeV$^2$. If the matching effect between the glue spin and helicity can be neglected, the glue helicity will be the same as the above value.
Asymptotics of QCD Factorization in Exclusive Hadronic Decays of B Mesons
Becher, T; Pecjak, B D; Becher, Thomas; Neubert, Matthias; Pecjak, Ben D.
2001-01-01
Using the renormalon calculus, we study the asymptotic behavior of the perturbative expansion of the hard-scattering kernels entering the QCD factorization formula for the nonleptonic weak decays B->D M, where M is a light meson. In the ``large-beta_0 limit'', the kernels are infrared finite and free of endpoint singularities to all orders of perturbation theory. The leading infrared renormalon singularity corresponding to a power correction of order Lambda/m_b vanishes if the light meson has a symmetric light-cone distribution amplitude. We calculate the Borel transforms and the corresponding momentum distribution functions of the hard-scattering kernels, and resum the series of O(beta_0^{n-1} alpha_s^n) corrections to explore the numerical significance of higher-order perturbative and power corrections. We also derive explicit expressions for the O(beta_0 alpha_s^2) contributions to the kernels, and for the renormalon singularities corresponding to power corrections of order (Lambda/m_b)^2. Finally, we stud...
QCD evolution equations from conformal symmetry
Braun, V M
2014-01-01
QCD evolution equations in $\\text{MS}$-like schemes can be recovered from the same equations in a modified theory, QCD in non-integer $d=4-2\\epsilon$ dimensions, which enjoys exact scale and conformal invariance at the critical point. Restrictions imposed by the conformal symmetry of the modified theory allow one to obtain complete evolution kernels in integer (physical) dimensions at the given order of perturbation theory from the spectrum of anomalous dimensions added by the calculation of the special conformal anomaly at one order less. We use this technique to derive two-loop evolution equations for flavor-nonsinglet quark-antiquark light-ray operators that encode the scale dependence of generalized hadron parton distributions.
Hadron physics from lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Schaefer, Andreas [Regensburg Univ. (Germany). Inst. for Theoretical Physics
2016-11-01
Particle physics experiments at modern high luminosity particle accelerators achieve orders of magnitude higher count rates than what was possible ten or twenty years ago. This extremely large statistics allows to draw far reaching conclusions even from minute signals, provided that these signals are well understood by theory. This is, however, ever more difficult to achieve. Presently, technical and scientific progress in general and experimental progress in particle physics in particular, shows typically an exponential growth rate. For example, data acquisition and analysis are, among many other factor, driven by the development of ever more efficient computers and thus by Moore's law. Theory has to keep up with this development by also achieving an exponential increase in precision, which is only possible using powerful computers. This is true for both types of calculations, analytic ones as, e.g., in quantum field perturbation theory, and purely numerical ones as in Lattice QCD. As stated above such calculations are absolutely indispensable to make best use of the extremely costly large particle physics experiments. Thus, it is economically reasonable to invest a certain percentage of the cost of accelerators and experiments in related theory efforts. The basic ideas behind Lattice QCD simulations are the following: Because quarks and gluons can never be observed individually but are always ''confined'' into colorless hadrons, like the proton, all quark-gluon states can be expressed in two different systems of basis states, namely in a quark-gluon basis and the basis of hadron states. The proton, e.g., is an eigenstate of the latter, a specific quark-gluon configuration is part of the former. In the quark-gluon basis a physical hadron, like a proton, is given by an extremely complicated multi-particle wave function containing all effects of quantum fluctuations. This state is so complicated that it is basically impossible to model it
String theoretic QCD axions in the light of PLANCK and BICEP2
Energy Technology Data Exchange (ETDEWEB)
Choi, Kiwoon [Center for Theoretical Physics of the Universe, IBS, Daejeon (Korea, Republic of); Department of Physics, KAIST, Daejeon (Korea, Republic of); Jeong, Kwang Sik [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Seo, Min-Seok [Center for Theoretical Physics of the Universe, IBS, Daejeon (Korea, Republic of)
2014-05-15
The QCD axion solving the strong CP problem may originate from antisymmetric tensor gauge fields in compactified string theory, with a decay constant around the GUT scale. Such possibility appears to be ruled out now by the detection of tensor modes by BICEP2 and the PLANCK constraints on isocurvature density perturbations. A more interesting and still viable possibility is that the string theoretic QCD axion is charged under an anomalous U(1){sub A} gauge symmetry. In such case, the axion decay constant can be much lower than the GUT scale if moduli are stabilized near the point of vanishing Fayet-Illiopoulos term, and U(1){sub A}-charged matter fields get a vacuum value far below the GUT scale due to a tachyonic SUSY breaking scalar mass. We examine the symmetry breaking pattern of such models during the inflationary epoch with the Hubble expansion rate 10{sup 14} GeV, and identify the range of the QCD axion decay constant, as well as the corresponding relic axion abundance, consistent with known cosmological constraints. In addition to the case that the PQ symmetry is restored during inflation, there are other viable scenarios, including that the PQ symmetry is broken during inflation at high scales around 10{sup 16}-10{sup 17} GeV due to a large Hubble-induced tachyonic scalar mass from the U(1){sub A} D-term, while the present axion scale is in the range 10{sup 9}-5 x 10{sup 13} GeV, where the present value larger than 10{sup 12} GeV requires a fine-tuning of the axion misalignment angle. We also discuss the implications of our results for the size of SUSY breaking soft masses.
Heavy-light mesons in lattice HQET and QCD
Energy Technology Data Exchange (ETDEWEB)
Guazzini, D.
2007-12-15
We present a study of a combination of HQET and relativistic QCD to extract the b-quark mass and the B{sub s}-meson decay constant from lattice quenched simulations. We start from a small volume, where one can directly simulate the b-quark, and compute the connection to a large volume, where finite size effects are negligible, through a finite size technique. The latter consists of steps extrapolated to the continuum limit, where the b-region is reached through interpolations guided by the effective theory. With the lattice spacing given in terms of the Sommer's scale r{sub 0} and the experimental B{sub s} and K masses, we get the final results for the renormalization group invariant mass M{sub b}=6.88(10) GeV, translating into anti m{sub b}(anti m{sub b})=4.42(6) GeV in the MS scheme, and f{sub B{sub s}}=191(6) MeV for the decay constant. A renormalization condition for the chromo-magnetic operator, responsible, at leading order in the heavy quark mass expansion of HQET, for the mass splitting between the pseudoscalar and the vector channel in mesonic heavy-light bound states, is provided in terms of lattice correlations functions which well suits a non-perturbative computation involving a large range of renormalization scales and no valence quarks. The two-loop expression of the corresponding anomalous dimension in the Schroedinger functional (SF) scheme is computed starting from results in the literature; it requires a one-loop calculation in the SF scheme with a non-vanishing background field. The cutoff effects affecting the scale evolution of the renormalization factors are studied at one-loop order, and confirmed by non-perturbative quenched computations to be negligible for the numerical precision achievable at present. (orig.)
