Analytic continuation and perturbative expansions in QCD
Czech Academy of Sciences Publication Activity Database
Caprini, I.; Fischer, Jan
2002-01-01
Roč. 24, - (2002), s. 127-135 ISSN 1434-6044 R&D Projects: GA MPO RP-4210/69 Institutional research plan: CEZ:AV0Z1010920 Keywords : perturbative expansion * quantum chromodynamics * infrared ambiguity * essential singularities Subject RIV: BF - Elementary Particles and High Energy Physics Impact factor: 6.162, year: 2002
The Operator Product Expansion Beyond Perturbation Theory in QCD
International Nuclear Information System (INIS)
Dominguez, C. A.
2011-01-01
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 τ-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.
Static QCD potential at rQCD-1: Perturbative expansion and operator-product expansion
International Nuclear Information System (INIS)
Sumino, Y.
2007-01-01
We analyze the static QCD potential V QCD (r) in the distance region 0.1 fm QCD (r) analytically. Higher-order terms are estimated by large-β 0 approximation or by renormalization group, and the renormalization scale is varied around the minimal-sensitivity scale. A 'Coulomb'+linear potential can be identified with the scale-independent and renormalon-free part of the prediction and can be separated from the renormalon-dominating part. (II) In the frame of OPE, we define two types of renormalization schemes for the leading Wilson coefficient. One scheme belongs to the class of conventional factorization schemes. The other scheme belongs to a new class, which is independent of the factorization scale, derived from a generalization of the Coulomb+linear potential of (I). The Wilson coefficient is free from IR renormalons and IR divergences in both schemes. We study properties of the Wilson coefficient and of the corresponding nonperturbative contribution δE US (r) in each scheme. (III) We compare numerically perturbative predictions of the Wilson coefficient and lattice computations of V QCD (r) when n l =0. We confirm either correctness or consistency (within uncertainties) of the theoretical predictions made in (II). Then we perform fits to simultaneously determine δE US (r) and r 0 Λ MS 3-loop (relation between lattice scale and Λ MS ). As for the former quantity, we improve bounds as compared to the previous determination; as for the latter quantity, our analysis provides a new method for its determination. We find that (a) δE US (r)=0 is disfavored, and (b) r 0 Λ MS 3-loop =0.574±0.042. We elucidate the mechanism for the sensitivities and examine sources of errors in detail
Numerical studies of QCD renormalons in high-order perturbative expansions
International Nuclear Information System (INIS)
Bauer, Clemens
2013-01-01
Perturbative expansions in four-dimensional non-Abelian gauge theories such as Quantum Chromodynamics (QCD) are expected to be divergent, at best asymptotic. One reason is that it is impossible to strictly exclude from the relevant Feynman diagrams those energy regions in which a perturbative treatment is inapplicable. The divergent nature of the series is then signaled by a rapid (factorial) growth of the perturbative expansion coefficients, commonly referred to as a renormalon. In QCD, the most severe divergences occur in the infrared (IR) limit and therefore they are classified as IR renormalons. Their appearance can be understood within the well-accepted Operator Product Expansion (OPE) framework. According to the OPE, the perturbative calculation of a physical observable must be amended by non-perturbative power corrections that come in the form of condensates, universal characteristics of the rich QCD vacuum structure. Adding up perturbative and non-perturbative contributions, the ambiguity due to the renormalon cancels and the physical observable is well-defined. Although the field has made considerable progress in the last twenty years, a proof of renormalon existence is still pending. It has only been tested assuming strong simplifications or in toy models. The aim of this thesis is to provide the first numerical evidence for renormalon existence in the gauge sector of QCD. We use Numerical Stochastic Perturbation Theory (NSPT) to directly obtain perturbative coefficients within lattice regularization, a means to replace continuum spacetime by a four-dimensional hypercubic lattice. A peculiar feature of NSPT are comparatively low simulation costs when reaching high expansion orders. We examine two distinct observables: the static self-energy of an isolated quark and the elementary plaquette. Following the OPE classification, the static quark self-energy is ideally suited for a renormalon study. Taking into account peculiarities of the lattice approach such
Analytic continuation in perturbative QCD
International Nuclear Information System (INIS)
Caprini, Irinel
2002-01-01
We discuss some attempts to improve standard perturbative expansion in QCD by using the analytic continuation in the momentum and the Borel complex planes. We first analyse the momentum-plane analyticity properties of the Borel-summed Green functions in perturbative QCD and the connection between the Landau singularities and the infrared renormalons. By using the analytic continuation in the Borel complex plane, we propose a new perturbative series replacing the standard expansion in powers of the normalized coupling constant a. The new expansion functions have branch point and essential singularities at the origin of the complex a-plane and divergent Taylor expansions in powers of a. On the other hand the modified expansion of the QCD correlators is convergent under rather conservative conditions. (author)
International Nuclear Information System (INIS)
Mueller, A.H.
1986-03-01
A brief review of some of the recent progress in perturbative QCD is given (heavy quark production, small-x physics, minijets and related topics, classical simulations in high energy reactions, coherence and the string effect)
The {β}-expansion formalism in perturbative QCD and its extension
Energy Technology Data Exchange (ETDEWEB)
Kataev, A.L. [Institute for Nuclear Research of the Academy of Sciences of Russia,60th October Anniversary Prospect 7a, 117312, Moscow (Russian Federation); Moscow Institute of Physics and Technology,Institutskii per. 9, 141700, Dolgoprudny, Moscow Region (Russian Federation); Mikhailov, S.V. [Bogoliubov Laboratory of Theoretical Physics, JINR,Joliot-Curie 6, 141980 Dubna (Russian Federation)
2016-11-11
We discuss the {β}-expansion for renormalization group invariant quantities tracing this expansion to the different contractions of the corresponding incomplete BPHZ R-operation. All of the coupling renormalizations, which follow from these contractions, should be taken into account for the {β}-expansion. We illustrate this feature considering the nonsinglet Adler function D{sup NS} in the third order of perturbation. We propose a generalization of the {β}-expansion for the renormalization group covariant quantities — the {β,γ}-expansion.
Perturbative QCD and exclusive processes
International Nuclear Information System (INIS)
Bennett, J.; Hawes, F.; Zhao, M.; Zyla, P.
1991-01-01
The authors discuss perturbation theory as applied to particle physics calculations. In particle physics one is generally interested in the scattering amplitude for a system going from some initial state to a final state. The intermediate state or states are unknown. To get the scattering amplitude it is necessary to sum the contributions from processes which pass through all possible intermediate states. Intermediate states involve the exchange of intermediate vector bosons between the particles, and with this interaction is associated a coupling constant α. Each additional boson exchange involves an additional contribution of α to the coupling. If α is less than 1, one can see that the relative contribution of higher order processes is less and less important as α falls. In QCD the gluons serve as the intermediate vector bosons exchanged by quarks and gluons, and the interaction constant is not really a constant, but depends upon the distance between the particles. At short distances the coupling is small, and one can assume perturbative expansions may converge rapidly. Exclusive scattering processes, as opposed to inclusive, are those in which all of the final state products are detected. The authors then discuss the application of perturbative QCD to the deuteron. The issues of chiral conservation and color transparancy are also discussed, in the scheme of large Q 2 interations, where perturbative QCD should be applicable
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.
CERN. Geneva
2013-01-01
Perturbative QCD is the general theoretical framework for describing hard scattering processes yielding multiparticle production at hadron colliders. In these lectures, we shall introduce fundamental features of perturbative QCD and describe its application to several high energy collider processes, including jet production in electron-positron annihilation, deep inelastic scattering, Higgs boson and gauge boson production at the LHC.
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....
International Nuclear Information System (INIS)
Collins, J.C.
1985-01-01
Progress in quantum chromodynamics in the past year is reviewed in these specific areas: proof of factorization for hadron-hadron collisions, fast calculation of higher order graphs, perturbative Monte Carlo calculations for hadron-hadron scattering, applicability of perturbative methods to heavy quark production, and understanding of the small-x problem. 22 refs
Basics of QCD perturbation theory
International Nuclear Information System (INIS)
Soper, D.E.
1997-01-01
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
Current issues in perturbative QCD
International Nuclear Information System (INIS)
Hinchliffe, I.
1994-12-01
This review talk discusses some issues of active research in perturbative QCD. The following topics are discussed: (1) current value of αs; (2) heavy quark production in hadron collisions; (3) production of Ψ and Υ in p anti p collisions; (4) prompt photon production; (5) small-x and related phenomena; and (6) particle multiplicity in heavy quark jets
New results in perturbative QCD
International Nuclear Information System (INIS)
Ellis, R.K.
1986-01-01
Three topics in perturbative QCD important for Super-collider physics are reviewed. The topics are: 1. (2 → 2) jet phenomena calculated in O(αs 3 ). 2. New techniques for the calculation of tree graphs. 3. Color coherence in jet phenomena. 31 references, 6 figures
Seven topics in perturbative QCD
International Nuclear Information System (INIS)
Buras, A.J.
1980-09-01
The following topics of perturbative QCD are discussed: (1) deep inelastic scattering; (2) higher order corrections to e + e - 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
Reggeon interactions in perturbative QCD
International Nuclear Information System (INIS)
Kirschner, R.
1994-08-01
We study the pairwise interaction of reggeized gluons and quarks in the Regge limit of perturbative QCD. The interactions are represented as integral kernels in the transverse momentum space and as operators in the impact parameter space. We observe conformal symmetry and holomorphic factorization in all cases. (orig.)
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.
Chiral symmetry in perturbative QCD
International Nuclear Information System (INIS)
Trueman, T.L.
1979-04-01
The chiral symmetry of quantum chromodynamics with massless quarks is unbroken in perturbation theory. Dimensional regularization is used. The ratio of the vector and axial vector renormalization constante is shown to be independent of the renormalization mass. The general results are explicitly verified to fourth order in g, the QCD coupling constant
Czech Academy of Sciences Publication Activity Database
Abbas, G.; Ananthanarayan, B.; Caprini, I.; Fischer, Jan
2013-01-01
Roč. 87, č. 1 (2013), "014008-1"-"014008-14" ISSN 1550-7998 R&D Projects: GA MŠk(CZ) LG13031 Institutional support: RVO:68378271 Keywords : perturbative expansion * Borel transformation * Adler function Subject RIV: BE - Theoretical Physics Impact factor: 4.864, year: 2013
The status of perturbative QCD
International Nuclear Information System (INIS)
Ellis, R.K.
1988-10-01
The advances in perturbative QCD are reviewed. The status of determinations of the coupling constant α/sub S/ and the parton distribution functions is presented. New theoretical results on the spin dependent structure functions of the proton are also reviewed. The theoretical description of the production of vector bosons, jets and heavy quarks is outlined with special emphasis on new results. Expected rates for top quark production at hadronic colliders are presented. 111 refs., 8 figs
Perturbative QCD at finite temperature
International Nuclear Information System (INIS)
Altherr, T.
1989-03-01
We discuss an application of finite temperature QCD to lepton-pair production in a quark-gluon plasma. The perturbative calculation is performed within the realtime formalism. After cancellation of infrared and mass singularities, the corrections at O (α s ) are found to be very small in the region where the mass of the Drell-Yan pair is much larger than the temperature of the plasma. Interesting effects, however, appear at the annihilation threshold of the thermalized quarks
A new perturbative approach to QCD
International Nuclear Information System (INIS)
Pervushin, V.N.; Kallies, W.; Sarikov, N.A.
1988-01-01
For the description of bound states in QED and QCD the physical perturbation theory on the spatial components of the vector over the exact solution, defined by the time one, is proposed. It is shown this perturbation theory in QCD can be redefined so that it reproduces the main elements of hadron physics: confinement, spectroscopy of light and heavy quarkonia, dual-resonance amplitudes, chiral Lagrangians and the parton model
Nuclear properties from perturbative QCD
International Nuclear Information System (INIS)
Close, F.E.; Roberts, R.G.; Ross, G.G.
1986-01-01
Two apparently different descriptions of quark distributions in a nucleus may in fact be connected. A ''duality'' between the QCD approach and the conventional model of nucleon binding leads to nuclear properties being simply related to the anomalous dimensions of QCD. (orig.)
Non-perturbative QCD correlation functions
Energy Technology Data Exchange (ETDEWEB)
Cyrol, Anton Konrad
2017-11-27
Functional methods provide access to the non-perturbative regime of quantum chromo- dynamics. Hence, they allow investigating confinement and chiral symmetry breaking. In this dissertation, correlation functions of Yang-Mills theory and unquenched two-flavor QCD are computed from the functional renormalization group. Employing a self-consistent vertex expansion of the effective action, Yang-Mills correlation functions are obtained in four as well as in three spacetime dimensions. To this end, confinement and Slavnov-Taylor identities are discussed. Our numerical results show very good agreement with corresponding lattice results. Next, unquenched two-flavor QCD is considered where it is shown that the unquenched two-flavor gluon propagator is insensitive to the pion mass. Furthermore, the necessity for consistent truncations is emphasized. Finally, correlation functions of finite-temperature Yang-Mills theory are computed in a truncation that includes the splitting of the gluon field into directions that are transverse and longitudinal to the heat bath. In particular, it includes the splitting of the three- and four-gluon vertices. The obtained gluon propagator allows to extract a Debye screening mass that coincides with the hard thermal loop screening mass at high temperatures, but is meaningful also at temperatures below the phase transition temperature.
Resolution of ambiguities in perturbative QCD
International Nuclear Information System (INIS)
Nakkagawa, Hisao; Niegawa, Akira.
1984-01-01
In the perturbative QCD analyses of the deeply inelastic processes, the coupling constant depends on at least two mass-scales, the renormalization scale and the factorization scale. By integrating the coupled renormalization group equations with respect to these two mass-scales, the running coupling constant is defined. A perturbative approximation then introduces a new ambiguity, the integration-path dependence, into the theory. We show that the problem of this new ambiguity is resolved by imposing Stevenson's principle of minimal sensitivity. Together with the analogous analysis of the operator matrix element or the cut vertex, we can completely solve the problem of getting an unambiguous perturbative QCD prediction. (author)
Consistent Perturbative Fixed Point Calculations in QCD and Supersymmetric QCD
DEFF Research Database (Denmark)
Ryttov, Thomas A.
2016-01-01
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 QCD and hadron physics
International Nuclear Information System (INIS)
Cobos-Martínez, J J
2016-01-01
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. (paper)
Chiral perturbation theory for lattice QCD
International Nuclear Information System (INIS)
Baer, Oliver
2010-01-01
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.)
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.)
Perturbative QCD and electromagnetic form factors
International Nuclear Information System (INIS)
Carlson, C.E.; Gross, F.
1987-01-01
We calculate nucleon magnetic form factors using perturbative QCD for several distribution amplitudes including a general one given in terms of Appell polynomials. We find that the magnitude and sign of both nucleon magnetic form factors can be explained within perturbative QCD. The observed normalization of G/sub Mp/ requires that the distribution amplitude be broader than its superhigh momentum transfer limit, and the G/sub Mn//G/sub Mp/ data may require the distribution amplitude to be asymmetric, in accord with distribution amplitudes derived from QCD sum rules. Some speculation as to how an asymmetric distribution amplitude can come about is offered. Finally, we show that the soft contributions corresponding to the particular distribution amplitudes we use need not be bigger than the data. 16 refs., 6 figs
On summation of perturbation expansions
International Nuclear Information System (INIS)
Horzela, A.
1985-04-01
The problem of the restoration of physical quantities defined by divergent perturbation expansions is analysed. The Pad'e and Borel summability is proved for alternating perturbation expansions with factorially growing coefficients. The proof is based on the methods of the classical moments theory. 17 refs. (author)
On-Shell Methods in Perturbative QCD
International Nuclear Information System (INIS)
Bern, Zvi; Dixon, Lance J.; Kosower, David A.
2007-01-01
We review on-shell methods for computing multi-parton scattering amplitudes in perturbative QCD, utilizing their unitarity and factorization properties. We focus on aspects which are useful for the construction of one-loop amplitudes needed for phenomenological studies at the Large Hadron Collider
Colour singlets in perturbative QCD
International Nuclear Information System (INIS)
Bassetto, A.
1979-01-01
In the axial gauge and at the leading log level, a definite and consistent picture seems to emerge of a parton decay into states in which many partons are found just before confinement should take place. They are grouped into colourless clusters in a number sufficient to exhaust the ''final'' state, still possessing a finite average mass. This result is peculiar of QCD, in particular of its non-abelian nature. Large transverse momenta or more generally average invariant quantities of partons are mainly due to the multiplicities involved in the branching processes. If eventually confinement would convert these clusters into hadrons (and this is of course the main issue which has still to be proven) without a large rearrangement of the colour lines, the picture we have found for colour singlets could apply to the real hadronic world. (author)
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.
Recent progress on perturbative QCD fragmentation functions
International Nuclear Information System (INIS)
Cheung, K.
1995-05-01
The recent development of perturbative QCD (PQCD) fragmentation functions has strong impact on quarkonium production. I shall summarize B c meson production based on these PQCD fragmentation functions, as well as, the highlights of some recent activities on applying these PQCD fragmentation functions to explain anomalous J/ψ and ψ' production at the Tevatron. Finally, I discuss a fragmentation model based on the PQCD fragmentation functions for heavy quarks fragmenting into heavy-light mesons
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.)
Analytic perturbation theory in analyzing some QCD observables
International Nuclear Information System (INIS)
Shirkov, D.V.
2001-01-01
The paper is devoted to application of recently devised ghost-free Analytic Perturbation Theory (APT) for analysis of some QCD observables. We start with the discussion of the main problem of the perturbative QCD - ghost singularities and with the resume of this trouble solution within the APT. By a few examples in the various energy and momentum transfer regions (with the flavor number f = 3, 4 and 5) we demonstrate the effect of improved convergence of the APT modified perturbative QCD expansion. Our first observation is that in the APT analysis the three-loop contribution (of an order of α s 3 ) is as a rule numerically inessential. This raises hope for practical solving the well-known problem of asymptotic nature of common QFT perturbation series. The second conclusion is that a common perturbative analysis of time-like events with the big π 2 term in the π 2 coefficient is not adequate at s ≤ 2 GeV 2 . In particular, this relates to τ decay. Then, for the 'high' (f = 5) region it is shown that the common two-loop (NLO, NLLA) perturbation approximation widely used there (at 10 GeV ≤ √s ≤ 170 GeV) for analysis of shape/events data contains a systematic negative error of a 1 - 2 per cent level for the extracted α bar s (2) values. Our physical conclusion is that the α bar s (M Z 2 ) value averaged over the f = 5 data s (M Z 2 )> APT; f= 5 ≅ 0.124 appreciably differs from the currently accepted 'world average' (= 0.118)
Towards finite density QCD with Taylor expansions
International Nuclear Information System (INIS)
Karsch, F.; Schaefer, B.-J.; Wagner, M.; Wambach, J.
2011-01-01
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.
A non-perturbative operator product expansion
International Nuclear Information System (INIS)
Bietenholz, W.; Cundy, N.; Goeckeler, M.
2009-10-01
Nucleon structure functions can be observed in Deep Inelastic Scattering experiments, but it is an outstanding challenge to confront them with fully non-perturbative QCD results. For this purpose we investigate the product of electromagnetic currents (with large photonmomenta) between quark states (of low momenta). By means of an Operator Product Expansion the structure function can be decomposed into matrix elements of local operators, and Wilson coefficients. For consistency both have to be computed non-perturbatively. Here we present precision results for a set of Wilson coefficients. They are evaluated from propagators for numerous quark momenta on the lattice, where the use of chiral fermions suppresses undesired operator mixing. This overdetermines the Wilson coefficients, but reliable results can be extracted by means of a Singular Value Decomposition. (orig.)
Perturbative QCD effects in heavy meson decays
International Nuclear Information System (INIS)
Szezepaniak, A.; Henley, E.M.
1991-01-01
The amplitude for the exclusive nonleptonic decay of a heavy meson into two light pseudoscalar mesons is analyzed using the factorization formalism of perturbative QCD for exclusive reactions at large momentum transfer. We calculate the form factor b → u transition and compare it to the old quark model calculation and the new one based on the light cone formulation of the full quark model wave function. The new results we obtain are smaller by a factor of 2 - 3 as compared to the old value. (orig.)
Perturbative current quark masses in QCD
International Nuclear Information System (INIS)
Scadron, M.D.
1982-01-01
Neutral PCAC current quark masses follow from the covariant light plane of QCD requirement that α-m-circumflex(M), which is not inconsistent with the spontaneous breakdown of chiral symmetry. The resulting current quark mass ratio (m sub(s)/m-circumflex) sub(curr)=5 and scale m-circumflex sub(curr)=62 MeV at M=2 Gev are compatible with the observed πNσ - term, the Goldberger-Treiman discrepancy, the low-lying 0 - , 1/2 + , 1 - , 3/2 + hadron mass spectrum, the flavor independence of the dynamically generated quark mass and the perturbative weak binding limit. (author)
Dynamical quark and gluon condensates from a modified perturbative QCD
International Nuclear Information System (INIS)
Cabo Montes de Oca, A.; Martinez Pedrera, D.
2004-12-01
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 massless version of the theory is explored. For this purpose, it is firstly presented a way to 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 even in the absence of the gluon one. The 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 massless QCD. The inability of lattice calculations in detecting this possibility could be related to the current limitations in treating the fermion determinants. (author)
Non-leading contributions in QCD: Summing the perturbative series
International Nuclear Information System (INIS)
Trentadue, L.
1984-01-01
This paper presents the results of a systematic analysis of the leading and non-leading contributions in perturbative QCD and addresses the question of logarithmic contributions to all orders of the perturbative series
A convergent reformulation of perturbative QCD
International Nuclear Information System (INIS)
Alves, R.J.G.
2000-10-01
We present and explore a new formulation of perturbative QCD based not on the renormalised coupling but on the dimensional transmutation parameter of the theory and the property of asymptotic scaling. The approach yields a continued function, the iterated function being that involved in the solution of the two-loop β-function equation. In the so-called large-b limit the continued function reduces to a continued fraction and the successive approximants are diagonal Pade approximants. We investigate numerically the convergence of successive approximants using the leading-b approximation, motivated by renormalons, to model the all-orders result. We consider the Adler D-function of vacuum polarisation, the Polarised Bjorken and Gross-LIewellyn Smith sum rules, the (unpolarised) Bjorken sum rule, and the Minkowskian quantities R τ and the R-ratio of e + e - annihilation. In contrast to diagonal Pade approximants the truncated continued function method gives remarkably stable large-order approximants in cases where infrared renormalon effects are important. We also use the new approach to determine the QCD fundamental parameters from the R τ and the R-ratio measurements, where we find Λ-tilde (3)/MS = 516 ± 48 MeV (which yields α s (μ = m τ ) = 0.360 -0.020 +0.021 ), and Λ-tilde (5)/MS = 299 -7 +6 MeV (which yields α s (μ = m z 0 ) = 0.1218 ± 0.0004), respectively. The evolution of the former value to the m z 0 energy results in α s (μ = m z 0 ) = 0.123 ± 0.002. These values are in line with other determinations available in the literature. We implement the Complete Renormalisation Group Improvement (CORGI) scheme throughout all the calculations. We report on how the mathematical concept of Stieltjes series can be used to assess the convergence of Pade approximants of perturbative series. We find that the combinations of UV renormalons which occur in perturbative QCD may or may not be Stieltjes series depending on the renormalisation scheme used. (author)
Resummation of perturbative QCD by pade approximants
International Nuclear Information System (INIS)
Gardi, E.
1997-01-01
In this lecture I present some of the new developments concerning the use of Pade Approximants (PA's) for resuming perturbative series in QCD. It is shown that PA's tend to reduce the renormalization scale and scheme dependence as compared to truncated series. In particular it is proven that in the limit where the β function is dominated by the 1-loop contribution, there is an exact symmetry that guarantees invariance of diagonal PA's under changing the renormalization scale. In addition it is shown that in the large β 0 approximation diagonal PA's can be interpreted as a systematic method for approximating the flow of momentum in Feynman diagrams. This corresponds to a new multiple scale generalization of the Brodsky-Lepage-Mackenzie (BLM) method to higher orders. I illustrate the method with the Bjorken sum rule and the vacuum polarization function. (author)
Perturbative QCD contributions to inclusive processes
International Nuclear Information System (INIS)
Ritbergen, T. van.
1996-01-01
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 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 τ-lepton was obtained. Then the top-quark-mass effects on the decay channels of a Higgs boson: Higgs→b-quarks and Higgs→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 2 -dependence of the lower moments ∫ 0 1 x N-1 F(x,q 2 )dx, N=2,4,6,8 of the structure functions F 2 and F L were obtained. (orig./HSI)
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).
The Glauber approach in perturbative QCD: nucleon case
International Nuclear Information System (INIS)
Ayala Filho, A.L.; Pelotas Univ., RS; Ducaty, M.B. Gay; Levin, E.M.; Petersburg Nuclear Physics Inst.,
1997-01-01
We investigate the shadowing corrections for the nucleon gluon distribution predicted from Glauber (Mueller) approach in perturbative QCD. This work is a digest for the nucleon case of the extended work prior presented by the authors
Non-perturbative Aspects of QCD and Parameterized Quark Propagator
Institute of Scientific and Technical Information of China (English)
HAN Ding-An; ZHOU Li-Juan; ZENG Ya-Guang; GU Yun-Ting; CAO Hui; MA Wei-Xing; MENG Cheng-Ju; PAN Ji-Huan
2008-01-01
Based on the Global Color Symmetry Model, the non-perturbative QCD vacuum is investigated in theparameterized fully dressed quark propagator. Our theoretical predictions for various quantities characterized the QCD vacuum are in agreement with those predicted by many other phenomenological QCD inspired models. The successful predictions clearly indicate the extensive validity of our parameterized quark propagator used here. A detailed discussion on the arbitrariness in determining the integration cut-off parameter of# in calculating QCD vacuum condensates and a good method, which avoided the dependence of calculating results on the cut-off parameter is also strongly recommended to readers.
Renormalisaton of composite operators in lattice QCD. Perturbative versus nonperturbative
Energy Technology Data Exchange (ETDEWEB)
Goeckeler, M.; Nakamura, Y. [Regensburg Univ. (Germany). Inst. fuer Theoretische Physik; Horsley, R. [Edinburgh Univ. (GB). School of Physics and Astronomy] (and others)
2010-07-01
The perturbative and nonperturbative renormalisation of quark-antiquark operators in lattice QCD with two flavours of clover fermions is investigated within the research programme of the QCDSF collaboration. Operators with up to three derivatives are considered. The nonperturbative results based on the RI-MOM scheme are compared with estimates from one- and two-loop lattice perturbation theory. (orig.)
Non-perturbative supersymmetry anomaly in supersymmetric QCD
International Nuclear Information System (INIS)
Shamir, Y.
1991-03-01
The zero modes of the Dirac operator in an instanton and other topologically non-trivial backgrounds are unstable in a large class of massless or partially massless supersymmetric gauge theories. We show that under a generic perturbation of the scalar fields all zero modes become resonances, and discuss the ensuing breakdown of conventional perturbation theory. As a result, despite of the presence of massless fermions, the field theoretic tunneling amplitude is not suppressed. In massless supersymmetric QCD with N c ≤ N f the effective potential is found to be negative and monotonically increasing in the weak coupling regime for scalar VEVs which lie on the perturbatively flat directions. Consequently, massless supersymmetric QCD with N c ≤ N f exhibits a non-perturbative supersymmetry anomaly and exists in a strongly interacting phase which closely resembles ordinary QCD. The same conclusions apply if small masses are added to the lagrangian and the massless limit is smooth. (author). 21 refs, 5 figs
Small-x physics in perturbative QCD
International Nuclear Information System (INIS)
Lipatov, L.N.