Combinatorics of Lattice QCD at Strong Coupling
Unger, Wolfgang
2014-01-01
Thermodynamics in the strong coupling limit of lattice QCD has features which may be similar to those of continuum QCD, such as a chiral critical end point and a nuclear liquid gas transition. Here I compare the combinatorics of staggered and Wilson fermions in the strong coupling limit for arbitrary number of colors and flavors. The partition functions can be considered as an expansions in hadronic spatial hoppings from the static limit, where both discretizations can be expressed via formulae with coefficients of distinct combinatorial interpretation. The corresponding multiplicites of hadronic states are evaluated using generalizations of Catalan numbers and Lucas polynomials. I outline how quantum Monte Carlo simulations can be carried out in general, and summarize recent results on the gauge corrections to the strong coupling limit.
Kozma, Gady
2012-01-01
We proved earlier that every measurable function on the circle, after a uniformly small perturbation, can be written as a power series (i.e. a series of exponentials with positive frequencies), which converges almost everywhere. Here we show that this result is basically sharp: the perturbation cannot be made smooth or even H\\"older. We discuss also a similar problem for perturbations with lacunary spectrum.
Energy Technology Data Exchange (ETDEWEB)
Roessner, Simon
2009-04-09
Quantum Chromodynamics (QCD) is the theory of the strong interaction within the Standard Model of elementary particles. Today's research in this area dedicates substantial resources to numeric solutions of the QCD field equations and experimental programs exploring the phases of QCD. This thesis proceeds along a complementary line - that of modelling QCD, with the aim of identifying its dominant degrees of freedom. This is possible by minimally coupling effective potentials for the Polyakov loop to Nambu-Jona-Lasinio models using temporal background fields to model chiral symmetry breaking respecting colour confinement. The fermion sign problem resulting from the minimal coupling is addressed in this work establishing a novel, systematically ordered approach. The modifications to the approximative order parameter of colour confinement, the Polyakov loop, are in direct connection with the fermion sign problem. Furthermore an effective coupling of quark densities of different flavours is induced. This mechanism, most likely also present in QCD, produces finite contributions to flavour off diagonal susceptibilities. Susceptibilities are amongst the most promising physical quantities for the experimental exploration of the phase transition at high temperatures and densities. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Harris, R.
1992-05-01
We present measurements of jet production and isolated prompt photon production in p{bar p} collisions at {radical}s = 1.8 TeV from the 1988--89 run of the Collider Detector at Fermilab (CDF). To test QCD with jets, the inclusive jet cross section (p{bar p} {yields} J + X) and two jet angular distributions (p{bar P} {yields} JJ + X) are compared to QCD predictions and are used to search for composite quarks. The ratio of the scaled jet cross sections at two Tevatron collision energies ({radical}s= 546 and 1800 GeV) is compared to QCD predictions for X{sub T} scaling violations. Also, we present the first evidence for QCD interference effects (color coherence) in third jet production (p{bar p} {yields} JJJ + X). To test QCD with photons, we present measurements of the transverse momentum spectrum of single isolated prompt photon production (p{bar p} {yields} {gamma} + X), double isolated prompt photon production (p{bar p} {yields} {gamma}{gamma} + X), and the angular distribution of photon-jet events (p{bar p} {yields} {gamma} J + X). We have also measured the isolated production ratio of {eta} and {pi}{sup 0} mesons (p{bar p} {yields} {eta} + X)/(p{bar p} {yields} {pi}{sup 0} + X) = 1.02 {plus minus} .15(stat) {plus minus} .23(sys).
Threshold resummation and higher order effects in QCD
Energy Technology Data Exchange (ETDEWEB)
Ringer, Felix Maximilian
2015-06-26
Quantum chromodynamics (QCD) is a quantum field theory that describes the strong interactions between quarks and gluons, the building blocks of all hadrons. Thanks to the experimental progress over the past decades, there has been an ever-growing need for QCD precision calculations for scattering processes involving hadrons. For processes at large momentum transfer, perturbative QCD offers a systematic approach for obtaining precise predictions. This approach relies on two key concepts: the asymptotic freedom of QCD and factorization. In a perturbative calculation at higher orders, the infrared cancellation between virtual and real emission diagrams generally leaves behind logarithmic contributions. In many observables relevant for hadronic scattering these logarithms are associated with a kinematic threshold and are hence known as ''threshold logarithms''. They become large when the available phase space for real gluon emission shrinks. In order to obtain a reliable prediction from QCD, the threshold logarithms need to be taken into account to all orders in the strong coupling constant, a procedure known as ''threshold resummation''. The main focus of my PhD thesis is on studies of QCD threshold resummation effects beyond the next-to-leading logarithmic order. Here we primarily consider the production of hadron pairs in hadronic collisions as an example. In addition, we also consider hadronic jet production, which is particularly interesting for the phenomenology at the LHC. For both processes, we fully take into account the non-trivial QCD color structure of the underlying partonic hard- scattering cross sections. We find that threshold resummation leads to sizable numerical effects in the kinematic regimes relevant for comparisons to experimental data.
Renormalization Group Invariance and Optimal QCD Renormalization Scale-Setting
Wu, Xing-Gang; Wang, Sheng-Quan; Fu, Hai-Bing; Ma, Hong-Hao; Brodsky, Stanley J; Mojaza, Matin
2014-01-01
A valid prediction from quantum field theory for a physical observable should be independent of the choice of renormalization scheme -- this is the primary requirement of renormalization group invariance (RGI). Satisfying scheme invariance is a challenging problem for perturbative QCD (pQCD), since truncated perturbation series do not automatically satisfy the requirements of the renormalization group. Two distinct approaches for satisfying the RGI principle have been suggested in the literature. One is the "Principle of Maximum Conformality" (PMC) in which the terms associated with the $\\beta$-function are absorbed into the scale of the running coupling at each perturbative order; its predictions are scheme and scale independent at every finite order. The other approach is the "Principle of Minimum Sensitivity" (PMS), which is based on local RGI; the PMS approach determines the optimal renormalization scale by requiring the slope of the approximant of an observable to vanish. In this paper, we present a deta...
Conformal couplings and "azimuthal matching" of QCD Pomerons
Marchal, N
2000-01-01
Using the asymptotic conformal invariance of perturbative QCD we derive the expression of the coupling of external states to all conformal spin-p components of the forward elastic amplitude. Using the wave-function formalism for structure functions at small x, we derive the perturbative coupling of the virtual photon for p= 1, which is maximal for linear transverse polarization. The non-perturbative coupling to the proton is discussed in terms of ``azimuthal matching'' between the proton color dipoles and the quark- antiquark configurations of the photon. As an application, the recent conjecture of a second QCD Pomeron related to the conformal spin-1 component is shown to rely upon a strong azimuthal matching of the p= 1 component in gamma* -proton scattering.
QCD collinear factorization, its extensions and the partonic distributions
Szymanowski, Lech
2012-01-01
I review the basics of the collinear factorization theorem applied primarily to deep inelastic scattering (DIS) involving forward parton distributions (PDFs) and the extensions of this theorem for exclusive processes probing non-forward parton distributions (GPDs), the generalized distribution amplitudes (GDAs) and the transition distribution amplitudes (TDAs). These QCD factorization theorem is an important tool in the description of hard processes in QCD. Whenever valid, it permits to represent the cross section or the scattering amplitude for such a process as a convolution in partonic momenta of a perturbatively calculable part (the coefficient function, CF) which involves the hard scale of the process with non-perturbative (soft) distributions of active partons inside the hadrons involved in a process. The reliability of the perturbatively determined hard part together with high precision experimental data on relevant observables gives a hope for the possibility to uncover fine details of interpartonic i...
Energy Technology Data Exchange (ETDEWEB)
Bolzoni, P.
2007-09-15
In this PhD thesis, we analyze and generalize the renormalization group approach to the resummation of large logarithms in the perturbative expansion due to soft and collinear multiparton emissions. In particular, we present a generalization of this approach to prompt photon production. It is interesting to see that also with the more intricate two-scale kinematics that characterizes prompt photon production in the soft limit, it remains true that resummation simply follows from general kinematic properties of the phase space. Also, this approach does not require a separate treatment of individual colour structures when more than one colour structure contributes to fixed order results. However, the resummation formulae obtained here turn out to be less predictive than previous results: this depends on the fact that here neither specific factorization properties of the cross section in the soft limit is assumed, nor that soft emission satisfies eikonal-like relations. We also derive resumation formulae to all logarithmic accuracy and valid for all values of rapidity for the prompt photon production and the Drell-Yan rapidity distributions. We show that for the fixed-target experiment E866/NuSea, the NLL resummation corrections are comparable to NLO fixed-order corrections and are crucial to obtain agreement with the data. Finally we outline also possible future applications of the renormalization group approach. (orig.)
Pion electric polarizability from lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Alexandru, Andrei; Lujan, Michael; Freeman, Walter; Lee, Frank [The George Washington University, 725 21st St. NW, Washington DC, 20052 (United States)
2016-01-22
Electromagnetic polarizabilities are important parameters for understanding the interaction between photons and hadrons. For pions these quantities are poorly constrained experimentally since they can only be measured indirectly. New experiments at CERN and Jefferson Lab are planned that will measure the polarizabilities more precisely. Lattice QCD can be used to compute these quantities directly in terms of quark and gluons degrees of freedom, using the background field method. We present results for the electric polarizability for two different quark masses, light enough to connect to chiral perturbation theory. These are currently the lightest quark masses used in polarizability studies.
Dyson--Schwinger Approach to Hamiltonian QCD
Campagnari, Davide R; Huber, Markus Q; Vastag, Peter; Ebadati, Ehsan
2016-01-01
Dyson--Schwinger equations are an established, powerful non-perturbative tool for QCD. In the Hamiltonian formulation of a quantum field theory they can be used to perform variational calculations with non-Gaussian wave functionals. By means of the DSEs the various $n$-point functions, needed in expectation values of observables like the Hamilton operator, can be thus expressed in terms of the variational kernels of our trial ansatz. Equations of motion for these variational kernels are derived by minimizing the energy density and solved numerically.
Fluctuations and correlations in high temperature QCD
Bellwied, R; Fodor, Z; Katz, S D; Pasztor, A; Ratti, C; Szabo, K K
2015-01-01
We calculate second- and fourth-order cumulants of conserved charges in a temperature range stretching from the QCD transition region towards the realm of (resummed) perturbation theory. We perform lattice simulations with staggered quarks; the continuum extrapolation is based on $N_t=10\\dots24$ in the crossover-region and $N_t=8\\dots16$ at higher temperatures. We find that the Hadron Resonance Gas model predictions describe the lattice data rather well in the confined phase. At high temperatures (above $\\sim$250 MeV) we find agreement with the three-loop Hard Thermal Loop results.
Dynamical gluon mass in QCD processes
Energy Technology Data Exchange (ETDEWEB)
Ducati, M.B. Gay; Sauter, W. [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Inst. de Fisica. Grupo de Fenomenologia de Particulas de Altas Energias (GFPAE)
2007-06-15
We perform phenomenological applications of modified gluon propagators and running coupling constants in scattering processes in Quantum Chromodynamics (QCD). The modified forms of propagators and running coupling constant are obtained by non-perturbative methods. The processes investigated includes the diffractive ones - proton-proton elastic scattering, light vector meson photo-production and double vector meson production in gamma-gamma scattering - as well as the pion and kaon meson form factors. The results are compared with experimental data (if available), showing a good agreement with a gluon with dynamical mass but do not indicate the correct gluon propagator functional form. (author)
Quarkonia at $T>0$ and lattice QCD
Rothkopf, Alexander
2016-01-01
We report here on recent progress in the determination of S-wave and P-wave heavy-quarkonium states at finite temperature. Our results are based on the combination of effective field theories with numerical lattice QCD simulations. These non-perturbative tools allow us to compute the heavy-quarkonium in-medium spectral functions, from which we in turn determine the melting temperatures of individual states and estimate phenomenologically relevant observables, such as the $\\psi^\\prime$ to J/$\\psi$ ratio in heavy-ion collisions.