1996-07-01
We review the parton model and the Regge approach to the QCD description of the deep-inelastic ep scattering at the small Bjorken variable x and demonstrate their relation with the DGLAP and BFKL evolution equations. It is shown, that in the leading logarithmic approximation the gluon is reggeized and the pomeron is a compound state of two reggeized gluons. The conformal invariance of the BFKL pomeron in the impact parameter space is used to investigate the scattering amplitudes at high energies and fixed momentum transfers. The remarkable properties of the Schroedinger equation for compound states of an arbitrary number of reggeized gluons in the multi-colour QCD are reviewed. The gauge-invariant effective action describing the gluon-Reggeon interactions is constructed. The known next-to-leading corrections to the QCD pomeron are discussed. (orig.)
Duality between QCD perturbative series and power corrections
International Nuclear Information System (INIS)
Narison, S.; Zakharov, V.I.
2009-01-01
We elaborate on the relation between perturbative and power-like corrections to short-distance sensitive QCD observables. We confront theoretical expectations with explicit perturbative calculations existing in literature. As is expected, the quadratic correction is dual to a long perturbative series and one should use one of them but not both. However, this might be true only for very long perturbative series, with number of terms needed in most cases exceeding the number of terms available. What has not been foreseen, the quartic corrections might also be dual to the perturbative series. If confirmed, this would imply a crucial modification of the dogma. We confront this quadratic correction against existing phenomenology (QCD (spectral) sum rules scales, determinations of light quark masses and of α s from τ-decay). We find no contradiction and (to some extent) better agreement with the data and with recent lattice calculations.
Duality between QCD perturbative series and power corrections
Energy Technology Data Exchange (ETDEWEB)
Narison, S. [Laboratoire de Physique Theorique et Astroparticules, CNRS-IN2P3 and Universite de Montpellier II, Case 070, Place Eugene, 34095 Montpellier Cedex 05 (France)], E-mail: snarison@yahoo.fr; Zakharov, V.I. [Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Munich (Germany); Institute of Theoretical and Experimental Physics, B. Cheremushkinskaya 25, Moscow 117218 (Russian Federation)], E-mail: xxz@mppmu.mpg.de
2009-08-31
We elaborate on the relation between perturbative and power-like corrections to short-distance sensitive QCD observables. We confront theoretical expectations with explicit perturbative calculations existing in literature. As is expected, the quadratic correction is dual to a long perturbative series and one should use one of them but not both. However, this might be true only for very long perturbative series, with number of terms needed in most cases exceeding the number of terms available. What has not been foreseen, the quartic corrections might also be dual to the perturbative series. If confirmed, this would imply a crucial modification of the dogma. We confront this quadratic correction against existing phenomenology (QCD (spectral) sum rules scales, determinations of light quark masses and of {alpha}{sub s} from {tau}-decay). We find no contradiction and (to some extent) better agreement with the data and with recent lattice calculations.
Heavy flavour production in perturbative QCD
International Nuclear Information System (INIS)
Nason, P.; Ridolfi, G.; Frixione, S.; Mangano, M.L.
1994-01-01
The status of heavy flavour production in QCD is reviewed. Recent results on the doubly-differential cross section are discussed for the photoproduction of heavy flavours. Comparison of experimental results with theoretical calculation is discussed both for b production at hadron colliders and c production in fixed-target hadroproduction and photoproduction. The possibility of using photoproduction of heavy flavour in order to determine the gluon density in the proton is also discussed. (author). 38 refs., 8 figs
Quasilocal quark models as effective theory of non-perturbative QCD
International Nuclear Information System (INIS)
Andrianov, A.A.
2006-01-01
We consider the Quasilocal Quark Model of NJL type (QNJLM) as effective theory of non-perturbative QCD including scalar (S), pseudo-scalar (P), vector (V) and axial-vector (A) four-fermion interaction with derivatives. In the presence of a strong attraction in the scalar channel the chiral symmetry is spontaneously broken and as a consequence the composite meson states are generated in all channels. With the help of Operator Product Expansion the appropriate set of Chiral Symmetry Restoration (CSR) Sum Rules in these channels are imposed as matching rules to QCD at intermediate energies. The mass spectrum and some decay constants for ground and excited meson states are calculated
Photon-photon inclusive scattering and perturbative QCD
International Nuclear Information System (INIS)
Maor, U.
1988-01-01
Perturbative QCD expectations and problems associated with the study of the photon structure function data are reviewed. An assessment is given for the viability and sensitivity of photon-photon scattering as a decisive tool for the determination of the QCD scale. Particular attention is given to the theoretical problems of singularity cancellations at x = 0 and threshold-associated difficulties at x = 1 and their implications on the actual data analysis. It is concluded that the experimental results, while not providing a decisive verification of QCD at small distances, do add to other independent experiments which are all consistent with the theory and suggest a reasonably well defined QCD scale parameter. The importance of the small Q 2 limit to photon-photon analysis is discussed and the data are examined in an attempt to identify and isolate the contributions of the hadronic and point-like sectors of the target photon. 21 refs., 7 figs. (author)
Non-perturbative renormalization of HQET and QCD
International Nuclear Information System (INIS)
Sommer, Rainer
2003-01-01
We discuss the necessity of non-perturbative renormalization in QCD and HQET and explain the general strategy for solving this problem. A few selected topics are discussed in some detail, namely the importance of off shell improvement in the MOM-scheme on the lattice, recent progress in the implementation of finite volume schemes and then particular emphasis is put on the recent idea to carry out a non-perturbative renormalization of the Heavy Quark Effective Theory (HQET)
Heavy quark form factors at two loops in perturbative QCD
International Nuclear Information System (INIS)
Ablinger, J.; Schneider, C.; Behring, A.; Falcioni, G.
2017-11-01
We present the results for heavy quark form factors at two-loop order in perturbative QCD for different currents, namely vector, axial-vector, scalar and pseudo-scalar currents, up to second order in the dimensional regularization parameter. We outline the necessary computational details, ultraviolet renormalization and corresponding universal infrared structure.
On ambiguities in the exponentiation of large QCD perturbative corrections
International Nuclear Information System (INIS)
Chyla, Jiri
1986-01-01
Ambiguities and some practical questions connected with the exponentiation of higher-order QCD perturbative corrections are discussed for the case of deep inelastic lepton-hadron scattering in the non-singlet channel. The importance of still higher-order calculations for resolving these ambiguities is stressed. (author)
Multiplicity and event shape in the perturbative QCD
International Nuclear Information System (INIS)
Tesima, K.
1995-01-01
The multiple hadroproduction in the perturbative QCD is briefly reviewed. There are a number of quantities which can be analysed with the use of the high-luminosity TRISTAN data. The analysis will contribute to clarifying some unsolved questions, and to the deeper understanding of the jet physics. (author)
Perturbative QCD lagrangian at large distances and stochastic dimensionality reduction
International Nuclear Information System (INIS)
Shintani, M.
1986-10-01
We construct a Lagrangian for perturbative QCD at large distances within the covariant operator formalism which explains the color confinement of quarks and gluons while maintaining unitarity of the S-matrix. It is also shown that when interactions are switched off, the mechanism of stochastic dimensionality reduction is operative in the system due to exact super-Lorentz symmetries. (orig.)
Heavy quark form factors at two loops in perturbative QCD
Energy Technology Data Exchange (ETDEWEB)
Ablinger, J.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Behring, A. [RWTH Aachen Univ. (Germany). Inst. fuer Theoretische Teilchenphysik und Kosmologie; Bluemlein, J.; Freitas, A. de; Marquard, P.; Rana, N. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Falcioni, G. [Nikhef, Amsterdam (Netherlands). Theory Group
2017-11-15
We present the results for heavy quark form factors at two-loop order in perturbative QCD for different currents, namely vector, axial-vector, scalar and pseudo-scalar currents, up to second order in the dimensional regularization parameter. We outline the necessary computational details, ultraviolet renormalization and corresponding universal infrared structure.
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 Debye mass in finite-T QCD
Kajantie, Keijo; Peisa, J; Rajantie, A; Rummukainen, K; Shaposhnikov, Mikhail E
1997-01-01
Employing a non-perturbative gauge invariant definition of the Debye screening mass m_D in the effective field theory approach to finite T QCD, we use 3d lattice simulations to determine the leading O(g^2) and to estimate the next-to-leading O(g^3) corrections to m_D in the high temperature region. The O(g^2) correction is large and modifies qualitatively the standard power-counting hierarchy picture of correlation lengths in high temperature 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.)
Aspects of perturbative QCD in Monte Carlo shower models
International Nuclear Information System (INIS)
Gottschalk, T.D.
1986-01-01
The perturbative QCD content of Monte Carlo models for high energy hadron-hadron scattering is examined. Particular attention is given to the recently developed backwards evolution formalism for initial state parton showers, and the merging of parton shower evolution with hard scattering cross sections. Shower estimates of K-factors are discussed, and a simple scheme is presented for incorporating 2 → QCD cross sections into shower model calculations without double counting. Additional issues in the development of hard scattering Monte Carlo models are summarized. 69 references, 20 figures
Modification of the perturbative QCD towards confinement
International Nuclear Information System (INIS)
Arodz, H.
1981-01-01
Modification of the low momentum behaviour of the perturbative SU(2) gauge theory is proposed. The modification is closely related (although not equivalent) to a nonstandard choice of boundary condition for the Euclidean 2-point gluonic Green function. In the resulting theory already single graphs lead to the confining potential between heavy, static quarks, V(r) = ar 2 for r → infinity. (author)
Kato expansion in quantum canonical perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Nikolaev, Andrey, E-mail: Andrey.Nikolaev@rdtex.ru [Institute of Computing for Physics and Technology, Protvino, Moscow Region, Russia and RDTeX LTD, Moscow (Russian Federation)
2016-06-15
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.
Kato expansion in quantum canonical perturbation theory
International Nuclear Information System (INIS)
Nikolaev, Andrey
2016-01-01
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’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.
Perturbative ambiguities in Coulomb gauge QCD
International Nuclear Information System (INIS)
Doust, P.
1987-01-01
The naive Coulomb gauge Feynman rules in non-abelian gauge theory give rise to ambiguous integrals, in addition to the usual ultraviolet divergences. Generalizing the work of Cheng and Tsai, these ambiguities are resolved to all orders in perturbation theory, by defining a gauge that interpolates smoothly between the Feynman gauge and the Coulomb gauge. The extra terms V 1 +V 2 of Christ and Lee are identified with certain two-loop ambiguous terms. However, there still seem to be unsolved problems connected with renormalisation. copyright 1987 Academic Press, Inc
Charmless decays of the B-meson in perturbative QCD
International Nuclear Information System (INIS)
Libo Guo; Dongsheng Du; Lianshou Liu
1999-01-01
Using the perturbative QCD method and Chau's six-quark-graph scheme, we report a theoretical calculation of exclusive nonleptonic decays of the B meson into two light pseudoscalar mesons in the context of the low-energy effective Hamiltonian. The contributions from both tree-level and one-loop diagrams are taken into account. Under the approximation of neglecting light quark and light meson masses, we find that (i) within perturbative QCD there is no singularity which exists in the computation of spacelike penguin diagrams when the BSW model is used; (ii) the contributions from spacelike-type (W-annihilation, W-exchange, spacelike penguin and penguin-annihilation) graphs are strongly suppressed relative to those from timelike-type (external W-emission, internal W-emission and timelike penguin) ones; (iii) our results are well below the experimental upper limits but lower than the BSW ones. (author)
Calculation of the Odderon intercept in perturbative QCD
International Nuclear Information System (INIS)
Gauron, P.; Lipatov, L.; Nicolescu, B.; Paris-6 Univ., 75
1993-01-01
The question of the equality of hadron-hadron and hadron-antihadron cross sections at very high energies is investigated. By using a variational method combined with conformal invariant techniques it is shown that the Odderon J-plane singularity in the leading logarithmic approximation of QCD lies above 1. Therefore, in the perturbative theory the difference between hadron-hadron and antihadron-hadron interactions grows with energy. (K.A.) 11 refs
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.
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.
Lattice QCD for Baryon Rich Matter – Beyond Taylor Expansions
International Nuclear Information System (INIS)
Bornyakov, V.; Boyda, D.; Goy, V.; Molochkov, A.; Nakamura, A.; Nikolaev, A.; Zakharov, V.I.
2016-01-01
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.
Threshold resummation in SCET vs. perturbative QCD. An analytic comparison
International Nuclear Information System (INIS)
Bonvini, Marco; Forte, Stefano; Ghezzi, Margherita; Ridolfi, Giovanni
2012-01-01
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 μ s that characterizes this approach. We derive a master formula that relates the SCET resummation to the QCD result for any choice of μ s . We then use it first, to show that if SCET resummation is performed in N-Mellin moment space by suitable choice of μ s it is equivalent to the standard perturbative approach. Next, we show that if SCET resummation is performed by choosing for μ 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 μ 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.)
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.)
Effective Lagrangians for SUSY QCD with properties seen in perturbation theory
International Nuclear Information System (INIS)
Sharatchandra, H.S.
1984-06-01
We construct effective Lagrangians for supersymmetric QCD which properly incorporate the relevant Ward identities and possess features encountered in perturbation theory. This shows that the unusual scenarios, proposed for SUSY QCD, are not necessary. (author)
Prompt atmospheric neutrino fluxes: perturbative QCD models and nuclear effects
Energy Technology Data Exchange (ETDEWEB)
Bhattacharya, Atri [Department of Physics, University of Arizona,1118 E. 4th St. Tucson, AZ 85704 (United States); Space sciences, Technologies and Astrophysics Research (STAR) Institute,Université de Liège,Bât. B5a, 4000 Liège (Belgium); Enberg, Rikard [Department of Physics and Astronomy, Uppsala University,Box 516, SE-75120 Uppsala (Sweden); Jeong, Yu Seon [Department of Physics and IPAP, Yonsei University,50 Yonsei-ro Seodaemun-gu, Seoul 03722 (Korea, Republic of); National Institute of Supercomputing and Networking, KISTI,245 Daehak-ro, Yuseong-gu, Daejeon 34141 (Korea, Republic of); Kim, C.S. [Department of Physics and IPAP, Yonsei University,50 Yonsei-ro Seodaemun-gu, Seoul 03722 (Korea, Republic of); Reno, Mary Hall [Department of Physics and Astronomy, University of Iowa,Iowa City, Iowa 52242 (United States); Sarcevic, Ina [Department of Physics, University of Arizona,1118 E. 4th St. Tucson, AZ 85704 (United States); Department of Astronomy, University of Arizona,933 N. Cherry Ave., Tucson, AZ 85721 (United States); Stasto, Anna [Department of Physics, 104 Davey Lab, The Pennsylvania State University,University Park, PA 16802 (United States)
2016-11-28
We evaluate the prompt atmospheric neutrino flux at high energies using three different frameworks for calculating the heavy quark production cross section in QCD: NLO perturbative QCD, k{sub T} factorization including low-x resummation, and the dipole model including parton saturation. We use QCD parameters, the value for the charm quark mass and the range for the factorization and renormalization scales that provide the best description of the total charm cross section measured at fixed target experiments, at RHIC and at LHC. Using these parameters we calculate differential cross sections for charm and bottom production and compare with the latest data on forward charm meson production from LHCb at 7 TeV and at 13 TeV, finding good agreement with the data. In addition, we investigate the role of nuclear shadowing by including nuclear parton distribution functions (PDF) for the target air nucleus using two different nuclear PDF schemes. Depending on the scheme used, we find the reduction of the flux due to nuclear effects varies from 10% to 50% at the highest energies. Finally, we compare our results with the IceCube limit on the prompt neutrino flux, which is already providing valuable information about some of the QCD models.
The scale of soft resummation in SCET vs perturbative QCD
International Nuclear Information System (INIS)
Bonvini, Marco; Forte, Stefano; Ghezzi, Margherita; Ridolfi, Giovanni
2013-01-01
We summarize and extend previous results on the comparison of threshold resummation, performed using soft-collinear effective theory (SCET) in the Becher-Neubert approach, to the standard perturbative QCD formalism based on factorization and resummation of Mellin moments of partonic cross sections. We show that the logarithmic accuracy of the SCET result can be extended by half a logarithmic order, thereby bringing it in full agreement with the standard QCD result if a suitable choice is made for the soft scale μ s which characterizes the SCET result. We provide a master formula relating the two approaches for other scale choices. We then show that with the Becher-Neubert scale choice the Landau pole, which in the perturbative QCD approach is usually removed through power- or exponentially suppressed terms, in the SCET approach is removed by logarithmically subleading terms which break factorization. Such terms may become leading for generic choices of parton distributions, and are always leading when resummation is used far enough from the hadronic threshold
The scale of soft resummation in SCET vs perturbative QCD
Energy Technology Data Exchange (ETDEWEB)
Bonvini, Marco [Deutsches Elektronen-Synchroton, DESY, Notkestraße 85, D-22603 Hamburg (Germany); Forte, Stefano, E-mail: Stefano.Forte@mi.infn.it [Dipartimento di Fisica, Università di Milano and INFN, Sezione di Milano, Via Celoria 16, I-20133 Milano (Italy); Ghezzi, Margherita [Dipartimento di Fisica, Sapienza Università di Roma and INFN, Sezione di Roma, Piazzale Aldo Moro 2, I-00185 Roma,Italy (Italy); Ridolfi, Giovanni [Dipartimento di Fisica, Università di Genova and INFN, Sezione di Genova, Via Dodecaneso 33, I-16146 Genova (Italy)
2013-08-15
We summarize and extend previous results on the comparison of threshold resummation, performed using soft-collinear effective theory (SCET) in the Becher-Neubert approach, to the standard perturbative QCD formalism based on factorization and resummation of Mellin moments of partonic cross sections. We show that the logarithmic accuracy of the SCET result can be extended by half a logarithmic order, thereby bringing it in full agreement with the standard QCD result if a suitable choice is made for the soft scale μ{sub s} which characterizes the SCET result. We provide a master formula relating the two approaches for other scale choices. We then show that with the Becher-Neubert scale choice the Landau pole, which in the perturbative QCD approach is usually removed through power- or exponentially suppressed terms, in the SCET approach is removed by logarithmically subleading terms which break factorization. Such terms may become leading for generic choices of parton distributions, and are always leading when resummation is used far enough from the hadronic threshold.
The scale of soft resummation in SCET vs perturbative QCD
International Nuclear Information System (INIS)
Bonvini, Marco; Forte, Stefano; Ghezzi, Margherita; Ridolfi, Giovanni
2013-01-01
We summarize and extend previous results on the comparison of threshold resummation, performed, using softcollinear effective theory (SCET), in the Becher-Neubert approach, to the standard perturbative QCD formalism based on factorization and resummation of Mellin moments of partonic cross sections. We show that the logarithmic accuracy of this SCET result can be extended by half a logarithmic order, thereby bringing it in full agreement with the standard QCD result if a suitable choice is made for the soft scale μ s which characterizes the SCET result. We provide a master formula relating the two approaches for other scale choices. We then show that with the Becher-Neubert scale choice the Landau pole, which in the perturbative QCD approach is usually removed through power- or exponentially suppressed terms, in the SCET approach is removed by logarithmically subleading terms which break factorization. Such terms may become leading for generic choices of parton distributions, and are always leading when resummation is used far enough from the hadronic threshold.
The scale of soft resummation in SCET vs perturbative QCD
Energy Technology Data Exchange (ETDEWEB)
Bonvini, Marco [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Forte, Stefano [Milano Univ. (Italy). Dipt. di Fisica; INFN, Milano (Italy); Ghezzi, Margherita [Rome-3 Univ. (Italy). Dipt. di Fisica; INFN, Roma (Italy); Ridolfi, Giovanni [Genova Univ. (Italy). Dipt. di Fisica; INFN, Genova (Italy)
2013-01-15
We summarize and extend previous results on the comparison of threshold resummation, performed, using softcollinear effective theory (SCET), in the Becher-Neubert approach, to the standard perturbative QCD formalism based on factorization and resummation of Mellin moments of partonic cross sections. We show that the logarithmic accuracy of this SCET result can be extended by half a logarithmic order, thereby bringing it in full agreement with the standard QCD result if a suitable choice is made for the soft scale {mu}{sub s} which characterizes the SCET result. We provide a master formula relating the two approaches for other scale choices. We then show that with the Becher-Neubert scale choice the Landau pole, which in the perturbative QCD approach is usually removed through power- or exponentially suppressed terms, in the SCET approach is removed by logarithmically subleading terms which break factorization. Such terms may become leading for generic choices of parton distributions, and are always leading when resummation is used far enough from the hadronic threshold.
Asymptotic perturbative QCD in elastic scattering, color transparency and ANN
International Nuclear Information System (INIS)
Botts, J.
1989-01-01
Sorting out the various perturbative contributions to wide angel elastic hadron-hadron scattering has been the subject of recent enquiry. Distinguishing the various contributions are the transverse size of the external hadrons and the interaction region and restrictions on the internal momenta flows. For wide angle elastic hadron-hadron scattering, the interaction between two types of perturbative processes, multiple and single scattering, can be the source of interference phenomena and interesting physics. In the following, after a brief description of the leading and non-leading processes, we shall give a picture of what perturbative QCD may have to say about elastic scattering, color transparency and the spin asymmetry, A NN . 9 refs., 5 figs
Non-perturbative O(a) improvement of lattice QCD
Lüscher, Martin; Sommer, Rainer; Weisz, P; Wolff, U; Luescher, Martin; Sint, Stefan; Sommer, Rainer; Weisz, Peter; Wolff, Ulli
1997-01-01
The coefficients multiplying the counterterms required for O($a$) improvement of the action and the isovector axial current in lattice QCD are computed non-perturbatively, in the quenched approximation and for bare gauge couplings $g_0$ in the range $0 \\leq g_0 \\leq 1$. A finite-size method based on the Schrödinger functional is employed, which enables us to perform all calculations at zero or nearly zero quark mass. As a by-product the critical hopping parameter $\\kappa_c$ is obtained at all couplings considered.
Geometric scaling in ultrahigh energy neutrinos and nonlinear perturbative QCD
International Nuclear Information System (INIS)
Machado, Magno 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. (author)
The heavy quark expansion of QCD
International Nuclear Information System (INIS)
Falk, A.F.
1997-01-01
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
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.
Operator expansion at short distance in QCD
Energy Technology Data Exchange (ETDEWEB)
Hubschmid, W [Bern Univ. (Switzerland). Inst. fuer Theoretische Physik; Mallik, S [Karlsruhe Univ. (T.H.) (Germany, F.R.). Inst. fuer Theoretische Kernphysik
1982-11-01
We present a method of calculating coefficients of gluon operators in the operator product expansion of two-point functions at short distance. It is based on a short-distance expansion of the singular part of the quark propagator in the gluon field, the latter being treated as external. We verify in full generality that the spin zero, gluon operator of dimension six does not contribute to the two-point functions of quark bilinears.
International Nuclear Information System (INIS)
Dominguez, Fabio; Marquet, C.; Mueller, A.H.; Wu Bin; Xiao, Bo-Wen
2008-01-01
We compare medium induced energy loss and p perpendicular -broadening in perturbative QCD with that of the trailing string picture of SYM theory. We consider finite and infinite extent matter as well as relativistic heavy quarks which correspond to those being produced in the medium or external to it. When expressed in terms of the appropriate saturation momentum, we find identical parametric forms for energy loss in perturbative QCD and SYM theory. We find simple correspondences between p perpendicular -broadening in QCD and in SYM theory although p perpendicular -broadening is radiation dominated in SYM theory and multiple scattering dominated in perturbative QCD
Pomeron in perturbative QCD - its elementary theory and possible phenomenology at HERA
International Nuclear Information System (INIS)
Kwiecinski, J.
1992-04-01
Theoretical ideas concerning the Pomeron in perturbative QCD are reviewed. The Lipatov equation with asymptotic freedom effects taken into account is recalled and the corresponding spectrum of eigenvalues controlling the bare Pomeron intercept analysed. Possible phenomenological implications of the perturbative QCD Pomeron for deep inelastic scattering at the HERA ep collider are briefly discussed. 9 figs., 49 refs. (author)
Accelerated convergence of perturbative QCD by conformal mappings in the Borel plane
International Nuclear Information System (INIS)
Caprini, I.; Fischer, J.
1998-01-01
The behaviour of the large order terms in perturbative QCD received much attention in recent years. The presence of instantons and certain classes of Feynman diagrams lead to increasing coefficients of the perturbative expansion of the QCD Green functions, making this series divergent and even Borel non-summable. In the present paper we adopt a definite prescription for the Borel summation and investigate the improvement of the low order expansion by using some information about the behaviour of the large order coefficients. We use the technique of conformal mappings to extend the convergence region of the Borel series, and exploit the behaviour of the Borel transform near the first renormalons. Our approach improves previous work where only the ultraviolet renormalons were considered. The polarization function, relevant for the hadronic τ decay, which allows the determinations of the strong coupling constant a s (m τ 2 ) is used. We consider the Adler function D(s), i.e. the logarithmic derivative of the vacuum polarization for massless quarks, and its QCD perturbative expansion (D(a s )) in terms of the running coupling a s (-s). The first 3 coefficients D n of Adler function D(s) are known from explicit calculations, while for large n they are expected to have a factorial growth. By applying the Borel method with the Principal Value (PV) prescription to avoid the infrared renormalons, we write D(a s ) in terms of its Borel transform B(u). The Borel integral is given as a function of a s for a model function resembling the Borel transform of the Adler function in the large β 0 limit. The data obtained by truncating the expansion at N=3 which corresponds to the physical situation are presented. Even at such low values of N our method gives very good results (the improvement increases with N, since the optimality is an asymptotic feature). Using this technique we calculated also the running coupling constant a s (m τ 2 ), for which we obtained the value 0
QCD and resonance physics Nonperturbative effects in operator expansion
International Nuclear Information System (INIS)
Shifman, M.A.; Vainshtein, A.L.; Zakharov, V.I.
1978-01-01
The aim of the paper is to show that QCD provides well-defined predictions for a single resonance. The crucial point is the inclusion of power corrections to asymptotic freedom which are due to nonperturbative effects of QCD. Apart from presenting a general outline in intuitive terms the operator expansion for the product of external currents is discussed. It is argued that the effect of nonperturbative terms is twofold: a) they induce vacuum expectation values such as (0.1Gsub(μv)sup(a)Gsub(μv)sup(a)10), Gsub(μv)sup(a) being the gluon field strength tensor and b) they break the operator expansion itself starting from some critical dimension. The latter effect is suppressed as a high power of Q -2 where Q is the momentum carried by a current. Both a) and b) are examplified in the instanton physics but the whole approach is of more general value
International Nuclear Information System (INIS)
West, G.
1990-01-01
The main thrust of this talk is to review and discuss various topics in both perturbative and non-perturbative QCD that are, by and large, model independent. This inevitably means that we shall rely heavily on the renormalization group and asymptotic freedom. Although this usually means that one has to concentrate on high energy phenomena, there are some physical processes even involving bound states which are certainly highly non-perturbative, where one can make some progress without becoming overly model independent. Experience with the EMC effect, where there are about as many ''explanations'' as authors, has surely taught us that it may well be worth returning to ''basics'' and thinking about general properties of QCD rather than guessing, essentially arbitrarily, what we think is its low energy structure. No doubt we shall have to await further numerical progress or for some inspired theoretical insight before we can, with confidence, attack these extremely difficult problems. So, with this in mine, I shall review a smattering of problems which do have a non-perturbative component and where some rather modest progress can actually be made; I emphasize the adjective ''modest''exclamation point
Non-perturbative chiral corrections for lattice QCD
International Nuclear Information System (INIS)
Thomas, A.W.; Leinweber, D.B.; Lu, D.H.
2002-01-01
We explore the chiral aspects of extrapolation of observables calculated within lattice QCD, using the nucleon magnetic moments as an example. Our analysis shows that the biggest effects of chiral dynamics occur for quark masses corresponding to a pion mass below 600 MeV. In this limited range chiral perturbation theory is not rapidly convergent, but we can develop some understanding of the behaviour through chiral quark models. This model dependent analysis leads us to a simple Pade approximant which builds in both the limits m π → 0 and m π → ∞ correctly and permits a consistent, model independent extrapolation to the physical pion mass which should be extremely reliable. (author)
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.
Perturbative corrections to B → D form factors in QCD
Wang, Yu-Ming; Wei, Yan-Bing; Shen, Yue-Long; Lü, Cai-Dian
2017-06-01
We compute perturbative QCD corrections to B → D form factors at leading power in Λ/ m b , at large hadronic recoil, from the light-cone sum rules (LCSR) with B-meson distribution amplitudes in HQET. QCD factorization for the vacuum-to- B-meson correlation function with an interpolating current for the D-meson is demonstrated explicitly at one loop with the power counting scheme {m}_c˜ O(√{Λ {m}_b}) . The jet functions encoding information of the hard-collinear dynamics in the above-mentioned correlation function are complicated by the appearance of an additional hard-collinear scale m c , compared to the counterparts entering the factorization formula of the vacuum-to- B-meson correction function for the construction of B → π from factors. Inspecting the next-to-leading-logarithmic sum rules for the form factors of B → Dℓν indicates that perturbative corrections to the hard-collinear functions are more profound than that for the hard functions, with the default theory inputs, in the physical kinematic region. We further compute the subleading power correction induced by the three-particle quark-gluon distribution amplitudes of the B-meson at tree level employing the background gluon field approach. The LCSR predictions for the semileptonic B → Dℓν form factors are then extrapolated to the entire kinematic region with the z-series parametrization. Phenomenological implications of our determinations for the form factors f BD +,0 ( q 2) are explored by investigating the (differential) branching fractions and the R( D) ratio of B → Dℓν and by determining the CKM matrix element |V cb | from the total decay rate of B → Dμν μ .
Topics in perturbative QCD beyond the leading order
International Nuclear Information System (INIS)
Buras, A.J.
1979-08-01
The basic structure of QCD formulae for various inclusive and semi-inclusive processes is presented. Next to leading order QCD corrections to inclusive deep-inelastic scattering are discussed in some detail. The methods for calculations of QCD corrections (leading, next to leading) to semi-inclusive processes are outlined. Some results of these calculations are discussed. 58 references
An integral equation for the continuation of perturbative expansions
International Nuclear Information System (INIS)
Ciulli, S.
1984-01-01
It is shown how a procedure for analytic continuation, based on methods of functional analysis, can be used to extend the results of a perturbative calculation to yield nonperturbative information which could not be obtained directly from a perturbative expansion
Cumulants in perturbation expansions for non-equilibrium field theory
International Nuclear Information System (INIS)
Fauser, R.
1995-11-01
The formulation of perturbation expansions for a quantum field theory of strongly interacting systems in a general non-equilibrium state is discussed. Non-vanishing initial correlations are included in the formulation of the perturbation expansion in terms of cumulants. The cumulants are shown to be the suitable candidate for summing up the perturbation expansion. Also a linked-cluster theorem for the perturbation series with cumulants is presented. Finally a generating functional of the perturbation series with initial correlations is studied. We apply the methods to a simple model of a fermion-boson system. (orig.)
The heavy quark-antiquark potential from lattice and perturbative QCD
Laschka, Alexander; Kaiser, Norbert; Weise, Wolfram
2009-01-01
The heavy quark-antiquark potential in perturbative QCD is subject to ambiguities. We show how to derive a well-defined and stable short-distance potential that can be matched to results from lattice QCD simulations at intermediate distances. The static potential as well as the order 1/m potential are discussed.
1999-01-01
Basic Properties of QCD: the Lagrangian, the running coupling, asymptotic freedom and colour confinement. Examples of perturbative calculations in electron- positron physics (total cross sections and event) Parton branching approach will be used to derive the evolution equations for hadron structure functions Comarison with data on deep inelastic scattering and jet production will be for hadron structure functions and jet fragmentation functions
High energy asymptotics of perturbative multi-color QCD
International Nuclear Information System (INIS)
Lipatov, L.N.
1993-01-01
The structure functions of deep-inelastic scattering at small-x satisfy two different equations in the leading logarithmic approximation (LLA). The first one -- the GLAP equation, describes the Q 2 -evolution of partonic distributions h i (x). The second one -- the BFKL, equation determines the x-dependence of parton densities H i (x, k perpendicular ). Analogous equations for matrix elements of higher twist operators were constructed in Refs. 3 and 4. Here the author discusses the possibility of finding an exact solution for multi-gluon compound states in LLA for the color group SU(N), in the limit N → ∞. The contributions of diagrams with many reggeized gluons are important for the unitarization of the perturbative Pomeron in QCD. It is shown that the Bethe-Salpeter equations for compound states of many reggeized gluons are conformally invariant in the two-dimensional impact parameter space. Their solutions can be written in holomorphically factorized form and there is a differential operator commuting with the holomorphic part of the corresponding Hamiltonian
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
International Nuclear Information System (INIS)
Kikkawa, Keiji
1983-01-01
The varidity of the perturbation method in the high temperature QCD is discussed. The skeleton expansion method takes account of plasmon effects and eliminates the electric infrared singularity but not the magnetic one. A possibility of eliminating the latter, which was recently proposed, is examined by a gauge invariant skeleton expansion. The magnetic singularity is unable to be eliminated by the perturbation method. This implies that some non-perturbative approaches must be incorporated in the high temperature QCD. (author)
Perturbative QCD Lagrangian at large distances and stochastic dimensionality reduction. Pt. 2
International Nuclear Information System (INIS)
Shintani, M.
1986-11-01
Using the method of stochastic dimensional reduction, we derive a four-dimensional quantum effective Lagrangian for the classical Yang-Mills system coupled to the Gaussian white noise. It is found that the Lagrangian coincides with the perturbative QCD at large distances constructed in our previous paper. That formalism is based on the local covariant operator formalism which maintains the unitarity of the S-matrix. Furthermore, we show the non-perturbative equivalence between super-Lorentz invariant sectors of the effective Lagrangian and two dimensional QCD coupled to the adjoint pseudo-scalars. This implies that stochastic dimensionality reduction by two is approximately operative in QCD at large distances. (orig.)
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.
Operator expansion in quantum chromodynamics beyond perturbation theory
International Nuclear Information System (INIS)
Novikov, V.A.; Shifman, M.A.; Vainshtejn, A.I.; Zakharov, V.I.
1980-01-01
The status of operator expansion at short distances is descussed within the frameworks of nonperturbatue QCD. The question of instanton effects is investigated in various aspects. Two-point functions induced by the gluonic currents are considered. It is shown that certain gluonic correlations vanish in the field of definite duality. It is proved that there does exist a very special relation between the expansion coefficients required by consistancy between instanton calculations and the general operator expansion. At last a certain modification of the naive version of operator expansion is proposed, which allows one to go beyond the critical power and construct, if necessary, an infinite series
Assuming Regge trajectories in holographic QCD: from OPE to Chiral Perturbation Theory
Cappiello, Luigi; Greynat, David
2015-01-01
The Soft Wall model in holographic QCD has Regge trajectories but wrong operator product expansion (OPE) for the two-point vectorial QCD Green function. We correct analytically this problem and describe the axial sector and chiral symmetry breaking. The low energy chiral parameters, $F_{\\pi}$ and $L_{10}$ , are well described analytically by the model in terms of Regge spacing and QCD condensates. The model nicely supports and extends previous theoretical analyses advocating Digamma function to study QCD two-point functions in different momentum regions.
On the meaning of perturbation expansions in quantum field theory
International Nuclear Information System (INIS)
Burdik, C.; Chyla, J.
1987-01-01
We reformulate perturbation expansions in renormalized quantum field theories in a way that allows straightforward handling of situations when in the conventional approach (i.e. in fixed renormalization scheme) these expansions are divergent. In our approach the results of perturbation calculations of physical quantities appear in the form of (under certain circumstances) convergent expansions in powers of a free parameter χ, characterising the procedure involved. This inherent ambiguity of perturbative calculations is conjectures to be an expression of the underlaying ambiguity in the separation of the full theory into its perturbative and nonperturbative parts. The close connection of our results with the Borel summation technique is demonstrated and their relation to conventional perturbation expansions in fixed renormalization scheme is clarified
Fundamental parameters of QCD from non-perturbative methods for two and four flavors
International Nuclear Information System (INIS)
Marinkovic, Marina
2013-01-01
The non-perturbative formulation of Quantumchromodynamics (QCD) on a four dimensional space-time Euclidean lattice together with the finite size techniques enable us to perform the renormalization of the QCD parameters non-perturbatively. In order to obtain precise predictions from lattice QCD, one needs to include the dynamical fermions into lattice QCD simulations. We consider QCD with two and four mass degenerate flavors of O(a) improved Wilson quarks. In this thesis, we improve the existing determinations of the fundamental parameters of two and four flavor QCD. In four flavor theory, we compute the precise value of the Λ parameter in the units of the scale L max defined in the hadronic regime. We also give the precise determination of the Schroedinger functional running coupling in four flavour theory and compare it to the perturbative results. The Monte Carlo simulations of lattice QCD within the Schroedinger Functional framework were performed with a platform independent program package Schroedinger Funktional Mass Preconditioned Hybrid Monte Carlo (SF-MP-HMC), developed as a part of this project. Finally, we compute the strange quark mass and the Λ parameter in two flavour theory, performing a well-controlled continuum limit and chiral extrapolation. To achieve this, we developed a universal program package for simulating two flavours of Wilson fermions, Mass Preconditioned Hybrid Monte Carlo (MP-HMC), which we used to run large scale simulations on small lattice spacings and on pion masses close to the physical value.
Evaluating results from the Relativistic Heavy Ion Collider with perturbative QCD and hydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Fries, R.J.; Nonaka, C.
2011-07-01
We review the basic concepts of perturbative quantum chromodynamics (QCD) and relativistic hydrodynamics, and their applications to hadron production in high energy nuclear collisions. We discuss results from the Relativistic Heavy Ion Collider (RHIC) in light of these theoretical approaches. Perturbative QCD and hydrodynamics together explain a large amount of experimental data gathered during the first decade of RHIC running, although some questions remain open. We focus primarily on practical aspects of the calculations, covering basic topics like perturbation theory, initial state nuclear effects, jet quenching models, ideal hydrodynamics, dissipative corrections, freeze-out and initial conditions. We conclude by comparing key results from RHIC to calculations.
Simultaneous analysis in renormalization and factorization scheme dependences in perturbative QCD
International Nuclear Information System (INIS)
Nakkagawa, Hisao; Niegawa, Akira.
1983-01-01
Combined and thorough investigations of both the factorization and the renormalization scheme dependences of perturbative QCD calculations are given. Our findings are that (i) by introducing a multiscale-dependent coupling the simultaneous parametrization of both scheme-dependences can be accomplished, (ii) Stevenson's optimization method works quite well so that it gives a remarkable prediction which forces us to exponentiate ''everything'' with uncorrected subprocess cross sections, and (iii) the perturbation series in QCD may converge when Stevenson's principle of minimal sensitivity is taken into account at each order of perturbative approximation. (author)
Non-perturbative QCD Effect on K-Factor of Drell-Yan Process
International Nuclear Information System (INIS)
Hou Zhaoyu; Zhi Haisu; Chen Junxiao
2006-01-01
By using a non-perturbative quark propagator with the lowest-dimensional condensate contributions from the QCD vacuum, the non-perturbative effect to K-factor of the Drell-Yan process is numerically investigated for 12 6 C- 12 6 C collision at the center-of-mass energy (s) 1/2 = 200 GeV, 630 GeV respectively. Calculated results show that the non-perturbative QCD effect has just a weak influence on K-factor in the two cases.
The 1/ N Expansion of Tensor Models Beyond Perturbation Theory
Gurau, Razvan
2014-09-01
We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants write as explicit series in 1/ N plus bounded rest terms. The mixed expansion recasts the problem of determining the subleading corrections in 1/ N into a simple combinatorial problem of counting trees decorated by a finite number of loop edges. As an aside, we use the mixed expansion to show that the (divergent) perturbative expansion of the tensor models is Borel summable and to prove that the cumulants respect an uniform scaling bound. In particular the quartically perturbed measures fall, in the N→ ∞ limit, in the universality class of Gaussian tensor models.
Developments in perturbative QCD? challenges from collider physics
Energy Technology Data Exchange (ETDEWEB)
Zeppenfeld, Dieter [Valencia Univ. (Spain). Dept. de Fisica Teorica]. E-mail: dieter@phenom.physics.wisc.edu
1996-07-01
The search for new phenomena at hadron colliders requires a good understanding of QCD processes. The analysis of multi-jet signatures in the top quark search at the Tevatron is one example, forward jet tagging and rapidity gap techniques in the analysis of weak boson scattering events at the LH C will be another important application. These topics are discussed in the context of multi-parton/multi-jet QCD processes. Also described are some of the calculation tools, like amplitude techniques and automatic code generation for tree level processes. (author)
Developments in perturbative QCD? challenges from collider physics
International Nuclear Information System (INIS)
Zeppenfeld, Dieter
1996-01-01
The search for new phenomena at hadron colliders requires a good understanding of QCD processes. The analysis of multi-jet signatures in the top quark search at the Tevatron is one example, forward jet tagging and rapidity gap techniques in the analysis of weak boson scattering events at the LH C will be another important application. These topics are discussed in the context of multi-parton/multi-jet QCD processes. Also described are some of the calculation tools, like amplitude techniques and automatic code generation for tree level processes. (author)
Perturbation expansions generated by an approximate propagator
International Nuclear Information System (INIS)
Znojil, M.
1987-01-01
Starting from a knowledge of an approximate propagator R at some trial energy guess E 0 , a new perturbative prescription for p-plet of bound states and of their energies is proposed. It generalizes the Rayleigh-Schroedinger (RS) degenerate perturbation theory to the nondiagonal operators R (eliminates a RS need of their diagnolisation) and defines an approximate Hamiltonian T by mere inversion. The deviation V of T from the exact Hamiltonian H is assumed small only after a substraction of a further auxiliary Hartree-Fock-like separable ''selfconsistent'' potential U of rank p. The convergence is illustrated numerically on the anharmonic oscillator example
Shadowing of gluons in perturbative QCD: A comparison of different models
International Nuclear Information System (INIS)
Jalilian-Marian, Jamal; Wang, Xin-Nian
2001-01-01
We investigate the different perturbative QCD-based models for nuclear shadowing of gluons. We show that, in the kinematic region appropriate to the BNL relativistic heavy ion collider experiment, all models give similar estimates for the magnitude of gluon shadowing. At scales relevant to CERN large hadron collider (LHC), there is a sizable difference between the predictions of the different models. However, the uncertainties in gluon shadowing coming from a different parametrization of the gluon distribution in nucleons, are larger than those due to different perturbative QCD models of gluon shadowing. We also investigate the effect of initial nonperturbative shadowing on the magnitude of perturbative shadowing and show that the magnitudes of perturbative and nonperturbative shadowing are comparable at RHIC but perturbative shadowing dominates over nonperturbative shadowing at smaller values of x reached at LHC
Controlling quark mass determinations non-perturbatively in three-flavour QCD
Campos, Isabel
2017-01-01
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.
International Nuclear Information System (INIS)
Kwiecinski, J.
1996-01-01
The perturbative QCD predictions for the small x behaviour of the nucleon structure functions F 2L (x,Q 2 ) and g 1 (x,Q 2 ) are summarized. The importance of the double logarithmic terms for the small x behaviour of the spin structure function g 1 (x,Q 2 ) is emphasized. These terms correspond to the contributions containing the leading powers of α s ln 2 (1/x) at each order of the perturbative expansion. In the non-singlet case they can be approximately accounted for by the ladder diagrams with quark (antiquark) exchange. We solve the corresponding integral equation with the running coupling effects taken into account and present estimate of the effective slope controlling the small x behaviour of the non-singlet spin structure function g 1 (x,Q 2 ) of a nucleon. (author)
Resummation of the QCD perturbative series for hard processes
International Nuclear Information System (INIS)
Catani, S.
1989-01-01
We study the region of inhibited radiation in hard hadronic processes, as for jet cross sections and heavy flavour production near threshold. The cases of deep inelastic scattering and Drell-Yan annihilation are explicitly considered. A general method to exponentiate leading and next-to-leading logarithms to all orders in perturbation theory is developed. A complete formula for the large N-moments is given and shown to agree with previous two-loop calculations. The resummation procedure suggests how to connect the perturbative and nonperturbative regions. The natural limit within the perturbative phase is shown to be the intrinsic transverse momentum. (orig.)
Studies of the Triple Pomeron Vertex in perturbative QCD and its applications in phenomenology
International Nuclear Information System (INIS)
Kutak, K.
2006-12-01
We study the properties of the Triple Pomeron Vertex in the perturbative QCD using the twist expansion method. Such analysis allows us to find the momenta configurations preferred by the vertex. When the momentum transfer is zero, the dominant contribution in the limit when N c →∞ comes from anticollinear pole. This is in agreement with result obtained without expanding, but by direct averaging of the Triple Pomeron Vertex over angles. Resulting theta functions show that the anticollinear configuration is optimal for the vertex. In the finite N c case the collinear term also contributes. Using the Triple Pomeron Vertex we construct a pomeron loop and we also consider four gluon propagation between two Triple Pomeron Vertices. We apply the Triple Pomeron Vertex to construct the Hamiltonian from which we derive the Balitsky-Kovchegov equation for an unintegrated gluon density. In order to apply this equation to phenomenology, we apply the Kwiecinski-Martin-Stasto model for higher order corrections to a linear part of the Balitsky-Kovchegov equation. We introduce the definition of the saturation scale which reflects properties of this equation. Finally, we use it for computation of observables, such as the F 2 structure function and diffractive Higgs boson production cross section. The impact of screening corrections on F 2 is negligible, but those effects turn out to be significant for diffractive Higgs boson production at LHC
Studies of the Triple PomeronVertex in perturbative QCD and its applications in phenomenology
Energy Technology Data Exchange (ETDEWEB)
Kutak, K.
2006-12-15
We study the properties of the Triple Pomeron Vertex in the perturbative QCD using the twist expansion method. Such analysis allows us to find the momenta configurations preferred by the vertex. When the momentum transfer is zero, the dominant contribution in the limit when N{sub c}{yields}{infinity} comes from anticollinear pole. This is in agreement with result obtained without expanding, but by direct averaging of the Triple Pomeron Vertex over angles. Resulting theta functions show that the anticollinear configuration is optimal for the vertex. In the finite N{sub c} case the collinear term also contributes. Using the Triple Pomeron Vertex we construct a pomeron loop and we also consider four gluon propagation between two Triple Pomeron Vertices. We apply the Triple Pomeron Vertex to construct the Hamiltonian from which we derive the Balitsky-Kovchegov equation for an unintegrated gluon density. In order to apply this equation to phenomenology, we apply the Kwiecinski-Martin-Stasto model for higher order corrections to a linear part of the Balitsky-Kovchegov equation. We introduce the definition of the saturation scale which reflects properties of this equation. Finally, we use it for computation of observables, such as the F{sub 2} structure function and diffractive Higgs boson production cross section. The impact of screening corrections on F{sub 2} is negligible, but those effects turn out to be significant for diffractive Higgs boson production at LHC.
Coupling-parameter expansion in thermodynamic perturbation theory.
Ramana, A Sai Venkata; Menon, S V G
2013-02-01
An approach to the coupling-parameter expansion in the liquid state theory of simple fluids is presented by combining the ideas of thermodynamic perturbation theory and integral equation theories. This hybrid scheme avoids the problems of the latter in the two phase region. A method to compute the perturbation series to any arbitrary order is developed and applied to square well fluids. Apart from the Helmholtz free energy, the method also gives the radial distribution function and the direct correlation function of the perturbed system. The theory is applied for square well fluids of variable ranges and compared with simulation data. While the convergence of perturbation series and the overall performance of the theory is good, improvements are needed for potentials with shorter ranges. Possible directions for further developments in the coupling-parameter expansion are indicated.
Convergent perturbation expansions for Euclidean quantum field theory
International Nuclear Information System (INIS)
Mack, G.; Pordt, A.
1984-09-01
Mayer perturbation theory is designed to provide computable convergent expansions which permit calculation of Greens functions in Euclidean Quantum Field Theory to arbitrary accuracy, including 'nonperturbative' contributions from large field fluctuations. Here we describe the expansions at the example of 3-dimensional lambdaphi 4 -theory (in continuous space). They are not essentially more complicated than standard perturbation theory. The n-th order term is expressed in terms of 0(n)-dimensional integrals, and is of order lambda 4 if 4k-3<=n<=4k. (orig.)
Lattice QCD at the physical point meets S U (2 ) chiral perturbation theory
Dürr, Stephan; Fodor, Zoltán; Hoelbling, Christian; Krieg, Stefan; Kurth, Thorsten; Lellouch, Laurent; Lippert, Thomas; Malak, Rehan; Métivet, Thibaut; Portelli, Antonin; Sastre, Alfonso; Szabó, Kálmán; Budapest-Marseille-Wuppertal Collaboration
2014-12-01
We perform a detailed, fully correlated study of the chiral behavior of the pion mass and decay constant, based on 2 +1 flavor lattice QCD simulations. These calculations are implemented using tree-level, O (a )-improved Wilson fermions, at four values of the lattice spacing down to 0.054 fm and all the way down to below the physical value of the pion mass. They allow a sharp comparison with the predictions of S U (2 ) chiral perturbation theory (χ PT ) and a determination of some of its low energy constants. In particular, we systematically explore the range of applicability of next-to-leading order (NLO) S U (2 ) χ PT in two different expansions: the first in quark mass (x expansion), and the second in pion mass (ξ expansion). We find that these expansions begin showing signs of failure for Mπ≳300 MeV , for the typical percent-level precision of our Nf=2 +1 lattice results. We further determine the LO low energy constants (LECs), F =88.0 ±1.3 ±0.2 and BMS ¯(2 GeV )=2.61 (6 )(1 ) GeV , and the related quark condensate, ΣMS ¯(2 GeV )=(272 ±4 ±1 MeV )3 , as well as the NLO ones, ℓ¯3=2.6 (5 )(3 ) and ℓ¯4=3.7 (4 )(2 ), with fully controlled uncertainties. We also explore the next-to-next-to-leading order (NNLO) expansions and the values of NNLO LECs. In addition, we show that the lattice results favor the presence of chiral logarithms. We further demonstrate how the absence of lattice results with pion masses below 200 MeV can lead to misleading results and conclusions. Our calculations allow a fully controlled, ab initio determination of the pion decay constant with a total 1% error, which is in excellent agreement with experiment.
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.)
The causal perturbation expansion revisited: Rescaling the interacting Dirac sea
International Nuclear Information System (INIS)
Finster, Felix; Grotz, Andreas
2010-01-01
The causal perturbation expansion defines the Dirac sea in the presence of a time-dependent external field. It yields an operator whose image generalizes the vacuum solutions of negative energy and thus gives a canonical splitting of the solution space into two subspaces. After giving a self-contained introduction to the ideas and techniques, we show that this operator is, in general, not idempotent. We modify the standard construction by a rescaling procedure giving a projector on the generalized negative-energy subspace. The resulting rescaled causal perturbation expansion uniquely defines the fermionic projector in terms of a series of distributional solutions of the Dirac equation. The technical core of the paper is to work out the combinatorics of the expansion in detail. It is also shown that the fermionic projector with interaction can be obtained from the free projector by a unitary transformation. We finally analyze the consequences of the rescaling procedure on the light-cone expansion.
The causal perturbation expansion revisited: Rescaling the interacting Dirac sea
Finster, Felix; Grotz, Andreas
2010-07-01
The causal perturbation expansion defines the Dirac sea in the presence of a time-dependent external field. It yields an operator whose image generalizes the vacuum solutions of negative energy and thus gives a canonical splitting of the solution space into two subspaces. After giving a self-contained introduction to the ideas and techniques, we show that this operator is, in general, not idempotent. We modify the standard construction by a rescaling procedure giving a projector on the generalized negative-energy subspace. The resulting rescaled causal perturbation expansion uniquely defines the fermionic projector in terms of a series of distributional solutions of the Dirac equation. The technical core of the paper is to work out the combinatorics of the expansion in detail. It is also shown that the fermionic projector with interaction can be obtained from the free projector by a unitary transformation. We finally analyze the consequences of the rescaling procedure on the light-cone expansion.
The gluon Reggeization in perturbative QCD at NLO
Energy Technology Data Exchange (ETDEWEB)
Fadin, V.S. [Novosibirsk State Univ., Institute for Nuclear Physics (Russian Federation)
2005-07-01
The gluon Reggeization is one of the outstanding properties of QCD. It is extremely important for description of high energy processes. In particular, it appears as the basis of the BFKL approach to summation of the terms strengthened by powers of log(1/x). The hypothesis is extremely powerful, since all scattering amplitudes are expressed in terms of the gluon trajectory and several Reggeon vertices. Now the hypothesis is proved in NLA (next-to leading approximation). The proof is based on bootstrap relations. It is shown that an infinite number of these relations is reduced to several bootstrap conditions on the gluon trajectory and the Reggeon vertices. It is shown that fulfillment of these conditions means a proof of the Reggeization hypothesis. All bootstraps conditions are formulated explicitly and are proved to be fulfilled.
Non-perturbative phenomena in QCD vacuum, hadrons, and quark-gluon plasma
International Nuclear Information System (INIS)
Shuryak, E.V.
1983-01-01
These lectures provide a brief review of recent progress in non-perturbative quantum chromodynamics (QCD). They are intended for non specialists, mainly experimentalists. The main object of discussion, the QCD vacuum, is a rather complicated medium. It may be studied either by infinitesimal probes producing microscopic excitations (=hadrons), or by finite excitations (say, heating some volume to a given temperature T). In the latter case, some qualitative changes (phase transitions) should take place. A summary is given of the extent to which such phenomena can be observed in the laboratory by proton-proton, proton-nucleus, and nucleus-nucleus collisions. (orig.)
Jet fragmentation and predictions of the resummed perturbative QCD
Energy Technology Data Exchange (ETDEWEB)
Safonov, Alexei Nikolayevich [Univ. of Florida, Gainesville, FL (United States)
2001-01-01
This dissertation is dedicated to the experimental analysis of jet fragmentation, the process of formation of jets of particles produced in high-energy collisions, and to the comparison of the results to the predictions of resummed perturbative calculations within Quantum Chromodynamics.
expansion method and travelling wave solutions for the perturbed ...
Indian Academy of Sciences (India)
Abstract. 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 (G /G)-expansion method. Based on this method, we obtain abundant exact travelling wave solutions of NLSE with. Kerr law nonlinearity with arbitrary ...
Quark content of the nucleon in QCD: Perturbative and nonperturbative aspects
International Nuclear Information System (INIS)
Stefanis, N.G.
1989-01-01
We elaborate on two proposed model distribution amplitudes for the nucleon, based on perturbative light-cone QCD supplemented by QCD sum rules. The novel nonperturbative features of these amplitudes are discussed in detail. Reasonable predictions for the Dirac form factor of the proton and the neutron are obtained, paying particular attention to the treatment of the effective coupling constant α s (Q 2 ) and the scale parameter Λ QCD . In addition, the stability properties of the sum rules for the moments of these model distribution amplitudes are analyzed. The range of values of the parameters entering the sum rules is estimated. Relying on expectation values of longitudinal-momentum fractions instead of moments, a heuristic interpretation of the physical content of the model distribution amplitudes is attempted
International Nuclear Information System (INIS)
Sivers, D.