Energy Technology Data Exchange (ETDEWEB)
Lutz, Matthias F.M., E-mail: m.lutz@gsi.de [GSI Helmholtzzentrum für Schwerionenforschung GmbH, D-64291 Darmstadt (Germany); Technische Universität Darmstadt, D-64289 Darmstadt (Germany); Lange, Jens Sören, E-mail: Soeren.Lange@exp2.physik.uni-giessen.de [II. Physikalisches Institut, Justus-Liebig-Universität Giessen, D-35392 Giessen (Germany); Pennington, Michael, E-mail: michaelp@jlab.org [Thomas Jefferson National Accelerator Facility, Newport News, VA 23606 (United States); Bettoni, Diego [Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, 44122 Ferrara (Italy); Brambilla, Nora [Physik Department, Technische Universität München, D-85747 Garching (Germany); Crede, Volker [Department of Physics, Florida State University, Tallahassee, FL 32306 (United States); Eidelman, Simon [Novosibirsk State University, Novosibirsk 630090 (Russian Federation); Budker Istitute of Nuclear Physics SB RAS, Novosibirsk 630090 (Russian Federation); Gillitzer, Albrecht [Institut für Kernphysik, Forschungszentrum Jülich GmbH, D-52425 Jülich (Germany); Gradl, Wolfgang [Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, D-55128 Mainz (Germany); Lang, Christian B. [Institut für Physik, Universität Graz, A-8010 Graz (Austria); Metag, Volker [II. Physikalisches Institut, Justus-Liebig-Universität Giessen, D-35392 Giessen (Germany); Nakano, Takashi [Research Center for Nuclear Physics, Osaka University, Osaka 567-0047 (Japan); and others
2016-04-15
We report on the EMMI Rapid Reaction Task Force meeting ‘Resonances in QCD’, which took place at GSI October 12–14, 2015. A group of 26 people met to discuss the physics of resonances in QCD. The aim of the meeting was defined by the following three key questions: • What is needed to understand the physics of resonances in QCD? • Where does QCD lead us to expect resonances with exotic quantum numbers? • What experimental efforts are required to arrive at a coherent picture? For light mesons and baryons only those with up, down and strange quark content were considered. For heavy–light and heavy–heavy meson systems, those with charm quarks were the focus. This document summarizes the discussions by the participants, which in turn led to the coherent conclusions we present here.
Zou, L P; Pak, D G
2013-01-01
We consider topological structure of classical vacuum solutions in quantum chromodynamics. Topologically non-equivalent vacuum configurations are classified by non-trivial second and third homotopy groups for coset of the color group SU(N) (N=2,3) under the action of maximal Abelian stability group. Starting with explicit vacuum knot configurations we study possible exact classical solutions as vacuum excitations. Exact analytic non-static knot solution in a simple CP^1 model in Euclidean space-time has been obtained. We construct an ansatz based on knot and monopole topological vacuum structure for searching new solutions in SU(2) and SU(3) QCD. We show that singular knot-like solutions in QCD in Minkowski space-time can be naturally obtained from knot solitons in integrable CP^1 models. A family of Skyrme type low energy effective theories of QCD admitting exact analytic solutions with non-vanishing Hopf charge is proposed.
Borsanyi, Sz; Kampert, K H; Katz, S D; Kawanai, T; Kovacs, T G; Mages, S W; Pasztor, A; Pittler, F; Redondo, J; Ringwald, A; Szabo, K K
2016-01-01
We present a full result for the equation of state (EoS) in 2+1+1 (up/down, strange and charm quarks are present) flavour lattice QCD. We extend this analysis and give the equation of state in 2+1+1+1 flavour QCD. In order to describe the evolution of the universe from temperatures several hundreds of GeV to several tens of MeV we also include the known effects of the electroweak theory and give the effective degree of freedoms. As another application of lattice QCD we calculate the topological susceptibility (chi) up to the few GeV temperature region. These two results, EoS and chi, can be used to predict the dark matter axion's mass in the post-inflation scenario and/or give the relationship between the axion's mass and the universal axionic angle, which acts as a initial condition of our universe.
Hubble parameter in QCD Universe for finite bulk viscosity
Energy Technology Data Exchange (ETDEWEB)
Tawfik, A.; Wahba, M. [Egyptian Center for Theoretical Physics (ECTP), MTI University, Al Mukattam, Cairo 11212 (Egypt); Mansour, H. [Department of Physics, Cairo University, Giza (Egypt); Harko, T. [Department of Physics and Center for Theoretical and Computational Physics, The University of Hong Kong, Pok Fu Lam Road, Hong Kong (China)
2010-12-01
We consider the influence of the perturbative bulk viscosity on the evolution of the Hubble parameter in the QCD era of the early Universe. For the geometry of the Universe we assume the homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker metric, while the background matter is assumed to be characterized by barotropic equations of state, obtained from recent lattice QCD simulations, and heavy-ion collisions, respectively. Taking into account a perturbative form for the bulk viscosity coefficient, we obtain the evolution of the Hubble parameter, and we compare it with its evolution for an ideal (non-viscous) cosmological matter. A numerical solution for the viscous QCD plasma in the framework of the causal Israel-Stewart thermodynamics is also obtained. Both the perturbative approach and the numerical solution qualitatively agree in reproducing the viscous corrections to the Hubble parameter, which in the viscous case turns out to be slightly different as compared to the non-viscous case. Our results are strictly limited within a very narrow temperature- or time-interval in the QCD era, where the quark-gluon plasma is likely dominant. (Copyright copyright 2010 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Phenomenology of the particle spectra in QCD jets in a modified leading logarithmic approximation
Energy Technology Data Exchange (ETDEWEB)
Dokshitzer, Yu.L. (Lund Univ. (Sweden). Dept. of Theoretical Physics); Khoze, V.A. (Durham Univ. (United Kingdom). Centre for Particle Theory); Troyan, S.I. (Institut Yadernoj Fiziki, Gatchina (Russia))
1992-07-01
A number of new results in the MLLA description of particle spectra in QCD jets have been derived and some more refined tests of the perturbative picture were discussed recently. In this paper we concentrate on the comparison of the perturbative predictions with existing data on particle momentum fraction distributions in e{sup +}e{sup -} annihilation into hadrons. (HSI).
Suppressing the QCD axion abundance by hidden monopoles
Energy Technology Data Exchange (ETDEWEB)
Kawasaki, Masahiro [Tokyo Univ., Chiba (Japan). Inst. for Cosmic Ray Research; Tokyo Univ., Chiba (Japan). Kavli IPMU (WPI), UTIAS; Takahashi, Fuminobu [Tokyo Univ., Miyagi (Japan). Dept. of Physics; Tokyo Univ., Chiba (Japan). Kavli IPMU (WPI), UTIAS; Yamada, Masaki [Tokyo Univ., Chiba (Japan). Inst. for Cosmic Ray Research; Tokyo Univ., Chiba (Japan). Kavli IPMU (WPI), UTIAS; DESY Hamburg (Germany)
2015-11-15
We study the Witten effect of hidden monopoles on the QCD axion dynamics, and show that its abundance as well as isocurvature perturbations can be significantly suppressed if there is a sufficient amount of hidden monopoles. When the hidden monopoles make up a significant fraction of dark matter, the Witten effect suppresses the abundance of axion with the decay constant smaller than 10{sup 12} GeV. The cosmological domain wall problem of the QCD axion can also be avoided, relaxing the upper bound on the decay constant when the Peccei-Quinn symmetry is spontaneously broken after inflation.