1979-10-01
Some aspects of a simple strategy for testing the validity of QCD perturbation theory are examined. The importance of explicit evaluation of higher-order contributions is illustrated by considering Z 0 decays. The recent progress toward understanding exclusive processes in QCD is discussed and some simple examples are given of how to isolate and test the separate components of the perturbation expansion in a hypothetical series of jet experiments
Nf=2 Lattice QCD and Chiral Perturbation Theory
International Nuclear Information System (INIS)
Scorzato, L.; Farchioni, F.; Hofmann, P.; Jansen, K.; Montvay, I.; Muenster, G.; Papinutto, M.; Scholz, E.E.; Shindler, A.; Ukita, N.; Urbach, C.; Wenger, U.; Wetzorke, I.
2006-01-01
By employing a twisted mass term, we compare recent results from lattice calculations of N f =2 dynamical Wilson fermions with Wilson Chiral Perturbation Theory (WChPT). The final goal is to determine some com- binations of Gasser-Leutwyler Low Energy Constants (LECs). A wide set of data with different lattice spacings (a ∼ 0.2 - 0.12 fm), different gauge actions (Wilson plaquette, DBW2) and different quark masses (down to the lowest pion mass allowed by lattice artifacts and including negative quark masses) provide a strong check of the applicability of WChPT in this regime and the scaling behaviours in the continuum limit
The FLUKA Monte Carlo, Non-Perturbative QCD and Cosmic Ray Cascades
International Nuclear Information System (INIS)
Battistoni, G.
2005-01-01
The FLUKA Monte Carlo code, presently used in cosmic ray physics, contains packages to sample soft hadronic processes which are built according to the Dual Parton Model. This is a phenomenological model capable of reproducing many of the features of hadronic collisions in the non perturbative QCD regime. The basic principles of the model are summarized and, as an example, the associated Lambda-K production is discussed. This is a process which has some relevance for the calculation of atmospheric neutrino fluxes
Leading non-cancelling infra-red divergences in perturbative QCD
International Nuclear Information System (INIS)
Carneiro, C.E.; Frenkel, J.; Thomaz, M.T.; Day, M.; Taylor, J.C.
1980-01-01
In QCD in perturbative theory, for the inclusive cross-section for the scattering of two coloured particles, graphs which contribute to the general leading order αs(αs/nΛ)(sup n) are identified and these contributions are added (Λ is the IR cut-off). The work is done in the Coulomb gauge; an appendix discusses the Feynman gauge. (Author) [pt
Determination of the QCD Λ-parameter and the accuracy of perturbation theory at high energies
International Nuclear Information System (INIS)
Dalla Brida, Mattia; Fritzsch, Patrick; Korzec, Tomasz; Ramos, Alberto; Sint, Stefan; Sommer, Rainer; Humboldt-Universitaet, Berlin
2016-04-01
We discuss the determination of the strong coupling α_M_S(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 which allows us to non-perturbatively reach very high energies, corresponding to α_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_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.
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.
Functional perturbative RG and CFT data in the ϵ -expansion
DEFF Research Database (Denmark)
Codello, A.; Safari, M.; Vacca, G. P.
2018-01-01
We show how the use of standard perturbative RG in dimensional regularization allows for a renormalization group-based computation of both the spectrum and a family of coefficients of the operator product expansion (OPE) for a given universality class. The task is greatly simplified by a straight......We show how the use of standard perturbative RG in dimensional regularization allows for a renormalization group-based computation of both the spectrum and a family of coefficients of the operator product expansion (OPE) for a given universality class. The task is greatly simplified...... several results for the whole family of renormalizable multi-critical models ϕ2 n. Whenever comparison is possible our RG results explicitly match the ones recently derived in CFT frameworks....
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
International Nuclear Information System (INIS)
Della Morte, M.; Simma, H.; Sommer, R.
2007-10-01
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 Schrodinger functional scheme, where the box size L is fixed by working at a prescribed value of the renormalized coupling. (orig.)
Towards a non-perturbative matching of HQET and QCD with dynamical light quarks
Energy Technology Data Exchange (ETDEWEB)
Della Morte, M. [CERN, Geneva (Switzerland). Physics Dept.; Fritzsch, P.; Heitger, J. [Muenster Univ. (Germany). Inst. fuer Theoretische Physik 1; Meyer, H.B. [Massachusets Institute of Technology, Center for Theoretical Physics, Cambridge, MA (United States); Simma, H.; Sommer, R. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2007-10-15
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{sub f} =2 are outlined. In particular, the matching of HQET and QCD requires relativistic QCD simulations in a volume with L{approx}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 Schrodinger functional scheme, where the box size L is fixed by working at a prescribed value of the renormalized coupling. (orig.)
Teruo, KISHIMOTO; Tetsuo, KAMMURI; Institute of Physics, University of Tsukuba; Department of Physics, Osaka University
1990-01-01
With the Dynamical Nuclear Field Theory (DNFT) in the Tamm-Dancoff representation we examine higher order corrections in the vibrational mode of a spherical nuclear system. Due to the effects of bubble diagrams, the perturbation expansion in terms of the unrenormalized coupling strength and boson energy fails at full self-consistency. On the other hand, it becomes applicable in the form of linked-cluster expansion when we use thses constants renormalized by the effect of bubble diagrams, in t...
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.)
Applicability of perturbative QCD and NLO power corrections for the pion form factor
International Nuclear Information System (INIS)
Yeh Tsungwen
2002-01-01
As is well recognized, the asymptotic of the perturbative QCD prediction for the pion form factor is much smaller than the upper end of the data. We investigate this problem. We first evaluate the next-to-leading-order (NLO) power correction for the pion form factor. The corrected form factor contains nonperturbative parameters which are determined from a χ 2 fit to the data. Interpreting these parameters leads to the fact that the involved strong interaction coupling constant should be identified as an effective coupling constant under a nonperturbative QCD vacuum. If the scale associated with the effective coupling constant is identified as 2 Q 2 , then Q 2 , the momentum transfer square for the pion form factor to be measured, can have a value about 1 GeV 2 , and , the averaged momentum fraction variable, can locate around 0.5. This circumstance is consistent with the asymptotic model for the pion wave function
Introduction to non-perturbative quantum chromodynamics; Introduction a QCD non perturbatif
Energy Technology Data Exchange (ETDEWEB)
Pene, O. [Paris-11 Univ., 91 - Orsay (France). Lab. de Physique Theorique et Hautes Energies
1995-12-31
Quantum chromodynamics is considered to be the theory of strong interaction. The main peculiarity of this theory is that its asymptotic states (hadrons) are different from its elementary fields (quarks and gluons). This property plays a great part in any physical process involving small momentum-energy transfers. In such a range perturbative methods are no longer allowed. This work focuses on other tools such as QCD symmetry, the quark model, Green functions and the sum rules. To get hadron characteristics numerically, QCD on lattices is used but only in the case of simple process involving no more than one hadron in the initial and final states because of the complexity of the Green function. Some examples using a Monte-Carlo simulation are given. (A.C.) 39 refs.
Smoothing expansion rate data to reconstruct cosmological matter perturbations
Energy Technology Data Exchange (ETDEWEB)
Gonzalez, J.E.; Alcaniz, J.S.; Carvalho, J.C., E-mail: javierernesto@on.br, E-mail: alcaniz@on.br, E-mail: jcarvalho@on.br [Departamento de Astronomia, Observatório Nacional, Rua Gal. José Cristino, 77, Rio de Janeiro, RJ 20921-400 (Brazil)
2017-08-01
The existing degeneracy between different dark energy and modified gravity cosmologies at the background level may be broken by analyzing quantities at the perturbative level. In this work, we apply a non-parametric smoothing (NPS) method to reconstruct the expansion history of the Universe ( H ( z )) from model-independent cosmic chronometers and high- z quasar data. Assuming a homogeneous and isotropic flat universe and general relativity (GR) as the gravity theory, we calculate the non-relativistic matter perturbations in the linear regime using the H ( z ) reconstruction and realistic values of Ω {sub m} {sub 0} and σ{sub 8} from Planck and WMAP-9 collaborations. We find a good agreement between the measurements of the growth rate and f σ{sub 8}( z ) from current large-scale structure observations and the estimates obtained from the reconstruction of the cosmic expansion history. Considering a recently proposed null test for GR using matter perturbations, we also apply the NPS method to reconstruct f σ{sub 8}( z ). For this case, we find a ∼ 3σ tension (good agreement) with the standard relativistic cosmology when the Planck (WMAP-9) priors are used.
Smoothing expansion rate data to reconstruct cosmological matter perturbations
International Nuclear Information System (INIS)
Gonzalez, J.E.; Alcaniz, J.S.; Carvalho, J.C.
2017-01-01
The existing degeneracy between different dark energy and modified gravity cosmologies at the background level may be broken by analyzing quantities at the perturbative level. In this work, we apply a non-parametric smoothing (NPS) method to reconstruct the expansion history of the Universe ( H ( z )) from model-independent cosmic chronometers and high- z quasar data. Assuming a homogeneous and isotropic flat universe and general relativity (GR) as the gravity theory, we calculate the non-relativistic matter perturbations in the linear regime using the H ( z ) reconstruction and realistic values of Ω m 0 and σ 8 from Planck and WMAP-9 collaborations. We find a good agreement between the measurements of the growth rate and f σ 8 ( z ) from current large-scale structure observations and the estimates obtained from the reconstruction of the cosmic expansion history. Considering a recently proposed null test for GR using matter perturbations, we also apply the NPS method to reconstruct f σ 8 ( z ). For this case, we find a ∼ 3σ tension (good agreement) with the standard relativistic cosmology when the Planck (WMAP-9) priors are used.
Nearly perturbative lattice-motivated QCD coupling with zero IR limit
Ayala, César; Cvetič, Gorazd; Kögerler, Reinhart; Kondrashuk, Igor
2018-03-01
The product of the gluon dressing function and the square of the ghost dressing function in the Landau gauge can be regarded to represent, apart from the inverse power corrections 1/{Q}2n, a nonperturbative generalization { \\mathcal A }({Q}2) of the perturbative QCD running coupling a({Q}2) (\\equiv {α }s({Q}2)/π ). Recent large volume lattice calculations for these dressing functions indicate that the coupling defined in such a way goes to zero as { \\mathcal A }({Q}2)∼ {Q}2 when the squared momenta Q 2 go to zero ({Q}2\\ll 1 {GeV}}2). In this work we construct such a QCD coupling { \\mathcal A }({Q}2) which fulfills also various other physically motivated conditions. At high momenta it becomes the underlying perturbative coupling a({Q}2) to a very high precision. And at intermediate low squared momenta {Q}2∼ 1 {GeV}}2 it gives results consistent with the data of the semihadronic τ lepton decays as measured by OPAL and ALEPH. The coupling is constructed in a dispersive way, resulting as a byproduct in the holomorphic behavior of { \\mathcal A }({Q}2) in the complex Q 2-plane which reflects the holomorphic behavior of the spacelike QCD observables. Application of the Borel sum rules to τ-decay V + A spectral functions allows us to obtain values for the gluon (dimension-4) condensate and the dimension-6 condensate, which reproduce the measured OPAL and ALEPH data to a significantly better precision than the perturbative \\overline{MS}} coupling approach.
Algebraic quantum field theory, perturbation theory, and the loop expansion
International Nuclear Information System (INIS)
Duetsch, M.; Fredenhagen, K.
2001-01-01
The perturbative treatment of quantum field theory is formulated within the framework of algebraic quantum field theory. We show that the algebra of interacting fields is additive, i.e. fully determined by its subalgebras associated to arbitrary small subregions of Minkowski space. We also give an algebraic formulation of the loop expansion by introducing a projective system A (n) of observables ''up to n loops'', where A (0) is the Poisson algebra of the classical field theory. Finally we give a local algebraic formulation for two cases of the quantum action principle and compare it with the usual formulation in terms of Green's functions. (orig.)
Production of transverse energy from minijets in next-to-leading order perturbative QCD
Eskola, Kari J
2000-01-01
We compute in next-to-leading order (NLO) perturbative QCD the transverse energy carried into the central rapidity unit of hadron or nuclear collisions by the partons freed in the few-GeV subcollisions. The formulation is based on a rapidity window and a measurement function of a new type. The behaviour of the NLO results as a function of the minimum transverse momentum and as a function of the scale choice is studied. The NLO results are found to be stable relative to the leading-order ones even in the few-GeV domain.
Infrared divergence enforces a rearranged perturbation expansion II QED
Matsson, L
1977-01-01
For pt.I see ibid., vol.39A, p.604 (1977). Part I showed, for the case of scalar electrodynamics, that the ordinary perturbation expansion (OPE) must, except in certain cases, be rearranged in order to carry out uniquely the infrared (IR) exponentiation in a translation- and gauge-invariant way. The uniqueness of the exponent of order alpha follows from requiring exact order-by-order agreement with the OPE before summation and also from requiring that exponentiation of all factorizable parts must be done before integration. This technique is applied to ordinary spinor QED and a similar result is obtained without making the gamma -matrix algebra more complicated than in the OPE. This technique explicitly exhibits the structure of the remaining IR-regular part, which appears in terms of a correlation expansion with respect to photon momenta. (9 refs).
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 test of the Witten-Veneziano formula from lattice QCD
International Nuclear Information System (INIS)
Cichy, Krzysztof; Jansen, Karl; Ottnad, Konstantin; Urbach, Carsten; Bonn Univ.
2015-10-01
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 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.
Operator product expansion in QCD at short distance. Part 2
Energy Technology Data Exchange (ETDEWEB)
Mallik, S
1984-03-19
We describe a simple momentum-space method of evaluating Wilson coefficients of gluon operators in an operator product expansion (OPE). This extends an earlier configuration-space method suitable for calculating the coefficients for light quarks. The method is illustrated by calculating the coefficients of the Lorentz scalar gluon operator of dimension four appearing in different two-point functions.
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}).
Non-Perturbative QCD Coupling and Beta Function from Light Front Holography
International Nuclear Information System (INIS)
Brodsky, Stanley J.
2010-01-01
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 α s AdS (Q 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 ∼ 1 GeV. The resulting β-function appears to capture the essential characteristics of the full β-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 α s AdS (Q 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.
Structure of Nonlocal quark vacuum condensate in non-perturbative QCD vacuum
International Nuclear Information System (INIS)
Xiang Qianfei; Ma Weixing; Zhou Lijuan; Jiang Weizhou
2014-01-01
Based on the Dyson-Schwinger Equations (DSEs) with the rainbow truncation, and Operator Product Expansion, the structure of nonlocal quark vacuum condensate in QCD, described by quark self-energy functions A_f and B_f given usually by the solutions of the DSEs of quark propagator, is predicted numerically. We also calculate the local quark vacuum condensate, quark-gluon mixed local vacuum condensate, and quark virtuality. The self-energy functions A_f and B_f are given by the parameterized quark propagator functions σ_v"f (p"2) and σ_s"f (p"2) of Roberts and Williams, instead of the numerical solutions of the DSEs. Our calculated results are in reasonable agreement with those of QCD sum rules, Lattice QCD calculations, and instanton model predictions, although the resulting local quark vacuum condensate for light quarks, u, d, s, are a little bit larger than those of the above theoretical predictions. We think the differences are caused by model dependence. The larger of strange quark vacuum condensate than u, d quark is due to the s quark mass which is more larger than u, d quark masses. Of course, the Roberts-Williams parameterized quark propagator is an empirical formulism, which approximately describes quark propagation. (authors)
Breakdown of the 1/N expansion in the continuum limit of strong coupling lattice QCD
International Nuclear Information System (INIS)
Bralic, N.; Pontificia Universidade Catolica de Chile, Santiago. Facultad de Fisica); Loewe, M.
1983-08-01
The restoration of lorentz covariance in the continuum limit of strong coupling lattice QCD is shown to require the breakdown of the 1/N expansion. With the leading 1/N appoximation becoming irrelevant in that limit. To leading order in 1/N lorentz convariance can be restored only as an approximate long distance symmetry a non conventional continuum limit with a non hermitian hamiltonian. (Author) [pt
International Nuclear Information System (INIS)
Gaillard, M.K.
1979-01-01
Selected topics in QCD phenomenology are reviewed: the development of an effective jet perturbation series with applications to factorization, energy flow analysis and photon physics; implications of non-perturbative phenomena for hard scattering processes and the pseudoscalar mass spectrum; resonance properties as extracted from the combined technologies of perturbative and non-perturbative QCD. (orig.)
Perturbation expansions of stochastic wavefunctions for open quantum systems
Ke, Yaling; Zhao, Yi
2017-11-01
Based on the stochastic unravelling of the reduced density operator in the Feynman path integral formalism for an open quantum system in touch with harmonic environments, a new non-Markovian stochastic Schrödinger equation (NMSSE) has been established that allows for the systematic perturbation expansion in the system-bath coupling to arbitrary order. This NMSSE can be transformed in a facile manner into the other two NMSSEs, i.e., non-Markovian quantum state diffusion and time-dependent wavepacket diffusion method. Benchmarked by numerically exact results, we have conducted a comparative study of the proposed method in its lowest order approximation, with perturbative quantum master equations in the symmetric spin-boson model and the realistic Fenna-Matthews-Olson complex. It is found that our method outperforms the second-order time-convolutionless quantum master equation in the whole parameter regime and even far better than the fourth-order in the slow bath and high temperature cases. Besides, the method is applicable on an equal footing for any kind of spectral density function and is expected to be a powerful tool to explore the quantum dynamics of large-scale systems, benefiting from the wavefunction framework and the time-local appearance within a single stochastic trajectory.
International Nuclear Information System (INIS)
Elias, V.; Steele, T.G.
1987-01-01
Several field theoretic aspects of the operator product expansion (OPE) augmentation of QCD have been examined. Gauge independence of quark self-energies at the mass shell corresponding to the mass m (characterizing the OPE expansion parameter m/p) has been verified to all orders of the OPE for dimension 3 and 5 chiral symmetry breaking condensates. Similarly, the necessary transversality of the quark condensate contribution to the gluon self-energy has been verified, provided that propagator masses appearing in the self-energy are equilibrated with the OPE mass parameter m
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.
Perturbative corrections to Λ_b→Λ form factors from QCD light-cone sum rules
International Nuclear Information System (INIS)
Wang, Yu-Ming; Shen, Yue-Long
2016-01-01
We compute radiative corrections to Λ_b→Λ from factors, at next-to-leading logarithmic accuracy, from QCD light-cone sum rules with Λ_b-baryon distribution amplitudes. Employing the diagrammatic approach factorization of the vacuum-to-Λ_b-baryon correlation function is justified at leading power in Λ/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 O(α_s) shift the Λ_b→Λ from factors at large recoil significantly and the dominant contribution originates from the next-to-leading order jet function instead of the hard coefficient functions. Having at hand the sum rule predictions for the Λ_b→Λ from factors we further investigate several decay observables in the electro-weak penguin Λ_b→Λ ℓ"+ℓ"− transitions in the factorization limit (i.e., ignoring the “non-factorizable' hadronic effects which cannot be expressed in terms of the Λ_b→Λ from factors), including the invariant mass distribution of the lepton pair, the forward-backward asymmetry in the dilepton system and the longitudinal polarization fraction of the leptonic sector.
Nonperturbative calculations in the framework of variational perturbation theory in QCD
Solovtsova, O. P.
2017-07-01
We discuss applications of the method based on the variational perturbation theory to perform calculations down to the lowest energy scale. The variational series is different from the conventional perturbative expansion and can be used to go beyond the weak-coupling regime. We apply this method to investigate the Borel representation of the light Adler function constructed from the τ data and to determine the residual condensates. It is shown that within the method suggested the optimal values of these lower dimension condensates are close to zero.
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.
All-loops calculation of the structure function x→0 in perturbative QCD
International Nuclear Information System (INIS)
Catani, S.
1991-01-01
We study in perturbative QCD the initial-state radiation associated to hadron processes in the semi-hard region of small x (x is the Bjorken variable). A recent analysis of the exclusive multi-gluon distributions to double (infrared and collinear) logarithmic accuracy is extended to the case of inclusive distributions, which we evaluate to single (infrared) logarithmic accuracy. Thus the resulting x→0 structure function or N→1 gluon anomalous dimension is computed to all-loops accuracy. For the inclusive distributions we are able to perform a calculation to such an accuracy by extensively using cancellations which originate from coherence of QCD radiation and the infrared regularity of real-virtual singularities. We find that the x→0 structure function satisfies the Lipatov equation. With the present study we therefore provide a new derivation of the Lipatov result in the context of hard collisions together with a fully exclusive description. We discuss the structure of the Lipatov equation in relation with the x→0 exclusive distributions previously obtained and with the Altarelli-Parisi equation valid for finite values of x. (orig.)
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.
S -wave K π contributions to the hadronic charmonium B decays in the perturbative QCD approach
Rui, Zhou; Wang, Wen-Fei
2018-02-01
We extend our recent works on the two-pion S -wave resonance contributions to the kaon-pion ones in the B meson hadronic charmonium decay modes based on the perturbative QCD approach. The S -wave K π timelike form factor in its distribution amplitudes is described by the LASS parametrization, which consists of the K0*(1430 ) resonant state together with an effective range nonresonant component. The predictions for the decays B →J /ψ K π in this work agree well with the experimental results from the BABAR and Belle collaborations. We also discuss theoretical uncertainties, indicating that the results of this work, which can be tested by the LHCb and Belle-II experiments, are reasonably accurate.
On the chiral perturbation theory for two-flavor two-color QCD at finite chemical potential
Czech Academy of Sciences Publication Activity Database
Brauner, Tomáš
2006-01-01
Roč. 21, č. 7 (2006), s. 559-569 ISSN 0217-7323 R&D Projects: GA ČR(CZ) GD202/05/H003 Institutional research plan: CEZ:AV0Z10480505 Keywords : two-color QCD * chiral perturbation theory * chemical potential Subject RIV: BE - Theoretical Physics Impact factor: 1.564, year: 2006
Maelger, J.; Reinosa, U.; Serreau, J.
2018-04-01
We extend a previous investigation [U. Reinosa et al., Phys. Rev. D 92, 025021 (2015), 10.1103/PhysRevD.92.025021] of the QCD phase diagram with heavy quarks in the context of background field methods by including the two-loop corrections to the background field effective potential. The nonperturbative dynamics in the pure-gauge sector is modeled by a phenomenological gluon mass term in the Landau-DeWitt gauge-fixed action, which results in an improved perturbative expansion. We investigate the phase diagram at nonzero temperature and (real or imaginary) chemical potential. Two-loop corrections yield an improved agreement with lattice data as compared to the leading-order results. We also compare with the results of nonperturbative continuum approaches. We further study the equation of state as well as the thermodynamic stability of the system at two-loop order. Finally, using simple thermodynamic arguments, we show that the behavior of the Polyakov loops as functions of the chemical potential complies with their interpretation in terms of quark and antiquark free energies.
International Nuclear Information System (INIS)
Levi, A.R.; Lubicz, V.; Rebbi, C.
1997-01-01
We discuss a general strategy to compute the coefficients of the QCD chiral Lagrangian using lattice QCD with Wilson fermions. This procedure requires the introduction of a lattice chiral Lagrangian as an intermediate step in the calculation. The QCD chiral Lagrangian is then obtained by expanding the lattice effective theory in increasing powers of the lattice spacing and the external momenta. In order to investigate the general structure of the lattice effective Lagrangian, we perform an analytical calculation at the leading order of the strong-coupling and large-N expansion. We find that the explicit chiral symmetry breaking, introduced on the lattice by the Wilson term, is reproduced in the effective theory by a set of additional terms, which do not have direct correspondence in the continuum chiral Lagrangian. We argue that these terms can be conveniently reabsorbed by a suitable renormalization procedure. This is shown explicitly at the leading order of the strong-coupling and large-N expansion. In fact, we find that at this order, as is known to be the case in the opposite weak-coupling limit, the vector and axial Ward identities of the continuum theory are reproduced on the lattice provided that the bare quark mass and the lattice operators are properly renormalized. copyright 1997 The American Physical Society
A non-perturbative exploration of the high energy regime in Nf=3 QCD. ALPHA Collaboration
Dalla Brida, Mattia; Fritzsch, Patrick; Korzec, Tomasz; Ramos, Alberto; Sint, Stefan; Sommer, Rainer
2018-05-01
Using continuum extrapolated lattice data we trace a family of running couplings in three-flavour QCD over a large range of scales from about 4 to 128 GeV. The scale is set by the finite space time volume so that recursive finite size techniques can be applied, and Schrödinger functional (SF) boundary conditions enable direct simulations in the chiral limit. Compared to earlier studies we have improved on both statistical and systematic errors. Using the SF coupling to implicitly define a reference scale 1/L_0≈ 4 GeV through \\bar{g}^2(L_0) =2.012, we quote L_0 Λ ^{N_f=3}_{{\\overline{MS}}} =0.0791(21). This error is dominated by statistics; in particular, the remnant perturbative uncertainty is negligible and very well controlled, by connecting to infinite renormalization scale from different scales 2^n/L_0 for n=0,1,\\ldots ,5. An intermediate step in this connection may involve any member of a one-parameter family of SF couplings. This provides an excellent opportunity for tests of perturbation theory some of which have been published in a letter (ALPHA collaboration, M. Dalla Brida et al. in Phys Rev Lett 117(18):182001, 2016). The results indicate that for our target precision of 3 per cent in L_0 Λ ^{N_f=3}_{{\\overline{MS}}}, a reliable estimate of the truncation error requires non-perturbative data for a sufficiently large range of values of α _s=\\bar{g}^2/(4π ). In the present work we reach this precision by studying scales that vary by a factor 2^5= 32, reaching down to α _s≈ 0.1. We here provide the details of our analysis and an extended discussion.
Current correlators in QCD: Operator product expansion versus large distance dynamics
International Nuclear Information System (INIS)
Shevchenko, V.I.; Simonov, Yu.A.
2004-01-01
We analyze the structure of current-current correlators in coordinate space in the large N c limit when the corresponding spectral density takes the form of an infinite sum over hadron poles. The latter are computed in the QCD string model with quarks at the ends, including the lowest states, for all channels. The corresponding correlators demonstrate reasonable qualitative agreement with the lattice data without any additional fits. Different issues concerning the structure of the short-distance operator product expansion are discussed
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...
CP violation induced by the double resonance for pure annihilation decay process in perturbative QCD
Energy Technology Data Exchange (ETDEWEB)
Lue, Gang; Li, Sheng-Tao; Wang, Yu-Ting [Henan University of Technology, College of Science, Zhengzhou (China); Lu, Ye [Guangxi Normal University, Department of Physics, Guilin (China)
2017-08-15
In a perturbative QCD approach we study the direct CP violation in the pure annihilation decay process of anti B{sup 0}{sub s} → π{sup +}π{sup -}π{sup +}π{sup -} induced by the ρ and ω double resonance effect. Generally, the CP violation is small in the pure annihilation type decay process. However, we find that the CP violation can be enhanced by double ρ-ω interference when the invariant masses of the π{sup +}π{sup -} pairs are in the vicinity of the ω resonance. For the decay process of anti B{sup 0}{sub s} → π{sup +}π{sup -}π{sup +}π{sup -}, the CP violation can reach A{sub CP}(anti B{sup 0}{sub s} → π{sup +}π{sup -}π{sup +}π{sup -}) = 27.20{sup +0.05+0.28+7.13}{sub -0.15-0.31-6.11}%. (orig.)
Penguin-dominated B→PV decays in NLO perturbative QCD
International Nuclear Information System (INIS)
Li Hsiangnan; Mishima, Satoshi
2006-01-01
We study the penguin-dominated B→PV decays, with P (V) representing a pseudoscalar (vector) meson, in the next-to-leading-order (NLO) perturbative QCD (PQCD) formalism, concentrating on the B→Kφ, πK*, ρK, and ωK modes. It is found that the NLO corrections dramatically enhance the B→ρK, ωK branching ratios, which were estimated to be small under the naive factorization assumption. The patterns of the direct CP asymmetries A CP (B 0 →ρ ± K ± )≅A CP (B ± →ρ 0 K ± ) and A CP (B 0 →π ± K* ± )>A CP (B ± →π 0 K* ± ) are predicted, differing from A CP (B 0 →π ± K ± )>>A CP (B ± →π 0 K ± ). 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 ρ 0 K S is as low as 0.5
The non-perturbative QCD Debye mass from a Wilson line operator
Laine, Mikko
1999-01-01
According to a proposal by Arnold and Yaffe, the non-perturbative g^2T-contribution to the Debye mass in the deconfined QCD plasma phase can be determined from a single Wilson line operator in the three-dimensional pure SU(3) gauge theory. We extend a previous SU(2) measurement of this quantity to the physical SU(3) case. We find a numerical coefficient which is more accurate and smaller than that obtained previously with another method, but still very large compared with the naive expectation: the correction is larger than the leading term up to T ~ 10^7 T_c, corresponding to g^2 ~ 0.4. At moderate temperatures T ~ 2 T_c, a consistent picture emerges where the Debye mass is m_D ~ 6T, the lightest gauge invariant screening mass in the system is ~ 3T, and the purely magnetic operators couple dominantly to a scale ~ 6T. Electric (~ gT) and magnetic (~ g^2T) scales are therefore strongly overlapping close to the phase transition, and the colour-electric fields play an essential role in the dynamics.
International Nuclear Information System (INIS)
Bakulev, Alexander P.
2010-01-01
Using the results on the electromagnetic pion Form Factor (FF) obtained in the O(α s ) QCD sum rules with non-local condensates [A.P. Bakulev, A.V. Pimikov, and N.G. Stefanis, Phys. Rev. D79 (2009) 093010] we determine the effective continuum threshold for the local duality approach. Then we apply it to construct the O(α s 2 ) estimation of the pion FF in the framework of the fractional analytic perturbation theory.
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...
International Nuclear Information System (INIS)
Kwiecinski, J.
1989-01-01
Recent results concerning the small x limit of parton distributions in perturbative QCD are reviewed. This includes in particular discussion of the bare Pomeron in perturbative QCD and of shadowing corrections. The minijet production processes and possible manifestation of semihard interactions in high energy pp-bar elastic scattering are also discussed. 46 refs., 8 figs. (author)
Perturbative expansion and the initial value problem of the K.d.V. equations
International Nuclear Information System (INIS)
Turchetti, G.
1980-01-01
For the potential K.d.V. equation is considered a perturbation expansion in which the initial condition is imposed on the zeroth order term. The N soliton solutions turn out to be rational functions in the expansion parameter so that the perturbation series can be exactly summed by the [N-1/N] Pade approximants; moreover the [n-1/n] and [n/n] Pade approximants for n [pt
Alternative integral equations and perturbation expansions for self-coupled scalar fields
International Nuclear Information System (INIS)
Ford, L.H.
1985-01-01
It is shown that the theory of a self-coupled scalar field may be expressed in terms of a class of integral equations which include the Yang-Feldman equation as a particular case. Other integral equations in this class could be used to generate alternative perturbation expansions which contain a nonanalytic dependence upon the coupling constant and are less ultraviolet divergent than the conventional perturbation expansion. (orig.)
Analytic solution to leading order coupled DGLAP evolution equations: A new perturbative QCD tool
International Nuclear Information System (INIS)
Block, Martin M.; Durand, Loyal; Ha, Phuoc; McKay, Douglas W.
2011-01-01
We have analytically solved the LO perturbative QCD singlet DGLAP equations [V. N. Gribov and L. N. Lipatov, Sov. J. Nucl. Phys. 15, 438 (1972)][G. Altarelli and G. Parisi, Nucl. Phys. B126, 298 (1977)][Y. L. Dokshitzer, Sov. Phys. JETP 46, 641 (1977)] using Laplace transform techniques. Newly developed, highly accurate, numerical inverse Laplace transform algorithms [M. M. Block, Eur. Phys. J. C 65, 1 (2010)][M. M. Block, Eur. Phys. J. C 68, 683 (2010)] allow us to write fully decoupled solutions for the singlet structure function F s (x,Q 2 ) and G(x,Q 2 ) as F s (x,Q 2 )=F s (F s0 (x 0 ),G 0 (x 0 )) and G(x,Q 2 )=G(F s0 (x 0 ),G 0 (x 0 )), where the x 0 are the Bjorken x values at Q 0 2 . Here F s and G are known functions--found using LO DGLAP splitting functions--of the initial boundary conditions F s0 (x)≡F s (x,Q 0 2 ) and G 0 (x)≡G(x,Q 0 2 ), i.e., the chosen starting functions at the virtuality Q 0 2 . For both G(x) and F s (x), we are able to either devolve or evolve each separately and rapidly, with very high numerical accuracy--a computational fractional precision of O(10 -9 ). Armed with this powerful new tool in the perturbative QCD arsenal, we compare our numerical results from the above equations with the published MSTW2008 and CTEQ6L LO gluon and singlet F s distributions [A. D. Martin, W. J. Stirling, R. S. Thorne, and G. Watt, Eur. Phys. J. C 63, 189 (2009)], starting from their initial values at Q 0 2 =1 GeV 2 and 1.69 GeV 2 , respectively, using their choice of α s (Q 2 ). This allows an important independent check on the accuracies of their evolution codes and, therefore, the computational accuracies of their published parton distributions. Our method completely decouples the two LO distributions, at the same time guaranteeing that both G and F s satisfy the singlet coupled DGLAP equations. It also allows one to easily obtain the effects of the starting functions on the evolved gluon and singlet structure functions, as functions of both Q
Experimental investigations of strong interaction in the non-perturbative QCD region
International Nuclear Information System (INIS)
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 π - + p → φφn (OZI forbidden), φK + K - n (OZI allowed), K - p → φφ(ΛΣ) (OZI allowed), and bar pp → φφ → φφπ 0 (OZI forbidden), φK + K - π 0 (OZI allowed). By comparing the OZI forbidden (glueball filter reactions) with the OZI allowed and previous 22 GeV/c π - p → φφn or φK + K - n data a further critical test of the so far unsuccessfully challenged hypothesis that our g T (2010), g T '(2300) and g T double-prime(2340) all with I G J PC = 0 + 2 ++ are produced by 1-3 2 ++ glueballs will be made. In the QGP search with a large-solid-angle TPC a good Ξ signal was observed. The ratio of Ξ to single strange quark particles such as λ is a better indication of strangeness enhancement in QGP formation. The data indicate enhancement by a factor ∼ 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 λ 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 60 and neutrino oscillations in a dense neutrino gas
Non-perturbative investigation of current correlators in twisted mass lattice QCD
International Nuclear Information System (INIS)
Petschlies, Marcus
2013-01-01
We present an investigation of hadronic current-current correlators based on the first principles of Quantum Chromodynamics. Specifically we apply the non-perturbative methods of twisted mass lattice QCD with dynamical up and down quark taking advantage of its automatic O(a) improvement. As a special application we discuss the calculation of the hadronic leading order contribution to the muon anomalous magnetic moment. The latter is regarded as a promising quantity for the search for physics beyond the standard model. The origin of the strong interest in the muon anomaly lies in the persistent discrepancy between the standard model estimate and its experimental measurement. In the theoretical determination the hadronic leading order part is currently afflicted with the largest uncertainty and a dedicated lattice investigation of the former can be of strong impact on future estimates. We discuss our study of all systematic uncertainties in the lattice calculation, including three lattice volumes, two lattice spacings, pion masses from 650 MeV to 290 MeV and the quark-disconnected contribution. We present a new method for the extrapolation to the physical point that softens the pion mass dependence of a μ hlo and allows for a linear extrapolation with small statistical uncertainty at the physical point. We determine the contribution of up and down quark as a μ hlo (N f =2)=5.69(15)10 -8 . The methods used for the muon are extended to the electron and tau lepton and we find a e hlo (N f =2)=1.512(43)10 -12 and a τ hlo (N f =2)=2.635(54)10 -6 . We estimate the charm contribution to a μ hlo in partially quenched tmLQCD with the result a μ hlo (charm)=1.447(24)(30)10 -9 in very good agreement with a dispersion-relation based result using experimental data for the hadronic R-ratio.
Energy Technology Data Exchange (ETDEWEB)
Palombi, F.
2007-06-15
We carry out the renormalization and the Symanzik O(a)-improvement programme for the static vector current in quenched lattice QCD. The scale independent ratio of the renormalization constants of the static vector and axial currents is obtained non-perturbatively from an axial Ward identity with Wilson-type light quarks and various lattice discretizations of the static action. The improvement coefficients c{sub V}{sup stat} and b{sub V}{sup stat} are obtained up to O(g{sub 4}{sup 0})-terms by enforcing improvement conditions respectively on the axial Ward identity and a three-point correlator of the static vector current. A comparison between the non-perturbative estimates and the corresponding one-loop results shows a non-negligible effect of the O(g{sub 4}{sup 0})-terms on the improvement coefficients but a good accuracy of the perturbative description of the ratio of the renormalization constants. (orig.)
The P(phi)2 Green's functions; asymptotic perturbation expansion
International Nuclear Information System (INIS)
Dimock, J.
1976-01-01
The real time Green's functions in the P(phi) 2 quantum field theory are infinitely differentiable functions of the coupling constant lambda up to and including lamba=0. It follows that the perturbation series are asymptotic as lambda→0 + . (Auth.)
International Nuclear Information System (INIS)
Sai Venkata Ramana, A.
2014-01-01
The coupling parameter series expansion and the high temperature series expansion in the thermodynamic perturbation theory of fluids are shown to be equivalent if the interaction potential is pairwise additive. As a consequence, for the class of fluids with the potential having a hardcore repulsion, if the hard-sphere fluid is chosen as reference system, the terms of coupling parameter series expansion for radial distribution function, direct correlation function, and Helmholtz free energy follow a scaling law with temperature. The scaling law is confirmed by application to square-well fluids
Convergence of perturbation theory expansion for the Yukawa interaction
International Nuclear Information System (INIS)
Basuev, A.G.
1975-01-01
It is shown that the perturbation theory series in the translational-invariant case and upon removal of the boson propagator cut-off for euclidian Green's functions converges when gsup(2)/2 2 is the mass of the boson and Δ(o) is the fermion propagator in the zero of kappa-space. This problem was previously considered by other methods in respect of pseudo-euclidian functions (for the S-matrix) and of euclidian Green's functions. (author)
Perturbative corrections to sigma sub(tot) (e+e- -> hadrons) in supersymmetric QCD
International Nuclear Information System (INIS)
Kataev, A.L.; Pivovarov, A.A.
1983-11-01
sigmasub(tot) (e + e - -> γsup(*) -> hadrons) have been calculated in QCD at two-loop level. Three-loop corrections due to gluon pair production are quoted accompanied by quark-antiquark two-jet events. (orig.)
Flow in a circular expansion pipe flow: effect of a vortex perturbation on localised turbulence
Energy Technology Data Exchange (ETDEWEB)
Selvam, Kamal; Peixinho, Jorge [Laboratoire Ondes Milieux Complexes, CNRS and Université du Havre, F-76600 Le Havre (France); Willis, Ashley P, E-mail: jorge.peixinho@univ-lehavre.fr [School of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH (United Kingdom)
2016-12-15
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. (paper)
The QCD form factor of massive quarks and applications
International Nuclear Information System (INIS)
Moch, S.
2009-11-01
We review the electromagnetic form factor of heavy quarks with emphasis on the QCD radiative corrections at two-loop order in the perturbative expansion. We discuss important properties of the heavy-quark form factor such as its exponentiation in the high-energy limit and its role in QCD factorization theorems for massive n-parton amplitudes. (orig.)
QCD non-perturbative study in radiative and pure-leptonic decays of Bc by wave function
International Nuclear Information System (INIS)
Guo Peng; Hou Zhaoyu; Zhi Haisu
2012-01-01
The radiative and pure-leptonic decays of B c mesons are of hadrons uncertainty in theoretical calculations. Using three types of the B c meson wave functions which describe the characteristics of the QCD non-perturbative and by controlling the parameters in them, the uncertainties of B c meson decay caused by the hadron decay model are studied in detail. The theoretical results show the branching ratios are (1.81981∼3.18961) × 10 -5 , which are sensitive to the type of wave functions. (authors)
J /ψ →Ds ,dπ , Ds ,dK decays with perturbative QCD approach
Sun, Junfeng; Yang, Yueling; Gao, Jie; Chang, Qin; Huang, Jinshu; Lu, Gongru
2016-08-01
Besides the conventional strong and electromagnetic decay modes, the J /ψ particle can also decay via the weak interaction in the standard model. In this paper, nonleptonic J /ψ →Ds ,dπ , Ds ,dK weak decays, corresponding to the externally emitted virtual W boson process, are investigated with the perturbative QCD approach. It is found that the branching ratio for the Cabibbo-favored J /ψ →Dsπ decay can reach up to O (10-10), which might be potentially measurable at the future high-luminosity experiments.
Dynamical breakdown of chiral symmetry and abnormal perturbation expansion
International Nuclear Information System (INIS)
Ebert, D.; Pervushin, V.N.
1976-01-01
Dynamical breakdown of γ 5 -symmetry is studied in the Abelian gauge theory of massless ''quarks'' interacting with massless vector ''gluons''. For this purpose the path-integral approach with bilocal fields as dynamical variables is used. The classical field equation defined by the stationary point of the generating functional turns out to be identical with the Schwinger-Dyson equation for the quark propagator. After a short discussion of the possible solutions of this equation an abnormal perturbation theory has been worked out
What galaxy masses perturb the local cosmic expansion?
Peñarrubia, Jorge; Fattahi, Azadeh
2017-06-01
We use 12 cosmological N-body simulations of Local Group systems (the apostle models) to inspect the relation between the virial mass of the main haloes (Mvir,1 and Mvir,2), the mass derived from the relative motion of the halo pair (Mtim), and that inferred from the local Hubble flow (Mlhf). We show that within the spherical collapse model (SCM), the correspondence between the three mass estimates is exact, I.e. Mlhf = Mtim = Mvir,1 + Mvir,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 Rvir, and that the amount of 'extravirial' mass tends to increase in galaxies with a slow accretion rate. In contrast, modelling the peculiar velocities around the Local Group returns an unbiased constraint on the virial mass ratio of the main galaxy pair. Adopting the outer halo profile found in N-body simulations, which scales as ρ ˜ R-4 at R ≳ Rvir, indicates that the galaxy masses perturbing the local Hubble flow roughly correspond to the asymptotically convergent (total) masses of the individual haloes. We show that estimates of Mvir based on the dynamics of tracers at R ≫ Rvir require a priori information on the internal matter distribution and the growth rate of the main galaxies, both of which are typically difficult to quantify.
Shear viscosity of the quark-gluon plasma in a weak magnetic field in perturbative QCD: Leading log
Li, Shiyong; Yee, Ho-Ung
2018-03-01
We compute the shear viscosity of two-flavor QCD plasma in an external magnetic field in perturbative QCD at leading log order, assuming that the magnetic field is weak or soft: e B ˜g4log (1 /g )T2. We work in the assumption that the magnetic field is homogeneous and static, and the electrodynamics is nondynamical in a formal limit e →0 while e B is kept fixed. We show that the shear viscosity takes a form η =η ¯(B ¯)T3/(g4log (1 /g )) with a dimensionless function η ¯(B ¯) in terms of a dimensionless variable B ¯=(e B )/(g4log (1 /g )T2). The variable B ¯ corresponds to the relative strength of the effect of cyclotron motions compared to the QCD collisions: B ¯˜lmfp/lcyclo. We provide a full numerical result for the scaled shear viscosity η ¯(B ¯).
Instantaneous stochastic perturbation theory
International Nuclear Information System (INIS)
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.
A comparison of jet production rates on the Z0 resonance to perturbative QCD
International Nuclear Information System (INIS)
Abreu, P.; Adam, W.; Adami, F.
1990-01-01
The production rates for 2-, 3-, 4- and 5-jet hardronic final states have been measured with the DELPHI detector at the e + e - storage ring LEP at centre of mass energies around 91.5 GeV. Fully corrected data are compared to O(α s 2 ) QCD matrix element calculations and the QCD scale parameter Λsub(anti Manti S) is determined for different parametrizations of the renormalization scale μ 2 . Including all uncertainties our result is α s (M Z 2 )=0.114±0.003[stat.]±0.004[syst.]±0.012[theor.]. (orig.)
Pion parameters in nuclear medium from chiral perturbation theory and virial expansion
International Nuclear Information System (INIS)
Mallik, S.; Sarkar, Sourav
2004-01-01
We consider two methods to find the effective parameters of the pion traversing a nuclear medium. One is the first order chiral perturbation theoretic evaluation of the pion pole contribution to the two-point function of the axial-vector current. The other is the exact, first order virial expansion of the pion self-energy. We find that, although the results of chiral perturbation theory are not valid at normal nuclear density, those from the virial expansion may be reliable at such density. The latter predicts both the mass shift and the in-medium decay width of the pion to be small, of about a few MeV
Investigation of the factorization scheme dependence of finite order perturbative QCD calculations
Czech Academy of Sciences Publication Activity Database
Kolář, Karel
-, č. 11 (2011), 005/1-005/44 ISSN 1126-6708 R&D Projects: GA MŠk LC527 Institutional research plan: CEZ:AV0Z10100502 Keywords : QCD * parton distribution functions * factorization schemes * NLO Monte Carlo event generators Subject RIV: BF - Elementary Particles and High Energy Physics Impact factor: 5.831, year: 2011
Generalized chiral perturbation theory
International Nuclear Information System (INIS)
Knecht, M.; Stern, J.
1994-01-01
The Generalized Chiral Perturbation Theory enlarges the framework of the standard χPT (Chiral Perturbation Theory), relaxing certain assumptions which do not necessarily follow from QCD or from experiment, and which are crucial for the usual formulation of the low energy expansion. In this way, experimental tests of the foundations of the standard χPT become possible. Emphasis is put on physical aspects rather than on formal developments of GχPT. (author). 31 refs
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.
Stochastic processes and the non-perturbative structure of the QCD vacuum
International Nuclear Information System (INIS)
Vilela Mendes, R.
1992-01-01
Based on a local Gaussian evaluation of the functional integral representation, a method is developed to obtain ground state functionals. The method is applied to the gluon sector of QCD. For the leading term in the ground state functional, stochastic techniques are used to check consistency of the quantum theory, finiteness of the mass gap and the scaling relation in the continuum limit. The functional also implies strong chromomagnetic fluctuations which constrain the propagators in the fermion sector. (orig.)
Functional perturbative RG and CFT data in the ε-expansion
Energy Technology Data Exchange (ETDEWEB)
Codello, A. [Southern Denmark Univ., Odense (Denmark). CP3-Origins; INFN-Sezione di Bologna, Bologna (Italy); Safari, M. [INFN-Sezione di Bologna, Bologna (Italy); Bologna Univ. (Italy). Dipt di Fisica e Astronomia; Vacca, G.P. [INFN-Sezione di Bologna, Bologna (Italy); Zanusso, O. [INFN-Sezione di Bologna, Bologna (Italy); Jena Univ. (Germany). Theoretisch-Physikalisches Inst.
2018-01-15
We show how the use of standard perturbative RG in dimensional regularization allows for a renormalization group-based computation of both the spectrum and a family of coefficients of the operator product expansion (OPE) for a given universality class. The task is greatly simplified by a straightforward generalization of perturbation theory to a functional perturbative RG approach. We illustrate our procedure in the ε-expansion by obtaining the next-to-leading corrections for the spectrum and the leading corrections for the OPE coefficients of Ising and Lee-Yang universality classes and then give several results for the whole family of renormalizable multi-critical models φ{sup 2n}. Whenever comparison is possible our RG results explicitly match the ones recently derived in CFT frameworks. (orig.)
Perturbative corrections to Λ{sub b}→Λ form factors from QCD light-cone sum rules
Energy Technology Data Exchange (ETDEWEB)
Wang, Yu-Ming [Fakultät für Physik, Universität Wien,Boltzmanngasse 5, 1090 Vienna (Austria); Physik Department T31, Technische Universität München,James-Franck-Straße 1, D-85748 Garching (Germany); Shen, Yue-Long [College of Information Science and Engineering, Ocean University of China,Songling Road 238, Qingdao, Shandong 266100 (China)
2016-02-29
We compute radiative corrections to Λ{sub b}→Λ from factors, at next-to-leading logarithmic accuracy, from QCD light-cone sum rules with Λ{sub b}-baryon distribution amplitudes. Employing the diagrammatic approach factorization of the vacuum-to-Λ{sub b}-baryon correlation function is justified at leading power in Λ/m{sub 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 O(α{sub s}) shift the Λ{sub b}→Λ from factors at large recoil significantly and the dominant contribution originates from the next-to-leading order jet function instead of the hard coefficient functions. Having at hand the sum rule predictions for the Λ{sub b}→Λ from factors we further investigate several decay observables in the electro-weak penguin Λ{sub b}→Λ ℓ{sup +}ℓ{sup −} transitions in the factorization limit (i.e., ignoring the “non-factorizable' hadronic effects which cannot be expressed in terms of the Λ{sub b}→Λ from factors), including the invariant mass distribution of the lepton pair, the forward-backward asymmetry in the dilepton system and the longitudinal polarization fraction of the leptonic sector.
International Nuclear Information System (INIS)
Radyushkin, A.V.; Slepchenko, L.A.
1983-01-01
Analysis of experimental status of quantum chromodynamics (QCD) has been carried out. A short introduction into QCD is given. QCD sum rules are considered. Jets in e + e - annihilation and inclusive processes of lepton-hadron and hadron-hadron scattering are considered. Effect of QCD corrections to perturbation theory on quark count is analyzed
Study of B0→J/ψD(*) and ηcD(*) in perturbative QCD
International Nuclear Information System (INIS)
Eilam, Gad; Ladisa, Massimo; Yang Yadong
2002-01-01
Motivated by recent interest in soft J/ψ production in B decays, we investigate B 0 →J/ψ D ( * ) and η c D ( * ) decays in perturbative QCD. We find that, within that framework, these decays are calculable since the heavy cc(bar sign) pair in the final states is created by a hard gluon. The branching ratios are estimated to be around 10 -7 -10 -8 , too small to be consistent with the data, suggesting that other mechanism(s) contribute to the observed excess of soft J/ψ in B 0 →J/ψ+X decays. The possibility of the production of a hybrid sd(bar sign)g meson with a mass of about 2 GeV is briefly entertained
Energy Technology Data Exchange (ETDEWEB)
Keller, G. (Max-Planck-Institut fuer Physik, Muenchen (Germany). Werner-Heisenberg-Institut); Kopper, C. (Goettingen Univ. (Germany). Inst. fuer Theoretische Physik)
1993-04-01
We give a rigorous and very detailed derivation of the short distance expansion for a product of two arbitrary composite operators in the framework of the perturbative Euclidean massive [Phi][sub 4][sup 4]. The technically almost trivial proof rests on an extension of the differential flow equation method to Green functions with bilocal insertions, for which we also establish a set of generalized Zimmermann identities and Lowenstein rules. (orig.).
International Nuclear Information System (INIS)
Carpenter, K.H.
1976-11-01
A description is given of FORTRAN programs for transient eddy current calculations in thin, non-magnetic conductors using a perturbation-polynomial expansion technique. Basic equations are presented as well as flow charts for the programs implementing them. The implementation is in two steps--a batch program to produce an intermediate data file and interactive programs to produce graphical output. FORTRAN source listings are included for all program elements, and sample inputs and outputs are given for the major programs
Perturbative expansion of Chern-Simons theory with non-compact gauge group
International Nuclear Information System (INIS)
Bar-Natan, D.; Witten, E.
1991-01-01
Naive imitation of the usual formulas for compact gauge group in quantizing three dimensional Chern-Simons gauge theory with non-compact gauge group leads to formulas that are wrong or unilluminating. In this paper, an appropriate modification is described, which puts the perturbative expansion in a standard manifestly 'unitary' format. The one loop contributions (which differ from naive extrapolation from the case of compact gauge group) are computed, and their topological invariance is verified. (orig.)
13. international QCD conference (QCD 06)
International Nuclear Information System (INIS)
2006-01-01
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
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.
Narison, Stephan
2007-07-01
About Stephan Narison; Outline of the book; Preface; Acknowledgements; Part I. General Introduction: 1. A short flash on particle physics; 2. The pre-QCD era; 3. The QCD story; 4. Field theory ingredients; Part II. QCD Gauge Theory: 5. Lagrangian and gauge invariance; 6. Quantization using path integral; 7. QCD and its global invariance; Part III. MS scheme for QCD and QED: Introduction; 8. Dimensional regularization; 9. The MS renormalization scheme; 10. Renormalization of operators using the background field method; 11. The renormalization group; 12. Other renormalization schemes; 13. MS scheme for QED; 14. High-precision low-energy QED tests; Part IV. Deep Inelastic Scattering at Hadron Colliders: 15. OPE for deep inelastic scattering; 16. Unpolarized lepton-hadron scattering; 17. The Altarelli-Parisi equation; 18. More on unpolarized deep inelastic scatterings; 19. Polarized deep-inelastic processes; 20. Drell-Yan process; 21. One 'prompt photon' inclusive production; Part V. Hard Processes in e+e- Collisions: Introduction; 22. One hadron inclusive production; 23. gg scatterings and the 'spin' of the photon; 24. QCD jets; 25. Total inclusive hadron productions; Part VI. Summary of QCD Tests and as Measurements; Part VII. Power Corrections in QCD: 26. Introduction; 27. The SVZ expansion; 28. Technologies for evaluating Wilson coefficients; 29. Renormalons; 30. Beyond the SVZ expansion; Part VIII. QCD Two-Point Functions: 31. References guide to original works; 32. (Pseudo)scalar correlators; 33. (Axial-)vector two-point functions; 34. Tensor-quark correlator; 35. Baryonic correlators; 36. Four-quark correlators; 37. Gluonia correlators; 38. Hybrid correlators; 39. Correlators in x-space; Part IX. QCD Non-Perturbative Methods: 40. Introduction; 41. Lattice gauge theory; 42. Chiral perturbation theory; 43. Models of the QCD effective action; 44. Heavy quark effective theory; 45. Potential approaches to quarkonia; 46. On monopole and confinement; Part X. QCD
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...
The perturbative (QCD) Pomeron and Odderon in the photon initiated reactions
International Nuclear Information System (INIS)
Ginzburg, I.F.