Suppressing the QCD axion abundance by hidden monopoles
Directory of Open Access Journals (Sweden)
Masahiro Kawasaki
2016-02-01
Full Text Available We study the Witten effect of hidden monopoles on the QCD axion dynamics, and show that its abundance as well as isocurvature perturbations can be significantly suppressed if there is a sufficient amount of hidden monopoles. When the hidden monopoles make up a significant fraction of dark matter, the Witten effect suppresses the abundance of axion with the decay constant smaller than 1012GeV. The cosmological domain wall problem of the QCD axion can also be avoided, relaxing the upper bound on the decay constant when the Peccei–Quinn symmetry is spontaneously broken after inflation.
Dimensional structural constants from chiral and conformal bosonization of QCD
Andrianov, A A; Ebert, D; Mann, T F; Mann, Th. Feld
1997-01-01
We derive the dimensional non-perturbative part of the QCD effective ac= tion for scalar and pseudoscalar meson fields by means of chiral and conformal bosonization. The related structural coupling constants L_5 and L_8 of th= e chiral lagrangian are estimated using general relations which are valid i= n a variety of chiral bosonization models without explicit reference to model parameters. The asymptotics for large scalar fields in QCD is elaborated,= and model-independent constraints on dimensional coupling constants of the effective meson lagrangian are evaluated. We determine also the interacti= on between scalar quarkonium and the gluon density and obtain the scalar glueball-quarkonium potential.
Some new results in O(a) improved lattice QCD
Luscher, Martin; Sommer, Rainer; Weisz, Peter; Wittig, Hartmut; Wolff, Ulli
1996-01-01
It is shown how on-shell O(a) improvement can be implemented non-perturbatively in lattice QCD with Wilson quarks. Improvement conditions are obtained by requiring the PCAC relation to hold exactly in certain matrix elements. These are derived from the QCD Schrödinger functional which enables us to simulate directly at vanishing quark masses. In the quenched approximation and for bare couplings in the range $0\\leq g_0\\leq 1$, we determine the improved action, the improved axial current, the additive renormalization of the quark mass and the isospin current normalization constants Z_A and Z_V.
Energy Technology Data Exchange (ETDEWEB)
Shindler, A. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2007-07-15
I review the theoretical foundations, properties as well as the simulation results obtained so far of a variant of the Wilson lattice QCD formulation: Wilson twisted mass lattice QCD. Emphasis is put on the discretization errors and on the effects of these discretization errors on the phase structure for Wilson-like fermions in the chiral limit. The possibility to use in lattice simulations different lattice actions for sea and valence quarks to ease the renormalization patterns of phenomenologically relevant local operators, is also discussed. (orig.)
Sadeghi, Jafar
2012-01-01
In this review article we consider a special case of D=5, $\\mathcal{N}=2$ supergravity called the STU model. We apply the gauge/gravity correspondence to the STU model to gain insight into properties of the quark-gluon plasma. Given that the quark-gluon plasma is in reality described by QCD, therefore we call our study STU/QCD correspondence. First, we investigate the thermodynamics and hydrodynamics of the STU background. Then we use dual picture of the theory, which is type IIB string theory, to obtain the drag force and jet-quenching parameter of an external probe quark.
Applications Of Chiral Perturbation Theory
Mohta, V
2005-01-01
Effective field theory techniques are used to describe the spectrum and interactions of hadrons. The mathematics of classical field theory and perturbative quantum field theory are reviewed. The physics of effective field theory and, in particular, of chiral perturbation theory and heavy baryon chiral perturbation theory are also reviewed. The geometry underlying heavy baryon chiral perturbation theory is described in detail. Results by Coleman et. al. in the physics literature are stated precisely and proven. A chiral perturbation theory is developed for a multiplet containing the recently- observed exotic baryons. A small coupling expansion is identified that allows the calculation of self-energy corrections to the exotic baryon masses. Opportunities in lattice calculations are discussed. Chiral perturbation theory is used to study the possibility of two multiplets of exotic baryons mixed by quark masses. A new symmetry constraint on reduced partial widths is identified. Predictions in the literature based ...
Chiral Random Matrix Theory and Chiral Perturbation Theory
Damgaard, P H
2011-01-01
Spontaneous breaking of chiral symmetry in QCD has traditionally been inferred indirectly through low-energy theorems and comparison with experiments. Thanks to the understanding of an unexpected connection between chiral Random Matrix Theory and chiral Perturbation Theory, the spontaneous breaking of chiral symmetry in QCD can now be shown unequivocally from first principles and lattice simulations. In these lectures I give an introduction to the subject, starting with an elementary discussion of spontaneous breaking of global symmetries.
Chiral Random Matrix Theory and Chiral Perturbation Theory
Energy Technology Data Exchange (ETDEWEB)
Damgaard, Poul H, E-mail: phdamg@nbi.dk [Niels Bohr International Academy and Discovery Center, The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen (Denmark)
2011-04-01
Spontaneous breaking of chiral symmetry in QCD has traditionally been inferred indirectly through low-energy theorems and comparison with experiments. Thanks to the understanding of an unexpected connection between chiral Random Matrix Theory and chiral Perturbation Theory, the spontaneous breaking of chiral symmetry in QCD can now be shown unequivocally from first principles and lattice simulations. In these lectures I give an introduction to the subject, starting with an elementary discussion of spontaneous breaking of global symmetries.
Akemann, G; Shifrin, L; Wettig, T
2007-01-01
For QCD at non-zero chemical potential $\\mu$, the Dirac eigenvalues are scattered in the complex plane. We define a notion of ordering for individual eigenvalues in this case and derive the distributions of individual eigenvalues from random matrix theory (RMT). We distinguish two cases depending on the parameter $\\alpha=\\mu^2 F^2 V$, where $V$ is the volume and $F$ is the familiar low-energy constant of chiral perturbation theory. For small $\\alpha$, we use a Fredholm determinant expansion and observe that already the first few terms give an excellent approximation. For large $\\alpha$, all spectral correlations are rotationally invariant, and exact results can be derived. We compare the RMT predictions to lattice data and in both cases find excellent agreement in the topological sectors $\
Energy Technology Data Exchange (ETDEWEB)
Karami, K.; Abdolmaleki, A.; Asadzadeh, S. [University of Kurdistan, Department of Physics, Sanandaj (Iran, Islamic Republic of); Safari, Z. [Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of)
2013-09-15
Within the framework of modified teleparallel gravity, we reconstruct a f(T) model corresponding to the QCD ghost dark energy scenario. For a spatially flat FRW universe containing only the pressureless matter, we obtain the time evolution of the torsion scalar T (or the Hubble parameter). Then, we calculate the effective torsion equation of state parameter of the QCD ghost f(T)-gravity model as well as the deceleration parameter of the universe. Furthermore, we fit the model parameters by using the latest observational data including SNeIa, CMB and BAO data. We also check the viability of our model using a cosmographic analysis approach. Moreover, we investigate the validity of the generalized second law (GSL) of gravitational thermodynamics for our model. Finally, we point out the growth rate of matter density perturbation. We conclude that in QCD ghost f(T)-gravity model, the universe begins a matter dominated phase and approaches a de Sitter regime at late times, as expected. Also this model is consistent with current data, passes the cosmographic test, satisfies the GSL and fits the data of the growth factor well as the {Lambda}CDM model. (orig.)