1992-07-01
The cross sections of neutral meson M production in the exclusive γγ → MM', γq → Mq or semiexclusive γγ → MX processes (two or three gluon exchange) in the semihard region s≥|t|>1 GeV 2 , μ 2 ≤M X 2 <|t| are calculated. The relation of investigated processes to the problem of the perturbative Pomeron and Odderon is discussed. The possibility of measurements is also discussed. (author) 23 refs.; 3 figs
Non-perturbative renormalization of left-left four-fermion operators in quenched lattice QCD
Guagnelli, M; Peña, C; Sint, S; Vladikas, A
2006-01-01
We define a family of Schroedinger Functional renormalization schemes for the four-quark multiplicatively renormalizable operators of the $\\Delta F = 1$ and $\\Delta F = 2$ effective weak Hamiltonians. Using the lattice regularization with quenched Wilson quarks, we compute non-perturbatively the renormalization group running of these operators in the continuum limit in a large range of renormalization scales. Continuum limit extrapolations are well controlled thanks to the implementation of two fermionic actions (Wilson and Clover). The ratio of the renormalization group invariant operator to its renormalized counterpart at a low energy scale, as well as the renormalization constant at this scale, is obtained for all schemes.
International Nuclear Information System (INIS)
Hasenfratz, P.
1983-01-01
The author presents a general introduction to lattice gauge theories and discusses non-perturbative methods in the gauge sector. He then shows how the lattice works in obtaining the string tension in SU(2). Lattice QCD at finite physical temperature is discussed. Universality tests in SU(2) lattice QCD are presented. SU(3) pure gauge theory is briefly dealt with. Finally, fermions on the lattice are considered. (Auth.)
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.)
Semileptonic decays of B_c meson to S-wave charmonium states in the perturbative QCD approach
International Nuclear Information System (INIS)
Rui, Zhou; Li, Hong; Wang, Guang-xin; Xiao, Ying
2016-01-01
Inspired by the recent measurement of the ratio of B_c branching fractions to J/ψπ"+ and J/ψμ"+ν_μ final states at the LHCb detector, we study the semileptonic decays of B_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_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_c meson. It is found that the predicted branching ratios range from 10"-"7 up to 10"-"2 and could be measured by the future LHCb experiment. Our prediction for the ratio of branching fractions (BR(B_c"+→J/Ψπ"+))/(BR(B_c"+→J/Ψμ"+ν_μ)) is in good agreement with the data. For B_c → Vlν_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.)
arXiv A non-perturbative exploration of the high energy regime in $N_\\text{f}=3$ QCD
Dalla Brida, Mattia; Korzec, Tomasz; Ramos, Alberto; Sint, Stefan; Sommer, Rainer
Using continuum extrapolated lattice data we trace a family of running couplings in three-flavour QCD over a large range of scales from about 4 to 128 GeV. The scale is set by the finite space time volume so that recursive finite size techniques can be applied, and Schr\\"odinger functional (SF) boundary conditions enable direct simulations in the chiral limit. Compared to earlier studies we have improved on both statistical and systematic errors. Using the SF coupling to implicitly define a reference scale $1/L_0\\approx 4$ GeV through $\\bar{g}^2(L_0) =2.012$, we quote $L_0 \\Lambda^{N_{\\rm f}=3}_{\\overline{\\rm MS}} =0.0791(21)$. This error is dominated by statistics; in particular, the remnant perturbative uncertainty is negligible and very well controlled, by connecting to infinite renormalization scale from different scales $2^n/L_0$ for $n=0,1,\\ldots,5$. An intermediate step in this connection may involve any member of a one-parameter family of SF couplings. This provides an excellent opportunity for tests ...
A complete basis for a perturbation expansion of the general N-body problem
International Nuclear Information System (INIS)
Laing, W Blake; Kelle, David W; Dunn, Martin; Watson, Deborah K
2009-01-01
We discuss a basis set developed to calculate perturbation coefficients in an expansion of the general N-body problem. This basis has two advantages. First, the basis is complete order-by-order for the perturbation series. Second, the number of independent basis tensors spanning the space for a given order does not scale with N, the number of particles, despite the generality of the problem. At first order, the number of basis tensors is 25 for all N, i.e. the problem scales as N 0 , although one would initially expect an N 6 scaling at first order. The perturbation series is expanded in inverse powers of the spatial dimension. This results in a maximally symmetric configuration at lowest order which has a point group isomorphic with the symmetric group, S N . The resulting perturbation series is order-by-order invariant under the N! operations of the S N point group which is responsible for the slower than exponential growth of the basis. In this paper, we demonstrate the completeness of the basis and perform the first test of this formalism through first order by comparing to an exactly solvable fully interacting problem of N particles with a two-body harmonic interaction potential
B-physics from non-perturbatively renormalized HQET in two-flavour lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Bernardoni, Fabio; Simma, Hubert [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Blossier, Benoit; Gerardin, Antoine [Paris-11 Univ., 91 - Orsay (France). Lab. de Physique Theorique; CNRS, Orsay (France); Bulava, John [CERN, Geneva (Switzerland). Physics Department; Della Morte, Michele; Hippel, Georg M. von [Mainz Univ. (Germany). Inst. fuer Kernphysik; Fritzsch, Patrick [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Garron, Nicolas [Trinity College, Dublin (Ireland). School of Mathematics; Heitger, Jochen [Muenster Univ. (Germany). Inst. fuer Theoretische Physik 1; Collaboration: ALPHA Collaboration
2012-10-15
We report on the ALPHA Collaboration's lattice B-physics programme based on N{sub 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 {approx} (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{sub (s)}-meson decay constants, f{sub B} and f{sub B{sub s}}.
Non-perturbative QCD. Renormalization, O(a)-improvement and matching to heavy quark effective theory
International Nuclear Information System (INIS)
Sommer, R.
2006-11-01
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. (orig.)
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.)
Diagrammatic many-body perturbation expansion for atoms and molecules. Pt. 6
International Nuclear Information System (INIS)
Moncrieff, D.; Baker, D.J.; Wilson, S.
1989-01-01
The efficient evaluation of the second-order expression in the many-body perturbation theory expansion for the correlation energy on vector processing and parallel processing computers is discussed. It is argued that the linked diagram theorem not only leads to the well known theoretical advantages of the many-body perturbation theory approach which allows the calculation of correlation energies for large (i.e. extended molecules or species containing heavy atoms) systems but also decouples the many-electron problem allowing efficient implementation on parallel processing machines. Furthermore, the computation associated with each of the resulting subproblems is very well suited to vector processing machines. Timing tests are reported for the CRAY 1 and CDC Cyber 205 vector processors, for a 1 processor implementation on the CRAY X-MP/48 and the ETA-10E, and for a 4 processor implementation on the Cray X-MP/48. (orig.)
International Nuclear Information System (INIS)
Bender, C.M.; Cooper, F.
1985-01-01
An apparent difference between formulating mean field perturbation theory for lambdaphi 4 field theory via path integrals or via functional differential equations when there are external sources present is shown not to exist when mean field theory is considered as the N = 1 limit of the 0(N)lambdaphi 4 field theory. A simply method is given for determining the 1/N expansion for the Green's functions in the presence of external sources by directly solving the functional differential equations order by order in 1/N. The 1/N expansion for the effective action GAMMA(phi,chi) is obtained by directly integrating the functional differential equations for the fields phi and chi (equivalent1/2lambda/Nphi/sub α/phi/sup α/-μ 2 ) in the presence of two external sources j = -deltaGAMMA/deltaphi, S = -deltaGAMMA/deltachi
International Nuclear Information System (INIS)
Cohen-Tannoudji, G.
1990-01-01
This paper is devoted to a review of the connections between quantumchromodynamics (QCD) and string theories. One reviews the phenomenological models leading to string pictures in non perturbative QCD and the string effects, related to soft gluon coherence, which arise in perturbative QCD. One tries to build a string theory which goes to QCD at the zero slope limit. A specific model, based on superstring theories is shown to agree with QCD four point amplitudes at the Born approximation and with one loop corrections. One shows how this approach can provide a theoretical framework to account for the phenomenological property of parton-hadron duality
International Nuclear Information System (INIS)
Cohen-Tannoudji, G.
1989-01-01
This series of lectures is devoted to review ot he connections between QCD and string theories. One reviews the phenomenological models leading to string pictures in non perturbative QCD and the string effects, related to soft gluon coherence, which arise in perturbative QCD. One tries to build a string theory which goes to QCD at the zero slope limit. A specific model, based on superstring theories is shown to agree with QCD four point amplitudes at the Born approximation and with one loop corrections. One shows how this approach can provide a theoretical framework to account for the phenomenological property of parton-hadron duality.(author)
International Nuclear Information System (INIS)
Brodsky, S.J.
1992-09-01
The quantization of gauge theory at fixed light-cone time τ = t - z/c provides new perspectives for solving non-perturbative problems in quantum chromodynamics. The light-cone Fock state expansion provides both a precise definition of the relativistic wavefunctions of hadrons as bound-states of quarks and gluons and a general calculus for predicting QCD processes at the amplitude level. Applications to exclusive processes and weak decay amplitudes are discussed. The problem of computing the hadronic spectrum and the corresponding light-cone wavefunctions of QCD in one space and one time dimension has been successfully reduced to the diagonalization of a discrete representation of the light-cone Hamiltonian. The problems confronting the solution of gauge theories in 3 + 1 dimensions in the light-cone quantization formalism,, including zero modes and non-perturbative renormalization, are reviewed
Studies in the renormalization-prescription dependence of perturbative calculations
International Nuclear Information System (INIS)
Celmaster, W.; Sivers, D.
1981-01-01
Now that the quantitative testing of perturbative quantum chromodynamics (QCD) has become a major experimental and theoretical effort, it is important to understand the renormalization-prescription dependence of perturbative calculations. We stress the phenomenological importance of finding a definition of the QCD expansion parameter which reduces the magnitude of high-order corrections. We give explicit arguments suggesting that a choice of coupling based on momentum-space subtraction can be phenomenologically useful. Examples from QCD and QED are used to illustrate these arguments, and we also discuss possibilities for refining them
Energy momentum tensor and operator product expansion in local causal perturbation theory
International Nuclear Information System (INIS)
Prange, D.
2000-09-01
We derive new examples for algebraic relations of interacting fields in local perturbative quantum field theory. The fundamental building blocks in this approach are time ordered products of free (composed) fields. We give explicit formulas for the construction of Poincare covariant ones, which were already known to exist through cohomological arguments. For a large class of theories the canonical energy momentum tensor is shown to be conserved. Classical theories without dimensionful couplings admit an improved tensor that is additionally traceless. On the example of φ 4 -theory we discuss the improved tensor in the quantum theory. Its trace receives an anomalous contribution due to its conservation. Moreover, we define an interacting bilocal normal product for scalar theories. This leads to an operator product expansion of two time ordered fields. (orig.) [de
International Nuclear Information System (INIS)
Kita, Takafumi
2009-01-01
Quantum-field-theoretic descriptions of interacting condensed bosons have suffered from the lack of self-consistent approximation schemes satisfying Goldstone's theorem and dynamical conservation laws simultaneously. We present a procedure to construct such approximations systematically by using either an exact relation for the interaction energy or the Hugenholtz-Pines relation to express the thermodynamic potential in a Luttinger-Ward form. Inspection of the self-consistent perturbation expansion up to the third order with respect to the interaction shows that the two relations yield a unique identical result at each order, reproducing the conserving-gapless mean-field theory [T. Kita, J. Phys. Soc. Jpn. 74, 1891 (2005)] as the lowest-order approximation. The uniqueness implies that the series becomes exact when infinite terms are retained. We also derive useful expressions for the entropy and superfluid density in terms of Green's function and a set of real-time dynamical equations to describe thermalization of the condensate.
International Nuclear Information System (INIS)
Muzinich, I.J.
1980-01-01
The quark model of hadrons, when all constituents and gluons are included, has the possibility of accommodating not only what are conventionally accepted quark model states but also exotics of various kinds and eventually nuclei themselves. Recently, a considerable theoretical framework has evolved around quarks and gluons known as quantum chromodynamics. This theory is still at a primitive level as far as our ability to perform calculations. However, it is the only possible field theory that contains any hope of understanding both quark freedom at high energies and their strong binding within hadrons. I present a possible viewpoint on how both features could be true without apparent conflict. I also make some speculation on the nature of the perturbation expansion in such a world. What these speculations lack in originally I hope is compensated for by clarity
Inner-shell correlations and Sturm expansions in coupled perturbation calculations of atomic systems
International Nuclear Information System (INIS)
Sherstyuk, A.I.; Solov'eva, G.S.
1995-01-01
It is shown that virtual Hartree-Fock orbitals in Sturm-type expansions can be used to calculate the response of atomic systems to an external field within the framework of the coupled perturbation theory with allowance for correlation effects. The corrected electron-electron interaction in a system with field-distorted orbitals is considered by adding a nonlocal potential to a one-electron Hartree-Fock operator within each group of equivalent elections. The remaining correlation effects are calculated by solving a system of equations for corrections to the radial functions. The system is solved iteratively, with each subsequent iteration corresponding to a correction of an increasingly higher order in the electron--electron interaction. The explicit expression derived for the polarizability contains one-and two-particle radial integrals of the Sturm functions
Energy Technology Data Exchange (ETDEWEB)
Brambilla, M.; Di Renzo, F. [Universita di Parma (Italy); INFN, Gruppo Collegato di Parma, Dipartimento di Fisica e Scienze della Terra, Parma (Italy); Hasegawa, M. [Universita di Parma (Italy); Bogoliubov Laboratory of Theoretical Physics, Dubna (Russian Federation); INFN, Gruppo Collegato di Parma, Dipartimento di Fisica e Scienze della Terra, Parma (Italy)
2014-07-15
This is the third of a series of papers on three-loop computation of renormalization constants for Lattice QCD. Our main points of interest are results for the regularization defined by the Iwasaki gauge action and n{sub f} Wilson fermions. Our results for quark bilinears renormalized according to the RI'-MOM scheme can be compared to non-perturbative results. The latter are available for twisted mass QCD: being defined in the chiral limit, the renormalization constants must be the same. We also address more general problems. In particular, we discuss a few methodological issues connected to summing the perturbative series such as the effectiveness of boosted perturbation theory and the disentanglement of irrelevant and finite-volume contributions. Discussing these issues we consider not only the new results of this paper, but also those for the regularization defined by the tree-level Symanzik improved gauge action and n{sub f} Wilson fermions, which we presented in a recent paper of ours. We finally comment on the extent to which the techniques we put at work in the NSPT context can provide a fresher look into the lattice version of the RI'-MOM scheme. (orig.)
International Nuclear Information System (INIS)
Hughes, S.
1977-01-01
An expression is derived for the solar radiation pressure disturbing function on an Earth satellite orbit which takes into account the variation of the solar radiation flux with distance from the Sun's centre and the absorption of radiation by the satellite. This expression is then expanded in terms of the Keplerian elements of the satellite and solar orbits using Kaula's method (Astr. J.; 67:300 (1962)). The Kaula inclination functions are replaced by an equivalent set of modified Allan (Proc. R. Soc. A.; 288:60 (1965)) inclination functions. The resulting expression reduces to the form commonly used in solar radiation pressure perturbation studies (e.g. Aksnes, Cel. Mech.; 13:89 (1976)), when certain terms are neglected. If, as happens quite often in practice, a satellite's orbit is in near-resonance with certain of these neglected terms, these near-resonant terms can cause changes in the satellite's orbital elements comparable to those produced by the largest term in Aksnes's expression. A new expression for the solar radiation pressure disturbing function expansion is suggested for use in future studies of satellite orbits perturbed by solar radiation pressure. (author)
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.
QCD: Renormalization for the practitioner
International Nuclear Information System (INIS)
Pascual, P.; Tarrach, R.
1984-01-01
These notes correspond to a GIFT (Grupo Interuniversitario de Fisica Teorica) course which was given by us in autumn 1983 at the University of Barcelona. Their main subject is renormalization in perturbative QCD and only the last chapter goes beyond perturbation theory. They are essentially self contained and their aim is to teach the student the techniques of perturbative QCD and the QCD sum rules. (orig./HSI)
International Nuclear Information System (INIS)
Passos, E.M.J. de
1976-01-01
The relationship between the Johnson-Baranger time-dependent folded diagram (JBFD) expansion, and the time independent methods of perturbation theory, are investigated. In the nondegenerate case, the JBFD expansion and the Rayleigh-Schroedinger perturbation expansion, for the ground state energy, are identical. On the other hand, in the degenerate case, for the nonhermitian effective interaction considered, the JBFD expansion, of the effective interaction, is equal to the perturbative expansion of the effective interaction of the nonhermitian eigenvalue problem of Bloch and Brandow-Des Cloizeaux. For the two hermitian effective interactions, the JBFD expansion of the effective interaction differs from the perturbation expansion of the effective interaction of the hermitian eigenvalue problem of Des Cloizeaux [pt
Non-perturbative plaquette in 3d pure SU(3)
Hietanen, A; Laine, Mikko; Rummukainen, K; Schröder, Y
2005-01-01
We present a determination of the elementary plaquette and, after the subsequent ultraviolet subtractions, of the finite part of the gluon condensate, in lattice regularization in three-dimensional pure SU(3) gauge theory. Through a change of regularization scheme to MSbar and a matching back to full four-dimensional QCD, this result determines the first non-perturbative contribution in the weak-coupling expansion of hot QCD pressure.
Hadron structure from lattice QCD
International Nuclear Information System (INIS)
Schaefer, Andreas
2008-01-01
Some elements and current developments of lattice QCD are reviewed, with special emphasis on hadron structure observables. In principle, high precision experimental and lattice data provide nowadays a very detailled picture of the internal structure of hadrons. However, to relate both, a very good controle of perturbative QCD is needed in many cases. Finally chiral perturbation theory is extremely helpful to boost the precision of lattice calculations. The mutual need and benefit of all four elements: experiment, lattice QCD, perturbative QCD and chiral perturbation theory is the main topic of this review
Conformal expansions and renormalons
Energy Technology Data Exchange (ETDEWEB)
Rathsman, J.
2000-02-07
The coefficients in perturbative expansions in gauge theories are factorially increasing, predominantly due to renormalons. This type of factorial increase is not expected in conformal theories. In QCD conformal relations between observables can be defined in the presence of a perturbative infrared fixed-point. Using the Banks-Zaks expansion the authors study the effect of the large-order behavior of the perturbative series on the conformal coefficients. The authors find that in general these coefficients become factorially increasing. However, when the factorial behavior genuinely originates in a renormalon integral, as implied by a postulated skeleton expansion, it does not affect the conformal coefficients. As a consequence, the conformal coefficients will indeed be free of renormalon divergence, in accordance with previous observations concerning the smallness of these coefficients for specific observables. The authors further show that the correspondence of the BLM method with the skeleton expansion implies a unique scale-setting procedure. The BLM coefficients can be interpreted as the conformal coefficients in the series relating the fixed-point value of the observable with that of the skeleton effective charge. Through the skeleton expansion the relevance of renormalon-free conformal coefficients extends to real-world QCD.
Yepez-Martinez, Tochtli; Civitarese, Osvaldo; Hess, Peter O.
2018-02-01
Starting from an algebraic model based on the QCD-Hamiltonian and previously applied to study meson states, we have developed an extension of it in order to explore the structure of baryon states. In developing our approach we have adapted concepts taken from group theory and non-perturbative many-body methods to describe states built from effective quarks and anti-quarks degrees of freedom. As a Hamiltonian we have used the QCD Hamiltonian written in the Coulomb Gauge, and expressed it in terms of effective quark-antiquark, di-quarks and di-antiquark excitations. To gain some insights about the relevant interactions of quarks in hadronic states, the Hamiltonian was approximately diagonalized by mapping quark-antiquark pairs and di-quarks (di-antiquarks) onto phonon states. In dealing with the structure of the vacuum of the theory, color-scalar and color-vector states are introduced to account for ground-state correlations. While the use of a purely color-scalar ground state is an obvious choice, so that colorless hadrons contain at least three quarks, the presence of coupled color-vector pairs in the ground state allows for colorless excitations resulting from the action of color objects upon it.
Nagata, Takeshi; Iwata, Suehiro
2004-02-22
The locally projected self-consistent field molecular orbital method for molecular interaction (LP SCF MI) is reformulated for multifragment systems. For the perturbation expansion, two types of the local excited orbitals are defined; one is fully local in the basis set on a fragment, and the other has to be partially delocalized to the basis sets on the other fragments. The perturbation expansion calculations only within single excitations (LP SE MP2) are tested for water dimer, hydrogen fluoride dimer, and colinear symmetric ArM+ Ar (M = Na and K). The calculated binding energies of LP SE MP2 are all close to the corresponding counterpoise corrected SCF binding energy. By adding the single excitations, the deficiency in LP SCF MI is thus removed. The results suggest that the exclusion of the charge-transfer effects in LP SCF MI might indeed be the cause of the underestimation for the binding energy. (c) 2004 American Institute of Physics.
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.
International Nuclear Information System (INIS)
Retey, A.; Vermaseren, J.A.M.
2001-01-01
We present the analytic next-to-next-to-leading QCD calculation of some higher moments of deep inelastic structure functions in the leading twist approximation. We give results for the moments N=1,3,5,7,9,11,13 of the structure function F 3 . Similarly we present the moments N=10,12 for the flavour singlet and N=12,14 for the non-singlet structure functions F 2 and F L . We have calculated both the three-loop anomalous dimensions of the corresponding operators and the three-loop coefficient functions of the moments of these structure functions
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
International Nuclear Information System (INIS)
Pordt, A.
1985-10-01
The author describes the Mayer expansion in Euclidean lattice field theory by comparing it with the statistical mechanics of polymer systems. In this connection he discusses the Borel summability and the analyticity of the activities on the lattice. Furthermore the relations between renormalization and the Mayer expansion are considered. (HSI)
Light-cone quantized QCD and novel hadron phenomenology
International Nuclear Information System (INIS)
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
A simple interpolation for high and low momentum transfers in QCD
International Nuclear Information System (INIS)
Mignaco, J.A.; Roditi, I.
1982-01-01
It is shown that a simple rational approximation for the function β(g) of the renormalization group provides a useful expansion parameter for the perturbative regime in QCD and, simultaneously, allows for confinement the functional integral approximation to this problem. (Author) [pt
Extended Krenciglowa-Kuo method and perturbation expansion of Q-box
International Nuclear Information System (INIS)
Shimizu, Genki; Otsuka, Takaharu; Takayanagi, Kazuo
2015-01-01
The Extended Krenciglowa-Kuo (EKK) method is a microscopic method to construct the energy-independent effective Hamiltonian H eff ; provided with an exact Q-box of the system, we can show which eigenstates are described by H eff given by the EKK method. In actual calculations, however, we can calculate the Q-box only up to a finite order in the perturbation theory. In this work, we examine the EKK method with the approximate Q-box, and show that the perturbative calculation of the Q-box does not harm the convergence properties of the EKK iterative method. (author)
Czech Academy of Sciences Publication Activity Database
Abbas, G.; Ananthanarayan, B.; Caprini, I.; Fischer, Jan
2013-01-01
Roč. 88, č. 3 (2013), "034026-1"-"034026-16" ISSN 1550-7998 Institutional support: RVO:68378271 Keywords : Borel transformation * asymptotic series * Adler function Subject RIV: BE - Theoretical Physics Impact factor: 4.864, year: 2013
What can we learn from sum rules for vertex functions in QCD
International Nuclear Information System (INIS)
Craigie, N.S.; Stern, J.
1982-04-01
We demonstrate that the light cone sum rules for vertex functions based on the operator product expansion and QCD perturbation theory lead to interesting relationships between various non-perturbative parameters associated with hadronic bound states (e.g. vertex couplings and decay constants). We also show that such sum rules provide a valuable means of estimating the matrix elements of the higher spin operators in the meson wave function. (author)
Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions
International Nuclear Information System (INIS)
Bruno, Mattia; Djukanovic, Dalibor; 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
2015-01-01
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 Lüscher-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
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.)
Skands, Peter
2011-01-01
These lectures are directed at a level suitable for graduate students in experimental and theoretical High Energy Physics. They are intended to give an introduction to the theory and phenomenology of quantum chromodynamics (QCD) as it is used in collider physics applications. The aim is to bring the reader to a level where informed decisions can be made concerning different approaches and their uncertainties. The material is divided into four main areas: 1) fundamentals, 2) perturbative QCD, ...
The pressure of hot QCD up to $g^{6}$ ln(1/g)
Kajantie, Keijou; Rummukainen, K; Schröder, Y
2003-01-01
The free energy density, or pressure, of QCD has at high temperatures an expansion in the coupling constant g, known so far up to order g^5. We compute here the last contribution which can be determined perturbatively, g^6 ln(1/g), by summing together results for the 4-loop vacuum energy densities of two different three-dimensional effective field theories. We also demonstrate that the inclusion of the new perturbative g^6 ln(1/g) terms, together with the so far unknown perturbative and non-perturbative g^6 terms, could potentially extend the applicability of the resummed coupling constant series down to surprisingly low temperatures.
Moments of structure functions in full QCD
International Nuclear Information System (INIS)
Dolgov, D.; Brower, R.; Capitani, S.; Negele, J.W.; Pochinsky, A.; Renner, D.; Eicker, N.; Lippert, T.; Schilling, K.; Edwards, R.G.; Heller, U.M.
2001-01-01
Moments of the quark density distribution, moments of the quark helicity distribution, and the tensor charge are calculated in full QCD. Calculations of matrix elements of operators from the operator product expansion have been performed on 16 3 x 32 lattices for Wilson fermions at β = 5.6 using configurations from the SESAM collaboration and at β = 5.5 using configurations from SCRI. One-loop perturbative renormalization corrections are included. Selected results are compared with corresponding quenched calculations and with calculations using cooled configurations
Hadronization of QCD and effective interactions
International Nuclear Information System (INIS)
Frank, M.R.
1994-01-01
An introductory treatment of hadronization through functional integral calculus and bifocal Bose fields is given. Emphasis is placed on the utility of this approach for providing a connection between QCD and effective hadronic field theories. The hadronic interactions obtained by this method are nonlocal due to the QCD substructure, yet, in the presence of an electromagnetic field, maintain the electromagnetic gauge invariance manifest at the quark level. A local chiral model which is structurally consistent with chiral perturbation theory is obtained through a derivative expansion of the nonlocalities with determined, finite coefficients. Tree-level calculations of the pion form factor and π - π scattering, which illustrate the dual constituent-quark-chiral-model nature of this approach, are presented
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.
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.
Yan, Da-Cheng; Yang, Ping; Liu, Xin; Xiao, Zhen-Jun
2018-06-01
In this paper, we will make systematic calculations for the branching ratios and the CP-violating asymmetries of the twenty one Bbars0 → PV decays by employing the perturbative QCD (PQCD) factorization approach. Besides the full leading-order (LO) contributions, all currently known next-to-leading order (NLO) contributions are taken into account. We found numerically that: (a) the NLO contributions can provide ∼ 40% enhancement to the LO PQCD predictions for B (Bbars0 →K0K bar * 0) and B (Bbars0 →K±K*∓), or a ∼ 37% reduction to B (Bbars0 →π-K*+); and we confirmed that the inclusion of the known NLO contributions can improve significantly the agreement between the theory and those currently available experimental measurements; (b) the total effects on the PQCD predictions for the relevant Bs0 → P transition form factors after the inclusion of the NLO twist-2 and twist-3 contributions is generally small in magnitude: less than 10% enhancement respect to the leading order result; (c) for the "tree" dominated decay Bbars0 →K+ρ- and the "color-suppressed-tree" decay Bbars0 →π0K*0, the big difference between the PQCD predictions for their branching ratios are induced by different topological structure and by interference effects among the decay amplitude AT,C and AP: constructive for the first decay but destructive for the second one; and (d) for Bbars0 → V (η ,η‧) decays, the complex pattern of the PQCD predictions for their branching ratios can be understood by rather different topological structures and the interference effects between the decay amplitude A (Vηq) and A (Vηs) due to the η-η‧ mixing.
Quasi-two-body decays B→ηc(1S,2S [ρ(770,ρ(1450,ρ(1700→] ππ in the perturbative QCD approach
Directory of Open Access Journals (Sweden)
Ya Li
2017-11-01
Full Text Available In this paper, we calculated the branching ratios of the quasi-two-body decays B→ηc(1S,2S [ρ(770,ρ(1450,ρ(1700→]ππ by employing the perturbative QCD (PQCD approach. The contributions from the P-wave resonances ρ(770, ρ(1450 and ρ(1700 were taken into account. The two-pion distribution amplitude ΦππP is parameterized by the vector current time-like form factor Fπ to study the considered decay modes. We found that (a the PQCD predictions for the branching ratios of the considered quasi-two-body decays are in the order of 10−7∼10−6, while the two-body decay rates B(B→ηc(1S,2S(ρ(1450,ρ(1700 are extracted from those for the corresponding quasi-two-body decays; (b the whole pattern of the pion form factor-squared |Fπ|2 measured by the BABAR Collaboration could be understood based on our theoretical results; (c the general expectation based on the similarity between B→ηcππ and B→J/ψππ decays are confirmed: R2(ηc≈0.45 is consistent with the measured R2(J/ψ≈0.56±0.09 within errors; and (d new ratios R3(ηc(1S and R4(ηc(2S among the branching ratios of the considered decay modes are defined and could be tested by future experiments.
Conformal Symmetry as a Template for QCD
Energy Technology Data Exchange (ETDEWEB)
Brodsky, S
2004-08-04
Conformal symmetry is broken in physical QCD; nevertheless, one can use conformal symmetry as a template, systematically correcting for its nonzero {beta} function as well as higher-twist effects. For example, commensurate scale relations which relate QCD observables to each other, such as the generalized Crewther relation, have no renormalization scale or scheme ambiguity and retain a convergent perturbative structure which reflects the underlying conformal symmetry of the classical theory. The ''conformal correspondence principle'' also dictates the form of the expansion basis for hadronic distribution amplitudes. The AdS/CFT correspondence connecting superstring theory to superconformal gauge theory has important implications for hadron phenomenology in the conformal limit, including an all-orders demonstration of counting rules for hard exclusive processes as well as determining essential aspects of hadronic light-front wavefunctions. Theoretical and phenomenological evidence is now accumulating that QCD couplings based on physical observables such as {tau} decay become constant at small virtuality; i.e., effective charges develop an infrared fixed point in contradiction to the usual assumption of singular growth in the infrared. The near-constant behavior of effective couplings also suggests that QCD can be approximated as a conformal theory even at relatively small momentum transfer. The importance of using an analytic effective charge such as the pinch scheme for unifying the electroweak and strong couplings and forces is also emphasized.
Conformal Symmetry as a Template for QCD
International Nuclear Information System (INIS)
Brodsky, S
2004-01-01
Conformal symmetry is broken in physical QCD; nevertheless, one can use conformal symmetry as a template, systematically correcting for its nonzero β function as well as higher-twist effects. For example, commensurate scale relations which relate QCD observables to each other, such as the generalized Crewther relation, have no renormalization scale or scheme ambiguity and retain a convergent perturbative structure which reflects the underlying conformal symmetry of the classical theory. The ''conformal correspondence principle'' also dictates the form of the expansion basis for hadronic distribution amplitudes. The AdS/CFT correspondence connecting superstring theory to superconformal gauge theory has important implications for hadron phenomenology in the conformal limit, including an all-orders demonstration of counting rules for hard exclusive processes as well as determining essential aspects of hadronic light-front wavefunctions. Theoretical and phenomenological evidence is now accumulating that QCD couplings based on physical observables such as τ decay become constant at small virtuality; i.e., effective charges develop an infrared fixed point in contradiction to the usual assumption of singular growth in the infrared. The near-constant behavior of effective couplings also suggests that QCD can be approximated as a conformal theory even at relatively small momentum transfer. The importance of using an analytic effective charge such as the pinch scheme for unifying the electroweak and strong couplings and forces is also emphasized
Quantum chromodynamics (QCD) and collider physics
International Nuclear Information System (INIS)
Ellis, R.K.; Stirling, W.J.
1990-01-01
This report discusses: fundamentals of perturbative QCD; QCD in e + e - → hadrons; deep inelastic scattering and parton distributions; the QCD parton model in hadron-hadron collisions; large p T jet production in hadron-hadron collisions; the production of vector bosons in hadronic collisions; and the production of heavy quarks
Meyer, C; The ATLAS collaboration
2014-01-01
The ATLAS collaboration has performed studies of a wide range of QCD phenomena, from soft particle to hard photon and jet production. Recent soft-QCD measurements include studies of underlying event and vector meson production. Differential measurements of inclusive and dijet production provide stringent tests of high-order QCD predictions and provide input for determination of parton density functions. Measurements of isolated inclusive and di-photons cross sections for high transverse momentum photons test theoretical predictions of perturbative QCD and constrain parton density functions. An overview of these results is given.
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.
Lattice QCD. A critical status report
Energy Technology Data Exchange (ETDEWEB)
Jansen, Karl
2008-10-15
The substantial progress that has been achieved in lattice QCD in the last years is pointed out. I compare the simulation cost and systematic effects of several lattice QCD formulations and discuss a number of topics such as lattice spacing scaling, applications of chiral perturbation theory, non-perturbative renormalization and finite volume effects. Additionally, the importance of demonstrating universality is emphasized. (orig.)
Lattice QCD. A critical status report
International Nuclear Information System (INIS)
Jansen, Karl
2008-10-01
The substantial progress that has been achieved in lattice QCD in the last years is pointed out. I compare the simulation cost and systematic effects of several lattice QCD formulations and discuss a number of topics such as lattice spacing scaling, applications of chiral perturbation theory, non-perturbative renormalization and finite volume effects. Additionally, the importance of demonstrating universality is emphasized. (orig.)
Introduction to non-perturbative heavy quark effective theory
International Nuclear Information System (INIS)
Sommer, R.
2010-08-01
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 Λ and λ 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) n+1 if the theory was treated including (1/m) n terms. Clearly, the weakest point of HQET is that it intrinsically is an expansion. In practise, carrying it
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
International Nuclear Information System (INIS)
Glover, N.
2008-01-01
The need for predictions of standard model processes at the LHC at leading order and beyond is motivated. Recent developments in computing scattering amplitudes are reviewed. I describe the limitations of tree-level predictions, and how they may be improved at next-to-leading order. The current status of the field is discussed. (author)
International Nuclear Information System (INIS)
Konishi, K.
1980-01-01
The author discusses, in an introductory fashion, the latest developments in the study of hadronic jets produced in hard processes, based on perturbative QCD. Emphasis is on jet calculus (and its applications and generalizations), and on the appearance of a parton-like consistent, over-all picture of jet evolution in momentum, colour, and real space-time. (Auth.)
International Nuclear Information System (INIS)
Furmanski, W.
1981-08-01
The effects of scaling violation in QCD are discussed in the perturbative scheme, based on the factorization of mass singularities in the light-like gauge. Some recent applications including the next-to-leading corrections are presented (large psub(T) scattering, numerical analysis of the leptoproduction data). A proposal is made for extending the method on the higher twist sector. (author)
Perturbation theory in light-cone gauge
International Nuclear Information System (INIS)
Vianello, Eliana
2000-01-01
Perturbation calculations are presented for the light-cone gauge Schwinger model. Eigenstates can be calculated perturbatively but the perturbation theory is nonstandard. We hope to extend the work to QCD 2 to resolve some outstanding issues in those theories
International Nuclear Information System (INIS)
Takahashi, M.; Bracken, P.; Cizek, J.; Paldus, J.
1995-01-01
The perturbation expansion coefficients for the ground-state energy of the half-filled one-dimensional Hubbard model with N = 4 ν + 2, (ν = 1,2,...) sites and satisfying cyclic boundary conditions were calculated in the Hueckel limit (U/β → 0), where β designates the one-electron hopping or resonance integral, and U, the two-electron on-site Coulomb integral. This was achieved by solving-order by order-the Lieb-Wu equations, a system of transcendental equations that determines the set of quasi-momenta (k i ) and spin variable τ α for this model. The exact values for these quantities were found for the N = 6 member ring up to the 20th order in terms of the coupling constant B = U/2β, as well as numerically for 10 ≤ N ≤ 50, and the N = 6 Lieb-Wu system was reduced to a system of sextic algebraic equations. These results are compared with those of the infinite system derived analytically by Misurkin and Ovchinnikov. It is further shown how the results of this article can be used for the interpolation by the root of a polynomial. It is demonstrated that a polynomial of relatively small degree provides a very good approximation for the energy in the intermediate coupling region. 20 refs., 3 tabs
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.
Energy Technology Data Exchange (ETDEWEB)
Eriksen, Janus J., E-mail: janusje@chem.au.dk; Jørgensen, Poul [qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, DK-8000 Aarhus C (Denmark); Matthews, Devin A. [The Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712 (United States); Gauss, Jürgen [Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, D-55128 Mainz (Germany)
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.
International Nuclear Information System (INIS)
Harada, Masayasu
2009-01-01
Chiral perturbation theory has been used for great number of phenomenological analyses in low energy QCD as well as the lattice QCD analyses since the creation of the theory by Weinberg in 1979 followed by its consolidation by Gasser and Leutwyler in 1984 and 85. The theory is now the highly established one as the approach based on the effective field theory to search for Green function including quantum correlations in the frame of the systematic expansion technique using Lagrangian which includes all of the terms allowed by the symmetry. This review has been intended to describe how systematically physical quantities are calculated in the framework of the chiral symmetry. Consequently many of the various phenomenological analyses are not taken up here for which other reports are to be referred. Further views are foreseen to be developed based on the theory in addition to numbers of results reported up to the present. Finally π-π scattering is taken up to discuss to what energy scale the theory is available. (S. Funahashi)
International Nuclear Information System (INIS)
Sidorov, A.V.; Tokarev, M.V.
1997-01-01
A detailed NNLO QCD analysis of new CCFR data on xF 3 structure function including the target mass, higher twist and nuclear corrections was performed and parametrizations of the perturbative and power terms of the structure function were constructed. The results of QCD analysis of the structure function were used to study the Q 2 -dependence of the Gross-Llewellyn Smith sum rule. The α S /π-expansion of S GLS (Q 2 ) was studied and parameters of the expansion were found to be s 1 =2.74±0.01, s 2 =-2.22±0.23, s 3 =-7.86±1.74 which are in good agreement with the perturbative QCD predictions for the Gross-Llewellyn Smith sum rule in the next-to-leading and next-to-next-to-leading order
Supersingular quantum perturbations
International Nuclear Information System (INIS)
Detwiler, L.C.; Klauder, J.R.
1975-01-01
A perturbation potential is called supersingular whenever generally every matrix element of the perturbation in the unperturbed eigenstates is infinite. It follows that supersingular perturbations do not have conventional perturbation expansions, say for energy eigenvalues. By invoking variational arguments, we determine the asymptotic behavior of the energy eigenvalues for asymptotically small values of the coupling constant of the supersingular perturbation
International Nuclear Information System (INIS)
Weiland, J.; Ichikawa, Y.H.; Wilhelmsson, H.
1977-12-01
The Bogoliubov-Mitropolsky perturbation method has been applied to the study of a perturbation on soliton solutions to the nonlinear Schroedinger equation. The results are compared to those of Karpman and Maslov using the inverse scattering method and to those by Ott and Sudan on the KdV equation. (auth.)
International Nuclear Information System (INIS)
Keitel, Jan; Bartosch, Lorenz
2012-01-01
We consider the zero-dimensional O(N) vector model as a simple example to calculate n-point correlation functions using perturbation theory, the large-N expansion and the functional renormalization group (FRG). Comparing our findings with exact results, we show that perturbation theory breaks down for moderate interactions for all N, as one should expect. While the interaction-induced shift of the free energy and the self-energy are well described by the large-N expansion even for small N, this is not the case for higher order correlation functions. However, using the FRG in its one-particle irreducible formalism, we see that very few running couplings suffice to get accurate results for arbitrary N in the strong coupling regime, outperforming the large-N expansion for small N. We further remark on how the derivative expansion, a well-known approximation strategy for the FRG, reduces to an exact method for the zero-dimensional O(N) vector model. (paper)
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.
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.)
International Nuclear Information System (INIS)
Bietenholz, W.; Rakow, P.E.L.
2011-03-01
The δ-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 δ-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 R π , which has been computed to the third order in the δ-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 δ-regime. This is very tedious, but results compatible with the predictions for M R π have been obtained. Then we show that an extrapolation of pion masses measured in a larger volume towards the δ-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 3 . (orig.)
Polarized and unpolarized nucleon structure functions from lattice QCD
International Nuclear Information System (INIS)
Goeckeler, M.; Technische Hochschule Aachen; Horsley, R.; Humboldt-Universitaet, Berlin; Ilgenfritz, E.M.; Perlt, H.; Rakow, P.; Schierholz, G.; Forschungszentrum Juelich GmbH; Schiller, A.
1995-06-01
We report on a high statistics quenched lattice QCD calculation of the deep-inelastic structure functions F 1 , F 2 , g 1 and g 2 of the proton and neutron. The theoretical basis for the calculation is the operator product expansion. We consider the moments of the leading twist operators up to spin four. Using Wilson fermions the calculation is done for three values of K, and we perform the extrapolation to the chiral limit. The renormalization constants, which lead us from lattice to continuum operators, are calculated in perturbation theory to one loop order. (orig.)
Higher order QCD corrections in exclusive charmless B decays
International Nuclear Information System (INIS)
Bell, G.
2006-10-01
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 Λ QCD /m b and allows for the systematic implementation of perturbative corrections. In particular, we consider hadronic two-body decays as B → ππ and perform a conceptual analysis of heavy-to-light form factors which encode the strong interaction effects in semi-leptonic decays as B → πlν. 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-relativistic bound states which can be
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
Tests of hard and soft QCD with $e^{+}e^{-}$ Annihilation Data
Kluth, S
2002-01-01
Experimental tests of QCD predictions for event shape distributions combining contributions from hard and soft processes are discussed. The hard processes are predicted by perturbative QCD calculations. The soft processes cannot be calculated directly using perturbative QCD, they are treated by a power correction model based on the analysis of infrared renormalons. Furthermore, an analysis of the gauge structure of QCD is presented using fits of the colour factors within the same combined QCD predictions.
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.
Simulations of dimensionally reduced effective theories of high temperature QCD
Hietanen, Ari
Quantum chromodynamics (QCD) is the theory describing interaction between quarks and gluons. At low temperatures, quarks are confined forming hadrons, e.g. protons and neutrons. However, at extremely high temperatures the hadrons break apart and the matter transforms into plasma of individual quarks and gluons. In this theses the quark gluon plasma (QGP) phase of QCD is studied using lattice techniques in the framework of dimensionally reduced effective theories EQCD and MQCD. Two quantities are in particular interest: the pressure (or grand potential) and the quark number susceptibility. At high temperatures the pressure admits a generalised coupling constant expansion, where some coefficients are non-perturbative. We determine the first such contribution of order g^6 by performing lattice simulations in MQCD. This requires high precision lattice calculations, which we perform with different number of colors N_c to obtain N_c-dependence on the coefficient. The quark number susceptibility is studied by perf...
Trottier, H. D.; Shakespeare, N. H.; Lepage, G. P.; MacKenzie, P. B.
2002-05-01
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 34 to 164) and couplings (from β~9 to β~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.
Foundations of quantum chromodynamics: Perturbative methods in gauge theories
International Nuclear Information System (INIS)
Muta, T.
1986-01-01
This volume develops the techniques of perturbative QCD in great detail starting with field theory. Aside from extensive treatments of the renormalization group technique, the operator product expansion formalism and their applications to short-distance reactions, this book provides a comprehensive introduction to gauge field theories. Examples and exercises are provided to amplify the discussions on important topics. Contents: Introduction; Elements of Quantum Chromodynamics; The Renormalization Group Method; Asymptotic Freedom; Operator Product Expansion Formalism; Applications; Renormalization Scheme Dependence; Factorization Theorem; Further Applications; Power Corrections; Infrared Problem. Power Correlations; Infrared Problem
Chiral perturbation theory with nucleons
International Nuclear Information System (INIS)
Meissner, U.G.
1991-09-01
I review the constraints posed on the interactions of pions, nucleons and photons by the spontaneously broken chiral symmetry of QCD. The framework to perform these calculations, chiral perturbation theory, is briefly discussed in the meson sector. The method is a simultaneous expansion of the Greens functions in powers of external moments and quark masses around the massless case, the chiral limit. To perform this expansion, use is made of a phenomenological Lagrangian which encodes the Ward-identities and pertinent symmetries of QCD. The concept of chiral power counting is introduced. The main part of the lectures of consists in describing how to include baryons (nucleons) and how the chiral structure is modified by the fact that the nucleon mass in the chiral limit does not vanish. Particular emphasis is put on working out applications to show the strengths and limitations of the methods. Some processes which are discussed are threshold photopion production, low-energy compton scattering off nucleons, πN scattering and the σ-term. The implications of the broken chiral symmetry on the nuclear forces are briefly described. An alternative approach, in which the baryons are treated as very heavy fields, is touched upon
The structure of gluon radiation in QCD
International Nuclear Information System (INIS)
Parke, S.; Mangano, M.
1989-08-01
For massless QCD the hard scattering amplitudes are naturally written in terms of the dual color expansion. here I present this expansion for purely gluonic processes and processes involving quark-antiquark pairs and gluons. The properties of the sub-amplitudes as well as explicit algebraic expressions are given for a number of these processes. Also, I demonstrate how to recover massless QED amplitudes from the dual expansion of massless QCD. 16 refs., 3 figs., 1 tab
The structure of gluon radiation in QCD
International Nuclear Information System (INIS)
Parke, S.; Mangano, M.
1990-01-01
For massless QCD the hard scattering amplitudes are naturally written in terms of the dual color expansion. Here I present this expansion for purely gluonic processes and processes involving quark-antiquark pairs and gluons. The properties of the sub-amplitudes as well as explicit algebraic expressions are given for a number of these processess. Finally, I demonstrate how to recover massless QED amplitudes from the dual expansion of massless QCD
Observations on discretization errors in twisted-mass lattice QCD
International Nuclear Information System (INIS)
Sharpe, Stephen R.
2005-01-01
I make a number of observations concerning discretization errors in twisted-mass lattice QCD that can be deduced by applying chiral perturbation theory including lattice artifacts. (1) The line along which the partially conserved axial current quark mass vanishes in the untwisted-mass-twisted-mass plane makes an angle to the twisted-mass axis which is a direct measure of O(a) terms in the chiral Lagrangian, and is found numerically to be large; (2) Numerical results for pionic quantities in the mass plane show the qualitative properties predicted by chiral perturbation theory, in particular, an asymmetry in slopes between positive and negative untwisted quark masses; (3) By extending the description of the 'Aoki regime' (where m q ∼a 2 Λ QCD 3 ) to next-to-leading order in chiral perturbation theory I show how the phase-transition lines and lines of maximal twist (using different definitions) extend into this region, and give predictions for the functional form of pionic quantities; (4) I argue that the recent claim that lattice artifacts at maximal twist have apparent infrared singularities in the chiral limit results from expanding about the incorrect vacuum state. Shifting to the correct vacuum (as can be done using chiral perturbation theory) the apparent singularities are summed into nonsingular, and furthermore predicted, forms. I further argue that there is no breakdown in the Symanzik expansion in powers of lattice spacing, and no barrier to simulating at maximal twist in the Aoki regime
Color-magnetic permeability of QCD vacuum
Energy Technology Data Exchange (ETDEWEB)
Saito, T [Kyoto Prefectural Univ. of Medicine (Japan); Shigemoto, K
1980-03-01
In the very strong background gauge field the QCD true vacuum has been shown to have lower energy than the ''perturbative vacuum.'' The color-magnetic permeability of the QCD true vacuum is then calculated to be 1/2 within the quark-one-loop approximation.
Recent developments in QCD for LHC physics
International Nuclear Information System (INIS)
Anastasiou, C.
2006-01-01
We will review recent theoretical developments in QCD, attempting to assess the phenomenological impact of new theoretical results and to identify potentially useful directions for the future. A part of the talk will be devoted to new imaginative ideas which are rapidly changing the traditional approach to QCD computations, and surprising theoretical discoveries from perturbative calculations on the structure of gauge theories. (author)
Understanding of QCD through solvable models
Energy Technology Data Exchange (ETDEWEB)
Bhattacharya, G.
1980-07-01
Various aspects of strong interaction physics are discussed. It is shown that several nontrivial features arise from non-perturbative 'solutions' of QCD-like models in (1+1) dimensions. An attempt is made to bring these features in (3+1) dimensional semiclassical treatments of 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).
Dirac spectral density and mass anomalous dimension in 2+1 flavor QCD
Directory of Open Access Journals (Sweden)
Nakayama Katsumasa
2018-01-01
Full Text Available We compute the Dirac spectral density of QCD in a wide range of eigenvalues by using a stochastic method. We use 2+1 flavor lattice ensembles generated with Mobius domain-wall fermion at three lattice spacings (a = 0:083; 0:055; 0:044 fm to estimate the continuum limit. The discretization effect can be minimized by a generalization of the valence domain-wall fermion. The spectral density at relatively high eigenvalues can be matched with perturbation theory. We compare the lattice results with the perturbative expansion available to O(α4s.
The time development of QCD jets
International Nuclear Information System (INIS)
Caneschi, L.
1979-01-01
The time development of jets in perturbative QCD is studied. In spite of the fact that the total time for the jet to develop increases indefinitely with increasing energy, quark antiquark pairs remain unscreened only an infinitesimal time. (author)
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
Perturbative quantum chromodynamics
International Nuclear Information System (INIS)
Radyushkin, A.V.
1987-01-01
The latest achievements in perturbative quantum chromodynamics (QCD) relating to the progress in factorization of small and large distances are presented. The following problems are concerned: Development of the theory of Sudakov effects on the basis of mean contour formalism. Development of nonlocal condensate formalism. Calculation of hadron wave functions and hadron distribution functions using QCD method of sum rules. Development of the theory of Regge behaviour in QCD, behaviour of structure functions at small x. Study of polarization effects in hadron processes with high momentum transfer
International Nuclear Information System (INIS)
Gervais, J.L.; Neveu, A.
1980-01-01
Recent works of the authors on string interpretation of the Wilson loop operators in QCD are reviewed in a self-contained fashion. Although most of the results habe already appeared in print, some new material is presented in renormalization of the Wilson loop operator and on the use of light-cone expansion to derive a linear string-like equation in light-cone formalism. (orig.)
International Nuclear Information System (INIS)
Trottier, H.D.; Shakespeare, N.H.; 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 β≅9 to β≅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
Lattice QCD results on soft and hard probes of strongly interacting matter
Kaczmarek, Olaf
2017-11-01
We present recent results from lattice QCD relevant for the study of strongly interacting matter as it is produced in heavy ion collision experiments. The equation of state at non-vanishing density from a Taylor expansion up to 6th order will be discussed for a strangeness neutral system and using the expansion coefficients of the series limits on the critical point are estimated. Chemical freeze-out temperatures from the STAR and ALICE Collaborations will be compared to lines of constant physics calculated from the Taylor expansion of QCD bulk thermodynamic quantities. We show that qualitative features of the √{sNN} dependence of skewness and kurtosis ratios of net proton-number fluctuations measured by the STAR Collaboration can be understood from QCD results for cumulants of conserved baryon-number fluctuations. As an example for recent progress towards the determination of spectral and transport properties of the QGP from lattice QCD, we will present constraints on the thermal photon rate determined from a spectral reconstruction of continuum extrapolated lattice correlation functions in combination with input from most recent perturbative calculations.
ChPT calculations for the analysis of lattice QCD data
International Nuclear Information System (INIS)
Greil, Ludwig
2014-01-01
We present calculations within the framework of three-flavor chiral perturbation theory (ChPT) for several observables (first moments of parton distributions, baryon octet masses and vector meson masses including phi-omega-mixing). We use lattice QCD data to determine the local couplings appearing in this chosen effective theory and we use these extrapolations to study the convergence of the chiral expansion around the symmetric point where all light quark masses have the same value. We also comment on the various benefits that stem from an expansion around the symmetric point.
Higgs boson production at hadron colliders at N3LO in QCD
Mistlberger, Bernhard
2018-05-01
We present the Higgs boson production cross section at Hadron colliders in the gluon fusion production mode through N3LO in perturbative QCD. Specifically, we work in an effective theory where the top quark is assumed to be infinitely heavy and all other quarks are considered to be massless. Our result is the first exact formula for a partonic hadron collider cross section at N3LO in perturbative QCD. Furthermore, our result is an analytic computation of a hadron collider cross section involving elliptic integrals. We derive numerical predictions for the Higgs boson cross section at the LHC. Previously this result was approximated by an expansion of the cross section around the production threshold of the Higgs boson and we compare our findings. Finally, we study the impact of our new result on the state of the art prediction for the Higgs boson cross section at the LHC.
International Nuclear Information System (INIS)
Honkonen, J.; Komarova, M.; Nalimov, M.
2002-01-01
Large order asymptotic behaviour of renormalization constants in the minimal subtraction scheme for the φ 4 (4 - ε) theory is discussed. Well-known results of the asymptotic 4 - ε expansion of critical indices are shown to be far from the large order asymptotic value. A convergent series for the model φ 4 (4 - ε) is then considered. Radius of convergence of the series for Green functions and for renormalisation group functions is studied. The results of the convergent expansion of critical indices in the 4 - ε scheme are revalued using the knowledge of large order asymptotics. Specific features of this procedure are discussed (Authors)
QCD contributions to vacuum polarization
International Nuclear Information System (INIS)
Reinders, L.J.; Rubinstein, H.R.; Yazaki, S.
1980-01-01
We have computed to lowest non-trivial order the perturbative and non-perturbative contributions to the vacuum polarization from all currents up to and including spin 2 ++ . These expressions are important, for example to evaluate QCD sum rules for heavy and light quark systems as shown by Shifman, Vainshtein and Zakharov. Most of the known ones are verified, one slightly changed, and many new ones are displayed. (orig.)
CERN. Geneva
2006-01-01
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.
International Nuclear Information System (INIS)
Wilson, S.; Silver, D.M.
1979-01-01
Third-order diagrammatic perturbation theory provides a simple and accurate description of the electronic structure of atoms and molecules beyond that afforded by independent electron models. The largest corrections to such treatments, the fourth-order terms, are presented and discussed. All of the diagrams, which arise when the closed-shell Hartree--Fock function is utilized as a reference function, are given through fourth order. 18 references
LHC physics: challenges for QCD
Frixione, S.
2003-01-01
I review the status of the comparisons between a few measurements at hadronic colliders and perturbative QCD predictions, which emphasize the need for improving the current computations. Such improvements will be mandatory for a satisfactory understanding of high-energy collisions at the LHC
Method of analytic continuation by duality in QCD: Beyond QCD sum rules
International Nuclear Information System (INIS)
Kremer, M.; Nasrallah, N.F.; Papadopoulos, N.A.; Schilcher, K.
1986-01-01
We present the method of analytic continuation by duality which allows the approximate continuation of QCD amplitudes to small values of the momentum variables where direct perturbative calculations are not possible. This allows a substantial extension of the domain of applications of hadronic QCD phenomenology. The method is illustrated by a simple example which shows its essential features
International Nuclear Information System (INIS)
Aurenche, P.; Douiri, A.; Baier, R.; Fontannaz, M.; Schiff, D.