Quenching parameter in a holographic thermal QCD
Patra, Binoy Krishna
2016-01-01
We have calculated the quenching parameter, $\\hat{q}$ in a model-independent way using the gauge-gravity duality. In earlier calculations, the geometry in the gravity side at finite temperature was usually taken as the pure AdS blackhole metric for which the dual gauge theory becomes conformally invariant unlike QCD. Therefore we use a metric which incorporates the fundamental quarks by embedding the coincident D7 branes in the Klebanov-Tseytlin background and a finite temperature is switched on by inserting a black hole into the background, known as OKS-BH metric. Further inclusion of an additional UV cap to the metric prepares the dual gauge theory to run similar to thermal QCD. Moreover $\\hat{q}$ is usually defined in the literature from the Glauber-model perturbative QCD evaluation of the Wilson loop, which has no reasons to hold if the coupling is large and is thus against the main idea of gauge-gravity duality. Thus we use an appropriate definition of $\\hat{q}$: $\\hat{q} L^- = 1/L^2$, where $L$ is the s...
QCD in heavy quark production and decay
Energy Technology Data Exchange (ETDEWEB)
Wiss, J. [Univ. of Illinois, Urbana, IL (United States)
1997-06-01
The author discusses how QCD is used to understand the physics of heavy quark production and decay dynamics. His discussion of production dynamics primarily concentrates on charm photoproduction data which are compared to perturbative QCD calculations which incorporate fragmentation effects. He begins his discussion of heavy quark decay by reviewing data on charm and beauty lifetimes. Present data on fully leptonic and semileptonic charm decay are then reviewed. Measurements of the hadronic weak current form factors are compared to the nonperturbative QCD-based predictions of Lattice Gauge Theories. He next discusses polarization phenomena present in charmed baryon decay. Heavy Quark Effective Theory predicts that the daughter baryon will recoil from the charmed parent with nearly 100% left-handed polarization, which is in excellent agreement with present data. He concludes by discussing nonleptonic charm decay which is traditionally analyzed in a factorization framework applicable to two-body and quasi-two-body nonleptonic decays. This discussion emphasizes the important role of final state interactions in influencing both the observed decay width of various two-body final states as well as modifying the interference between interfering resonance channels which contribute to specific multibody decays. 50 refs., 77 figs.
B0-B0bar mixing in the static approximation from the Schroedinger Functional and twisted mass QCD
Palombi, F.; Papinutto, M.; Pena., C; Wittig, H.
2005-01-01
We discuss the renormalisation properties of parity-odd Delta B=2 operators with the heavy quark treated in the static approximation. Via twisted mass QCD (tmQCD), these operators provide the matrix elements relevant for the B0-B0bar mixing amplitude. The layout of a non-perturbative renormalisation programme for the operator basis, using Schroedinger Functional techniques, is described. Finally, we report our results for a one-loop perturbative study of various renormalisation schemes with W...
Baryon interactions in lattice QCD: the direct method vs. the HAL QCD potential method
Iritani, Takumi
2016-01-01
We make a detailed comparison between the direct method and the HAL QCD potential method for the baryon-baryon interactions, taking the $\\Xi\\Xi$ system at $m_\\pi= 0.51$ GeV in 2+1 flavor QCD and using both smeared and wall quark sources. The energy shift $\\Delta E_\\mathrm{eff}(t)$ in the direct method shows the strong dependence on the choice of quark source operators, which means that the results with either (or both) source are false. The time-dependent HAL QCD method, on the other hand, gives the quark source independent $\\Xi\\Xi$ potential, thanks to the derivative expansion of the potential, which absorbs the source dependence to the next leading order correction. The HAL QCD potential predicts the absence of the bound state in the $\\Xi\\Xi$($^1$S$_0$) channel at $m_\\pi= 0.51$ GeV, which is also confirmed by the volume dependence of finite volume energy from the potential. We also demonstrate that the origin of the fake plateau in the effective energy shift $\\Delta E_\\mathrm{eff}(t)$ at $t \\sim 1$ fm can b...
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; Deshpande, Abhay L.; Gao, Haiyan; McKeown, Robert D.; Meyer, Curtis A.; Meziani, Zein-Eddine; Milner, Richard G.; Qiu, Jianwei; Richards, David G.; Roberts, Craig D.
2015-02-26
This White Paper presents the recommendations and scientific conclusions from the Town Meeting on QCD and Hadronic Physics that took place in the period 13-15 September 2014 at Temple University as part of the NSAC 2014 Long Range Planning process. The meeting was held in coordination with the Town Meeting on Phases of QCD and included a full day of joint plenary sessions of the two meetings. The goals of the meeting were to report and highlight progress in hadron physics in the seven years since the 2007 Long Range Plan (LRP07), and present a vision for the future by identifying the key questions and plausible paths to solutions which should define the next decade. The introductory summary details the recommendations and their supporting rationales, as determined at the Town Meeting on QCD and Hadron Physics, and the endorsements that were voted upon. The larger document is organized as follows. Section 2 highlights major progress since the 2007 LRP. It is followed, in Section 3, by a brief overview of the physics program planned for the immediate future. Finally, Section 4 provides an overview of the physics motivations and goals associated with the next QCD frontier: the Electron-Ion-Collider.
Mueller, Katharina
2016-01-01
Recent measurements from the ATLAS, CMS and LHCb collaborations are testing QCD with unprecedented precision and in a new energy regime. Inclusive jet, isolated photon, vector boson and heavy quark production cross section measurements are reported here including a selection of first results at the new frontier collision energy of 13 TeV.
Phenomenology from lattice QCD
Lellouch, L P
2003-01-01
After a short presentation of lattice QCD and some of its current practical limitations, I review recent progress in applications to phenomenology. Emphasis is placed on heavy-quark masses and on hadronic weak matrix elements relevant for constraining the CKM unitarity triangle. The main numerical results are highlighted in boxes.
Nuclear Parity Violation from Lattice QCD
Kurth, Thorsten; Rinaldi, Enrico; Vranas, Pavlos; Nicholson, Amy; Strother, Mark; Walker-Loud, Andre
2015-01-01
The electroweak interaction at the level of quarks and gluons are well understood from precision measurements in high energy collider experiments. Relating these fundamental parameters to Hadronic Parity Violation in nuclei however remains an outstanding theoretical challenge. One of the most interesting observables in this respect is the parity violating hadronic neutral current: it is hard to measure in collider experiments and is thus the least constrained observable of the Standard Model. Precision measurements of parity violating transitions in nuclei can help to improve these constraints. In these systems however, the weak interaction is masked by effects of the seven orders of magnitude stronger non-perturbative strong interaction. Therefore, in order to relate experimental measurements of the parity violating pion-nucleon couplings to the fundamental Lagrangian of the SM, these non-perturbative effects have to be well understood. In this paper, we are going to present a Lattice QCD approach for comput...
Recent results on QCD thermodynamics: lattice QCD versus Hadron Resonance Gas model
Borsanyi, Szabolcs; Hoelbling, Christian; Katz, Sandor D; Krieg, Stefan; Ratti, Claudia; Szabo, Kalman K
2010-01-01
We present our most recent investigations on the QCD cross-over transition temperatures with 2+1 staggered flavours and one-link stout improvement [JHEP 1009:073, 2010]. We extend our previous two studies [Phys. Lett. B643 (2006) 46, JHEP 0906:088 (2009)] by choosing even finer lattices ($N_t$=16) and we work again with physical quark masses. All these results are confronted with the predictions of the Hadron Resonance Gas model and Chiral Perturbation Theory for temperatures below the transition region. Our results can be reproduced by using the physical spectrum in these analytic calculations. A comparison with the results of the hotQCD collaboration is also discussed.
Nayfeh, Ali H
2008-01-01
1. Introduction 1 2. Straightforward Expansions and Sources of Nonuniformity 23 3. The Method of Strained Coordinates 56 4. The Methods of Matched and Composite Asymptotic Expansions 110 5. Variation of Parameters and Methods of Averaging 159 6. The Method of Multiple Scales 228 7. Asymptotic Solutions of Linear Equations 308 References and Author Index 387 Subject Index 417
Higher Twist Distribution Amplitudes of the Nucleon in QCD
Braun, V M; Mahnke, N; Stein, E
2000-01-01
We present the first systematic study of higher-twist light-cone distribution amplitudes of the nucleon in QCD. We find that the valence three-quark state is described at small transverse separations by eight independent distribution amplitudes. One of them is leading twist-3, three distributions are twist-4 and twist-5, respectively, and one is twist-6. A complete set of distribution amplitudes is constructed, which satisfies equations of motion and constraints that follow from conformal expansion. Nonperturbative input parameters are estimated from QCD sum rules.
Generalized Weinberg Sum Rules in Deconstructed QCD
Sekhar-Chivukula, R; Tanabashi, Masaharu; Kurachi, Masafumi; Tanabashi, Masaharu
2004-01-01
Recently, Son and Stephanov have considered an "open moose" as a possible dual model of a QCD-like theory of chiral symmetry breaking. In this note we demonstrate that although the Weinberg sum rules are satisfied in any such model, the relevant sums converge very slowly and in a manner unlike QCD. Further, we show that such a model satisfies a set of generalized sum rules. These sum rules can be understood by looking at the operator product expansion for the correlation function of chiral currents, and correspond to the absence of low-dimension gauge-invariant chiral symmetry breaking condensates. These results imply that, regardless of the couplings and F-constants chosen, the open moose is not the dual of any QCD-like theory of chiral symmetry breaking. We also show that the generalized sum rules lead to a compact expression for the difference of vector- and axial-current correlation functions. This expression allows for a simple formula for the S parameter (L_10), which implies that S is always positive a...
QCD phase diagram from finite energy sum rules
Ayala, Alejandro; Dominguez, C A; Gutierrez, Enif; Loewe, M; Raya, Alfredo
2011-01-01
We study the QCD phase diagram at finite temperature and baryon chemical potential by relating the behavior of the light-quark condensate to the threshold energy for the onset of perturbative QCD. These parameters are connected to the chiral symmetry restoration and the deconfinement phase transition, respectively. This relation is obtained in the framework of finite energy QCD sum rules at finite temperature and density, with input from Schwinger-Dyson methods to determine the light-quark condensate. Results indicate that both critical temperatures are basically the same within some 3% accuracy. We also obtain bounds for the position of the critical end point, mu_{B c} >~ 300 MeV and T_c <~ 185 MeV.
Revisiting strong coupling QCD at finite baryon density and temperature
Fromm, M
2008-01-01
The strong coupling limit ($\\beta_{gauge}=0$) of lattice QCD with staggered fermions enjoys the same non-perturbative properties as continuum QCD, namely confinement and chiral symmetry breaking. In contrast to the situation at weak coupling, the sign problem which appears at finite density can be brought under control for a determination of the full (mu,T) phase diagram by Monte Carlo simulations. Further difficulties with efficiency and ergodicity of the simulations, especially at the strongly first-order, low-T, finite-mu transition, are addressed respectively with a worm algorithm and multicanonical sampling. Our simulations reveal sizeable corrections to the old results of Karsch and Muetter. Comparison with analytic mean-field determinations of the phase diagram shows discrepancies of O(10) in the location of the QCD critical point.
Topics in Effective Field Theory for Lattice QCD
Walker-Loud, A
2006-01-01
In this work, we extend and apply effective field theory techniques to systematically understand a subset of lattice artifacts which pollute the lattice correlation functions for a few processes of physical interest. Where possible, we compare to existing lattice QCD calculations. In particular, we extend the heavy baryon Lagrangian to the next order in partially quenched chiral perturbation theory and use it to compute the masses of the lightest spin-1/2 and spin-3/2 baryons to next-to-next-to leading order. We then construct the twisted mass chiral Lagrangian for baryons and apply it to compute the lattice spacing corrections to the baryon masses simulated with twisted mass lattice QCD. We extend computations of the nucleon electromagnetic structure to account for finite volume effects, as these observables are particularly sensitive to the finite extent of the lattice. We resolve subtle peculiarities for lattice QCD simulations of polarizabilities and we show that using background field techniques, one can...
Pion Structure in Qcd: from Theory to Lattice to Experimental Data
Bakulev, A. P.; Mikhailov, S. V.; Pimikov, A. V.; Stefanis, N. G.
We describe the present status of the pion distribution amplitude (DA) as it originates from several sources: (i) a nonperturbative approach based on QCD sum rules with nonlocal condensates, (ii) an O(as) QCD analysis of the CLEO data on Fgg*p(Q2) with asymptotic and renormalon models for higher twists and (iii) recent high-precision lattice QCD calculations of the second moment of the pion DA. We show predictions for the pion electromagnetic form factor, obtained in analytic QCD perturbation theory, and compare it with the JLab data on Fp(Q2). We also discuss in this context an improved model for nonlocal condensates in QCD and show its consequences for the pion DA and the gg*p transition form factor. We include a brief analysis of meson-induced massive lepton (muon) Drell-Yan production for the process p-Nm+m-X, considering both an unpolarized nucleon target and longitudinally polarized protons.
The generalized scheme-independent Crewther relation in QCD
Energy Technology Data Exchange (ETDEWEB)
Shen, Jian-Ming; Wu, Xing-Gang; Ma, Yang; Brodsky, Stanley J.
2017-07-01
The Principle of Maximal Conformality (PMC) provides a systematic way to set the renormalization scales order-by-order for any perturbative QCD calculable processes. The resulting predictions are independent of the choice of renormalization scheme, a requirement of renormalization group invariance. The Crewther relation, which was originally derived as a consequence of conformally invariant field theory, provides a remarkable connection between two observables when the β function vanishes: one can show that the product of the Bjorken sum rule for spin-dependent deep inelastic lepton–nucleon scattering times the Adler function, defined from the cross section for electron–positron annihilation into hadrons, has no pQCD radiative corrections. The “Generalized Crewther Relation” relates these two observables for physical QCD with nonzero β function; specifically, it connects the non-singlet Adler function (Dns) to the Bjorken sum rule coefficient for polarized deep-inelastic electron scattering (CBjp) at leading twist. A scheme-dependent ΔCSB-term appears in the analysis in order to compensate for the conformal symmetry breaking (CSB) terms from perturbative QCD. In conventional analyses, this normally leads to unphysical dependence in both the choice of the renormalization scheme and the choice of the initial scale at any finite order. However, by applying PMC scale-setting, we can fix the scales of the QCD coupling unambiguously at every order of pQCD. The result is that both Dns and the inverse coefficient CBjp-1 have identical pQCD coefficients, which also exactly match the coefficients of the corresponding conformal theory. Thus one obtains a new generalized Crewther relation for QCD which connects two effective charges, αˆd(Q)=Σi≥1αˆg1i(Qi), at their respective physical scales. This identity is independent of the choice of the renormalization scheme at any finite order, and the dependence on the choice of the initial scale is negligible. Similar
The generalized scheme-independent Crewther relation in QCD
Directory of Open Access Journals (Sweden)
Jian-Ming Shen
2017-07-01
Full Text Available The Principle of Maximal Conformality (PMC provides a systematic way to set the renormalization scales order-by-order for any perturbative QCD calculable processes. The resulting predictions are independent of the choice of renormalization scheme, a requirement of renormalization group invariance. The Crewther relation, which was originally derived as a consequence of conformally invariant field theory, provides a remarkable connection between two observables when the β function vanishes: one can show that the product of the Bjorken sum rule for spin-dependent deep inelastic lepton–nucleon scattering times the Adler function, defined from the cross section for electron–positron annihilation into hadrons, has no pQCD radiative corrections. The “Generalized Crewther Relation” relates these two observables for physical QCD with nonzero β function; specifically, it connects the non-singlet Adler function (Dns to the Bjorken sum rule coefficient for polarized deep-inelastic electron scattering (CBjp at leading twist. A scheme-dependent ΔCSB-term appears in the analysis in order to compensate for the conformal symmetry breaking (CSB terms from perturbative QCD. In conventional analyses, this normally leads to unphysical dependence in both the choice of the renormalization scheme and the choice of the initial scale at any finite order. However, by applying PMC scale-setting, we can fix the scales of the QCD coupling unambiguously at every order of pQCD. The result is that both Dns and the inverse coefficient CBjp−1 have identical pQCD coefficients, which also exactly match the coefficients of the corresponding conformal theory. Thus one obtains a new generalized Crewther relation for QCD which connects two effective charges, αˆd(Q=∑i≥1αˆg1i(Qi, at their respective physical scales. This identity is independent of the choice of the renormalization scheme at any finite order, and the dependence on the choice of the initial scale is
Differential Higgs boson pair production at next-to-next-to-leading order in QCD
Energy Technology Data Exchange (ETDEWEB)
Florian, Daniel de; Mazzitelli, Javier [UNSAM, Campus Miguelete, Buenos Aires (Argentina). International Center for Advanced Studies (ICAS); Grazzini, Massimiliano; Hanga, Catalin; Lindert, Jonas M. [Zuerich Univ. (Switzerland). Physik-Inst.; Kallweit, Stefan [Mainz Univ. (Germany). PRISMA Cluster of Excellence; Maierhoefer, Philipp [Freiburg Univ. (Germany). Physikalisches Inst.; Rathlev, Dirk [Deutsches Elektronen-Synchrotron, Hamburg (Germany). Theory Group
2016-06-15
We report on the first fully differential calculation for double Higgs boson production through gluon fusion in hadron collisions up to next-to-next-to-leading order (NNLO) in QCD perturbation theory. The calculation is performed in the heavy-top limit of the Standard Model, and in the phenomenological results we focus on pp collisions at √(s)=14 TeV. We present differential distributions through NNLO for various observables including the transverse-momentum and rapidity distributions of the two Higgs bosons. NNLO corrections are at the level of 10%-25% with respect to the next-to-leading order (NLO) prediction with a residual scale uncertainty of 5%-15% and an overall mild phase-space dependence. Only at NNLO the perturbative expansion starts to converge yielding overlapping scale uncertainty bands between NNLO and NLO in most of the phase-space. The calculation includes NLO predictions for pp→HH+jet+X. Corrections to the corresponding distributions exceed 50% with a residual scale dependence of 20%-30%.
Differential Higgs Boson Pair Production at Next-to-Next-to-Leading Order in QCD
de Florian, Daniel; Hanga, Catalin; Kallweit, Stefan; Lindert, Jonas M; Maierhöfer, Philipp; Mazzitelli, Javier; Rathlev, Dirk
2016-01-01
We report on the first fully differential calculation for double Higgs boson production through gluon fusion in hadron collisions up to next-to-next-to-leading order (NNLO) in QCD perturbation theory. The calculation is performed in the heavy-top limit of the Standard Model, and in the phenomenological results we focus on pp collisions at 14 TeV. We present differential distributions through NNLO for various observables including the transverse-momentum and rapidity distributions of the two Higgs bosons. NNLO corrections are at the level of 10%-25% with respect to the next-to-leading order (NLO) prediction with a residual scale uncertainty of 5%-15% and an overall mild phase-space dependence. Only at NNLO the perturbative expansion starts to converge yielding overlapping scale uncertainty bands between NNLO and NLO in most of the phase-space. The calculation includes NLO predictions for pp -> HH+jet+X. Corrections to the corresponding distributions exceed 50% with a residual scale dependence of 20%-30%.