1985-01-01
We calculate the corrections of order αsub(s) to the process γγ->HX where both initial photons are real. The analytic expressions are given and a detailed discussion of the variation of the corrections with psub(T) and rapidity is presented. The dependence on the factorization prescription and scale is also discussed. Using the equivalent photon approximation the cross-section for e + e - ->e + e - HX is calculated both in the PEP/PETRA and LEP energy range. Based on the vector meson dominance model the non perturbative background is estimated and its importance for present and future experiments is emphasized. (orig.)
International Nuclear Information System (INIS)
Reya, E.
1982-01-01
The some of motivations for color and the numerous qualitative successes of QCD are presented. Non-leading higher order contributions to the (x, Q 2 )-dependence of scaling violations of non-singlet and singlet structure functions are discussed, especially non-perturbative correction to deep inelastic processes such as higher twist contributions. Finally the topic of how to account theoretically for the existence of free fractionally charged particles by concentrating mainly on spontaneously breaking SU(3) color is presented. (M.F.W.)
International Nuclear Information System (INIS)
Dominicis, C. de
1961-01-01
The grand partition function Z (α,β) of a quantum system is studied, using diagrammatic representations of the perturbation expansion. For a fermions system, it is possible to show, by proper resummation, without approximations but under some 'regularity hypothesis', that Log Z (α,β) takes a form where, besides trivial dependences, α and β only appear through a statistical factor F k - = [1 + e -α+βε k 0 -βW k ] -1 . W k is a (real) self-consistent potential, generalized to all orders and can be defined by a stationary condition on Log Z (α,β) under variations of F k - . The thermodynamical quantities take a form analogous to the expressions Landau introduced for the Fermi liquids. The zero temperature limit (for isotropic systems) gives back Goldstone expressions for the ground state of a system. (author) [fr
Czech Academy of Sciences Publication Activity Database
Caprini, I.; Fischer, Jan
2011-01-01
Roč. 84, č. 5 (2011), 054019/1-054019/15 ISSN 1550-7998 R&D Projects: GA MŠk LA08015 Institutional research plan: CEZ:AV0Z10100502 Keywords : quantum chromodynamics, * conformal mapping * tau lepton decay Subject RIV: BF - Elementary Particles and High Energy Physics Impact factor: 4.558, year: 2011
The supercritical pomeron in QCD
International Nuclear Information System (INIS)
White, A. R.
1998-01-01
Deep-inelastic diffractive scaling violations have provided fundamental insight into the QCD pomeron, suggesting a single gluon inner structure rather than that of a perturbative two-gluon bound state. This talk outlines a derivation of a high-energy, transverse momentum cut-off, confining solution of QCD. The pomeron, in first approximation, is a single reggeized gluon plus a ''wee parton'' component that compensates for the color and particle properties of the gluon. This solution corresponds to a super-critical phase of Reggeon Field Theory
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
Briceño, R. A.
2016-11-01
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.
Holographic models and the QCD trace anomaly
International Nuclear Information System (INIS)
Goity, Jose L.; Trinchero, Roberto C.
2012-01-01
Five dimensional dilaton models are considered as possible holographic duals of the pure gauge QCD vacuum. In the framework of these models, the QCD trace anomaly equation is considered. Each quantity appearing in that equation is computed by holographic means. Two exact solutions for different dilaton potentials corresponding to perturbative and non-perturbative β-functions are studied. It is shown that in the perturbative case, where the β-function is the QCD one at leading order, the resulting space is not asymptotically AdS. In the non-perturbative case, the model considered presents confinement of static quarks and leads to a non-vanishing gluon condensate, although it does not correspond to an asymptotically free theory. In both cases analyses based on the trace anomaly and on Wilson loops are carried out.
International Nuclear Information System (INIS)
Sidorov, A.V.; Tokarev, M.V.
1997-01-01
A detailed NNLO QCD analysis of new CCFR data on xF 3 structure function including the target mass, higher twist and nuclear corrections was performed and parametrizations of the perturbative and power terms of the structure function were constructed. The results of QDC analysis of the structure function were used to study the Q 2 -dependence of the Gross-Llewellyn-Smith sum rule. The α s /π-expansion of S GLS (Q 2 ) was studied and parameters of the expansion were found to be s 1 =2.74±0.01, s 2 =-2.22±0.23, s 3 =-7.86±1.74 which are in good agreement with the perturbative QCD predictions for the Gross-Llewellyn-Smith sum rule in the next-to-leading and next-to-next-leading order
Lattice regularized chiral perturbation theory
International Nuclear Information System (INIS)
Borasoy, Bugra; Lewis, Randy; Ouimet, Pierre-Philippe A.
2004-01-01
Chiral perturbation theory can be defined and regularized on a spacetime lattice. A few motivations are discussed here, and an explicit lattice Lagrangian is reviewed. A particular aspect of the connection between lattice chiral perturbation theory and lattice QCD is explored through a study of the Wess-Zumino-Witten term
Asymptotics of QCD factorization in exclusive hadronic decays of B mesons
International Nuclear Information System (INIS)
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-bar 0 →D (*)+ M - , where M is a light meson. In the 'large-β 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 Λ QCD /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(β 0 n-1 α s n ) corrections to explore the numerical significance of higher-order perturbative and power corrections. We also derive explicit expressions for the O(β 0 α s 2 ) contributions to the kernels, and for the renormalon singularities corresponding to power corrections of order (Λ QCD /m b ) 2 . Finally, we study the limit m c →0 relevant to charmless hadronic decays such as B→ππ
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.)
An Introduction to Perturbative Methods in Gauge Theories
International Nuclear Information System (INIS)
T Muta
1998-01-01
This volume develops the techniques of perturbative QCD in great pedagogical detail starting with field theory. Aside from extensive treatments of the renormalization group technique, the operator product expansion formalism and their applications to short-distance reactions, this book provides a comprehensive introduction to gauge theories. Examples and exercises are provided to amplify the discussions on important topics. This is an ideal textbook on the subject of quantum chromodynamics and is essential for researchers and graduate students in high energy physics, nuclear physics and mathematical physics
Perturbative quantum chromodynamics
International Nuclear Information System (INIS)
Brodsky, S.J.
1979-12-01
The application of QCD to hadron dynamics at short distances, where asymptotic freedom allows a systematic perturbative approach, is addressed. The main theme of the approach is to incorporate systematically the effects of the hadronic wave function in large momentum transfer exclusive and inclusive reactions. Although it is conventional to treat the hadron as a classical source of on-shell quarks, there are important dynamical effects due to hadronic constituent structure which lead to a broader testing ground for QCD. QCD predictions are discussed for exclusive processes and form factors at large momentum transfer in which the short-distance behavior and the finite compositeness of the hadronic wave functions play crucial roles. Many of the standard tests of QCD are reviewed including the predictions for R = sigma/sub e + e - →had//sigma/sub e + e - →μ + μ - /, the structure functions of hadrons and photons, jet phenomena, and the QCD corrections to deep inelastic processes. The exclusive-inclusive connection in QCD, the effects of power-law scale-breaking contributions, and the important role of the available energy in controlling logarithmic scale violations are also discussed. 150 references, 44 figures
International Nuclear Information System (INIS)
Ecker, G.
1995-11-01
After a brief introduction to chiral perturbation theory, the effective field theory of the standard model at low energies, two recent applications are reviewed: elastic pion-pion scattering to two-loop accuracy and the complete renormalized pion-nucleon Lagrangian to O(P 3 ) in the chiral expansion. (author)
Self-consistent areas law in QCD
International Nuclear Information System (INIS)
Makeenko, Yu.M.; Migdal, A.A.
1980-01-01
The problem of obtaining the self-consistent areas law in quantum chromodynamics (QCD) is considered from the point of view of the quark confinement. The exact equation for the loop average in multicolor QCD is reduced to a bootstrap form. Its iterations yield new manifestly gauge invariant perturbation theory in the loop space, reproducing asymptotic freedom. For large loops, the areas law apprears to be a self-consistent solution
Analyzing Bs - anti Bs mixing. Non-perturbative contributions to bag parameters from sum rules
International Nuclear Information System (INIS)
Mannel, T.; Pivovarov, A.A.; Russian Academy of Sciecnes, Moscow
2007-03-01
We use QCD sum rules to compute matrix elements of the ΔB=2 operators appearing in the heavy-quark expansion of the width difference of the B s mass eigenstates. Our analysis includes the leading-order operators Q and Q S , as well as the subleading operators R 2 and R 3 , which appear at next-to-leading order in the 1/m 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.)
Dynamical effects of QCD vacuum structure
International Nuclear Information System (INIS)
Ferreira, Erasmo
1994-01-01
The role of the QCD vacuum structure in the determination of the properties of states and processes occurring in the confinement regime of QCD is reviewed. The finite range of the vacuum correlations is discussed, and an analytical form is suggested for the correlation functions. The role of the vacuum quantum numbers in the phenomenology of high-energy scattering is reviewed. The vacuum correlation model of non-perturbative QCD is mentioned as a bridge between the fundamental theory and the description of the experiments. (author). 13 refs., 1 fig
Precision Light Flavor Physics from Lattice QCD
Murphy, David
In this thesis we present three distinct contributions to the study of light flavor physics using the techniques of lattice QCD. These results are arranged into four self-contained papers. The first two papers concern global fits of the quark mass, lattice spacing, and finite volume dependence of the pseudoscalar meson masses and decay constants, computed in a series of lattice QCD simulations, to partially quenched SU(2) and SU(3) chiral perturbation theory (chiPT). These fits determine a subset of the low energy constants of chiral perturbation theory -- in some cases with increased precision, and in other cases for the first time -- which, once determined, can be used to compute other observables and amplitudes in chiPT. We also use our formalism to self-consistently probe the behavior of the (asymptotic) chiral expansion as a function of the quark masses by repeating the fits with different subsets of the data. The third paper concerns the first lattice QCD calculation of the semileptonic K0 → pi-l +nul ( Kl3) form factor at vanishing momentum transfer, f+Kpi(0), with physical mass domain wall quarks. The value of this form factor can be combined with a Standard Model analysis of the experimentally measured K0 → pi -l+nu l decay rate to extract a precise value of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element Vus, and to test unitarity of the CKM matrix. We also discuss lattice calculations of the pion and kaon decay constants, which can be used to extract Vud through an analogous Standard Model analysis of experimental constraints on leptonic pion and kaon decays. The final paper explores the recently proposed exact one flavor algorithm (EOFA). This algorithm has been shown to drastically reduce the memory footprint required to simulate single quark flavors on the lattice relative to the widely used rational hybrid Monte Carlo (RHMC) algorithm, while also offering modest O(20%) speed-ups. We independently derive the exact one flavor action, explore its
Transition temperature to the superconducting phase of QCD at high baryon density
International Nuclear Information System (INIS)
Brown, William E.; Liu, James T.; Ren, Hai-cang
2000-01-01
Recent interest in the study of color superconductivity has focused on the regime of high baryon density where perturbative QCD may be employed. Based on the dominant one-gluon-exchange interaction, both the transition temperature and zero temperature gap have been determined to leading order in the coupling g. While the leading non-BCS behavior T C ∼μg -5 e -κ/g is easily obtained, the pre-exponential factor has proved more difficult to evaluate. Focusing on the transition temperature, we present a perturbative derivation of this factor, exact to leading order in g. This approach is first motivated by the study of a toy model and involves working to second order in the perturbative expansion. We compare this result to the zero temperature gap. Additionally, we extend the analysis to the case of higher angular momentum for longitudinal and transverse quark pairing. (c) 2000 The American Physical Society
Testing QCD with Hypothetical Tau Leptons
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.
1998-10-21
We construct new tests of perturbative QCD by considering a hypothetical {tau} lepton of arbitrary mass, which decays hadronically through the electromagnetic current. We can explicitly compute its hadronic width ratio directly as an integral over the e{sup +}e{sup -} annihilation cross section ratio, R{sub e{sup +}e{sup -}}. Furthermore, we can design a set of commensurate scale relations and perturbative QCD tests by varying the weight function away from the form associated with the V-A decay of the physical {tau}. This method allows the wide range of the R{sub e{sup +}e{sup -}} data to be used as a probe of perturbative QCD.
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.
Analytical Computation of Energy-Energy Correlation at Next-to-Leading Order in QCD.
Dixon, Lance J; Luo, Ming-Xing; Shtabovenko, Vladyslav; Yang, Tong-Zhi; Zhu, Hua Xing
2018-03-09
The energy-energy correlation (EEC) between two detectors in e^{+}e^{-} annihilation was computed analytically at leading order in QCD almost 40 years ago, and numerically at next-to-leading order (NLO) starting in the 1980s. We present the first analytical result for the EEC at NLO, which is remarkably simple, and facilitates analytical study of the perturbative structure of the EEC. We provide the expansion of the EEC in the collinear and back-to-back regions through next-to-leading power, information which should aid resummation in these regions.
Large N lattice QCD and its extended strong-weak connection to the hypersphere
International Nuclear Information System (INIS)
Christensen, Alexander S.; Myers, Joyce C.; Pedersen, Peter D.
2014-01-01
We calculate an effective Polyakov line action of QCD at large N c and large N f from a combined lattice strong coupling and hopping expansion working to second order in both, where the order is defined by the number of windings in the Polyakov line. We compare with the action, truncated at the same order, of continuum QCD on S 1 ×S d at weak coupling from one loop perturbation theory, and find that a large N c correspondence of equations of motion found in http://dx.doi.org/10.1007/JHEP10(2012)067 at leading order, can be extended to the next order. Throughout the paper, we review the background necessary for computing higher order corrections to the lattice effective action, in order to make higher order comparisons more straightforward
The QCD equation of state for two flavours at non-zero chemical potential
Ejiri, S; Döring, M; Hands, S J; Kaczmarek, O; Karsch, Frithjof; Laermann, E; Redlich, K
2006-01-01
We present results of a simulation of 2 flavour QCD on a $16^3\\times4$ lattice using p4-improved staggered fermions with bare quark mass $m/T=0.4$. Derivatives of the thermodynamic grand canonical partition function $Z(V,T,\\mu_u,\\mu_d)$ with respect to chemical potentials $\\mu_{u,d}$ for different quark flavours are calculated up to sixth order, enabling estimates of the pressure and the quark number density as well as the chiral condensate and various susceptibilities as functions of $\\mu_{u,d}$ via Taylor series expansion. Results are compared to high temperature perturbation theory as well as a hadron resonance gas model. We also analyze baryon as well as isospin fluctuations and discuss the relation to the chiral critical point in the QCD phase diagram. We moreover discuss the dependence of the heavy quark free energy on the chemical potential.
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 QCD coupling in the pre-asymptotic region
Energy Technology Data Exchange (ETDEWEB)
Burgio, G.; Di Renzo, F.; Parrinello, C.; Pittori, C
1999-03-01
We study deviations from the perturbative asymptotic behaviour in the running QCD coupling by analysing non-perturbative measurements of {alpha}{sub s}(p) at low momenta (p {approx} 2 GeV) as obtained from the lattice three-gluon vertex. Our exploratory study provides some evidence for power corrections to the perturbative running proportional to 1/p{sup 2}.
The running coupling of QCD with four flavors
International Nuclear Information System (INIS)
Tekin, Fatih; Wolff, Ulli; Sommer, Rainer
2010-06-01
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.)
Measuring infrared contributions to the QCD pressure
Kajantie, Keijo; Rummukainen, K; Schröder, Y
2002-01-01
For the pressure (or free energy) of QCD, four-dimensional (4d) lattice data is available at zero baryon density up to a few times the critical temperature $T_c$. Perturbation theory, on the other hand, has serious convergence problems even at very high temperatures. In a combined analytical and three-dimensional (3d) lattice method, we show that it is possible to compute the QCD pressure from about $2 T_c$ to infinity. The numerical accuracy is good enough to resolve in principle, e.g., logarithmic contributions related to 4-loop perturbation theory.
Setting the renormalization scale in QCD: The principle of maximum conformality
DEFF Research Database (Denmark)
Brodsky, S. J.; Di Giustino, L.
2012-01-01
A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale mu of the running coupling alpha(s)(mu(2)). The purpose of the running coupling in any gauge theory is to sum all terms involving the beta function; in fact, when the renormali......A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale mu of the running coupling alpha(s)(mu(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 nonconformal beta not equal 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...
Strong coupling QCD and the (π+,π-) reaction
International Nuclear Information System (INIS)
Miller, G.A.; Washington Univ., Seattle, WA
1989-01-01
Previous six-quark bag model calculations are in disagreement with new (π + , π - ) data, but conventional nucleonic calculations are generally successful. Six-quark bag models are related to perturbative QCD. I argue that the strong coupling limit of QCD (SCQCD) is a more appropriate starting point for nuclear physics. 15 refs., 3 figs
Pion form factor within QCD instanton vacuum model
International Nuclear Information System (INIS)
Dorokhov, A.E.
1997-01-01
Instanton induced pion wave function is constructed. It provides an intrinsic k 1 dependence which suppress soft virtual one-gluon exchanges and thus legitimate the perturbative QCD (pQCD) calculations of the pion electromagnetic form factor in the region of momentum transfers above the scale. (author)
QCD with jets and photons at ATLAS and CMS
AUTHOR|(INSPIRE)INSPIRE-00265099; 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 $\\alpha_{S}$.
Instantons in the QCD vacuum and in deep inelastic scattering
International Nuclear Information System (INIS)
Ringwald, A.; Schrempp, F.
1999-01-01
We give a brief status report on our on-going investigation of the prospects to discover QCD instantons in deep inelastic scattering (DIS) at HERA. A recent high-quality lattice study of the topological structure of the QCD vacuum is exploited to provide crucial support of our predictions for DIS, based on instanton perturbation theory
Determinations of the QCD strong coupling αsub(s) and the scale Λsub(QCD)
International Nuclear Information System (INIS)
Duke, D.W.; Roberts, R.G.
1984-08-01
The authors review determinations, via experiment of the strong coupling of QCD, αsub(s). In almost every case, the results are used of perturbative QCD to make the necessary extraction from data. These include scaling violations of deep inelastic scattering, e + e - annihilation experiments (including quarkonium decays) and lepton pair production. Finally estimates for Λ from lattice calculations are listed. (author)
NNLO QCD corrections to the $B\\to X_s \\gamma$ matrix elements using interpolation in $m_c$
Misiak, M; Misiak, Mikolaj; Steinhauser, Matthias
2007-01-01
One of the most troublesome contributions to the NNLO QCD corrections to B -> X_s gamma originates from three-loop matrix elements of four-quark operators. A part of this contribution that is proportional to the QCD beta-function coefficient beta_0 was found in 2003 as an expansion in m_c/m_b. In the present paper, we evaluate the asymptotic behaviour of the complete contribution for m_c >> m_b/2. The asymptotic form of the beta_0-part matches the small-m_c expansion very well at the threshold m_c = m_b/2. For the remaining part, we perform an interpolation down to the measured value of m_c, assuming that the beta_0-part is a good approximation at m_c=0. Combining our results with other contributions to the NNLO QCD corrections, we find BR(B -> X_s gamma) = (3.15 +_ 0.23) x 10^-4 for E_gamma > 1.6 GeV in the B-meson rest frame. The indicated error has been obtained by adding in quadrature the following uncertainties: non-perturbative (5%), parametric (3%), higher-order perturbative (3%), and the interpolation...
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.)
International Nuclear Information System (INIS)
Kaneko, T.; Hashimoto, S.; Aoki, S.; Hoffmann, R.
2007-03-01
We perform a non-perturbative determination of the improvement coefficient c 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 A is imposed at constant physics. Combining our results with the perturbative expansion, c A is now known rather precisely for a -1 >or similar 1.6 GeV. (orig.)
Testing QCD with current algebra
International Nuclear Information System (INIS)
Leutwyler, H.
1984-01-01
Spontaneously broken chiral symmetry fixes the low energy structure of QCD to a large extent. I show how to determine the Green's functions to first nonleading order in a simultaneous expansion in powers of the momenta and of the u- and d-quark masses. In particular, I discuss the corrections of order M π 2 to the low energy theorems for ππ scattering. 19 refs., 1 tab. (author)
Alkofer, Reinhard; von Smekal, Lorenz
2001-11-01
Recent studies of QCD Green's functions and their applications in hadronic physics are reviewed. We discuss the definition of the generating functional in gauge theories, in particular, the rôle of redundant degrees of freedom, possibilities of a complete gauge fixing versus gauge fixing in presence of Gribov copies, BRS invariance and positivity. The apparent contradiction between positivity and colour antiscreening in combination with BRS invariance in QCD is considered. Evidence for the violation of positivity by quarks and transverse gluons in the covariant gauge is collected, and it is argued that this is one manifestation of confinement. We summarise the derivation of the Dyson-Schwinger equations (DSEs) of QED and QCD. For the latter, the implications of BRS invariance on the Green's functions are explored. The possible influence of instantons on DSEs is discussed in a two-dimensional model. In QED in (2+1) and (3+1) dimensions, the solutions for Green's functions provide tests of truncation schemes which can under certain circumstances be extended to the DSEs of QCD. We discuss some limitations of such extensions and assess the validity of assumptions for QCD as motivated from studies in QED. Truncation schemes for DSEs are discussed in axial and related gauges, as well as in the Landau gauge. Furthermore, we review the available results from a systematic non-perturbative expansion scheme established for Landau gauge QCD. Comparisons to related lattice results, where available, are presented. The applications of QCD Green's functions to hadron physics are summarised. Properties of ground state mesons are discussed on the basis of the ladder Bethe-Salpeter equation for quarks and antiquarks. The Goldstone nature of pseudoscalar mesons and a mechanism for diquark confinement beyond the ladder approximation are reviewed. We discuss some properties of ground state baryons based on their description as Bethe-Salpeter/Faddeev bound states of quark
Variational techniques in non-perturbative QCD
Kovner, Alex; Kovner, Alex
2004-01-01
We review attempts to apply the variational principle to understand the vacuum of non-abelian gauge theories. In particular, we focus on the method explored by Ian Kogan and collaborators, which imposes exact gauge invariance on the trial Gaussian wave functional prior to the minimization of energy. We describe the application of the method to a toy model -- confining compact QED in 2+1 dimensions -- where it works wonderfully and reproduces all known non-trivial results. We then follow its applications to pure Yang-Mills theory in 3+1 dimensions at zero and finite temperature. Among the results of the variational calculation are dynamical mass generation and the analytic description of the deconfinement phase transition.
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.
Gribov-Lipatov relation in perturbative QCD
International Nuclear Information System (INIS)
Pavlenko, O.P.; Snigipev, A.M.; Zinov'ev, G.M.
1982-01-01
It is shown that at small X the violation of the Gribov-Lipatov relation between the distribution Dsub(A)sup(B)(X, Qsup(2)) (where X is a fraction of parton longitudinal momentum, Q 2 is a square of momentum transfer) and fragmentation anti Dsub(A)sup(B)(X, Qsup(2)) functions depends on the order in which their X- and Q 2 -asymptotic behaviours are investigated
Energy Technology Data Exchange (ETDEWEB)
Brodsky, S.
2004-11-30
In these lectures, I survey a number of applications of light-front methods to hadron and nuclear physics phenomenology and dynamics, including light-front statistical physics. 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. Given the LFWFs, one can compute form factors, heavy hadron decay amplitudes, hadron distribution amplitudes, and the generalized parton distributions underlying deeply virtual Compton scattering. The quantum fluctuations represented by the light-front Fock expansion leads to novel QCD phenomena such as color transparency, intrinsic heavy quark distributions, diffractive dissociation, and hidden-color components of nuclear wavefunctions. A new test of hidden color in deuteron photodisintegration is proposed. The origin of leading-twist phenomena such as the diffractive component of deep inelastic scattering, single-spin asymmetries, nuclear shadowing and antishadowing is also discussed; these phenomena cannot be described by light-front wavefunctions of the target computed in isolation. Part of the anomalous NuTeV results for the weak mixing angle {theta}{sub W} could be due to the non-universality of nuclear antishadowing for charged and neutral currents.
Challenges for QCD theory: some personal reflections
International Nuclear Information System (INIS)
Sjöstrand, T
2013-01-01
At the LHC all processes are QCD ones, whether ‘signal’ or ‘background’. In this review the frontiers of current QCD research are addressed, towards increased understanding, improved calculational precision, and role in potential future discoveries. Issues raised include: - the limits of perturbative QCD calculations and parton distribution usage,; - the nature of multiparton interactions,; - the impact of colour reconnection on physical observables,; - the need for progress on hadronization modelling,; - the improvements of parton showers and their combination with the matrix-element description,; - the use of QCD concepts in Beyond-the-Standard-Model scenarios and; - the key position of event generators and other software in the successful exploration of LHC physics. On the way, several questions are posed, where further studies are needed. (paper)
International Nuclear Information System (INIS)
Ellis, J.
1978-05-01
A review is given of reliable quantum chromodynamics predictions which either have or soon can be verified by experiment. Included are a discussion of the classic application of quantum chromodynamics perturbation theory and asymptotic freedom to predict scaling violations in deep inelastic leptoproduction experiments, with emphasis on the first direct experimental confirmation of the numerical values of the anomalous dimensions; a review of recent advances in developing and justifying quantum chromodynamics perturbation theory predictions for a number of physical applications not underwritten by the operator product expansion and renormalization group arguments; and mention of attempts to consider the reliability of quantum chromodynamics perturbation theory predictions, given the fact that nonperturbative effects are presumably crucial in quantum chromodynamics. 100 references
Solving QCD via multi-Regge theory
International Nuclear Information System (INIS)
White, A. R.
1998-01-01
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 ∼ a Regge pole at small Q 2 and a single gluon at larger Q 2 . (F 2 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
Calculating hadronic properties in strong QCD
International Nuclear Information System (INIS)
Pennington, M.R.
1996-01-01
This talk gives a brief review of the progress that has been made in calculating the properties of hadrons in strong QCD. In keeping with this meeting I will concentrate on those properties that can be studied with electromagnetic probes. Though perturbative QCD is highly successful, it only applies in a limited kinematic regime, where hard scattering occur, and the quarks move in the interaction region as if they are free, pointlike objects. However, the bulk of strong interactions are governed by the long distance regime, where the strong interaction is strong. It is this regime of length scales of the order of a Fermi, that determines the spectrum of light hadrons and their properties. The calculation of these properties requires an understanding of non-perturbative QCD, of confinement and chiral symmetry breaking. (author)
Wilson's operator expansion: can it fail
International Nuclear Information System (INIS)
Novikov, V.A.; Shifman, M.A.; Vainshtein, A.I.; Zakharov, V.I.
1984-01-01
The status of poperator product expansion (OPE) in the presence of nonperturbative effects is duscussed within the framework of some simople models 4d Higgs model, 2d sigma-model and Schwinger model are considered. The general formulation of OPE is presented and it is demonstrated that there exists a consistent procedure allowing one to define unabiguously both coefficient functions and matrix elements of compositie operators. One of the key elements of the procedure is introduction of an auxiliary paramparameter, the normalization point μ. The two extremss considered are lambda phi 4 theory with no spontaneous breaking of the symmetry and O(N) sigma model in the limit N→infinity. In the former case there is only perturbative contribution to (phi 2 ) while in the latter case the perturbative pieces are suppressed by 1/N factors. Numerically QCD is much closer to the O(N) sigma model in the large N limit. Comments on specific features of QCD are presented
Relating hard QCD processes through universality of mass singularities
International Nuclear Information System (INIS)
Amati, D.; Petronzio, R.; Veneziano, G.
1978-01-01
Hard QCD processes involving final jets are studied and compared by means of a simple approach to mass singularities. This is based on the Lee-Nauenberg-Kinoshita theorem and on a rather subtle use of gauge invariance in hard collinear gluon bremsstrahlung. One-loop results are easily derived for processes involving any number of initial quarks and/or currents. The method greatly simplifies the computation of higher-order loops at the leading log level and the preliminary results allow one to conclude that the crucial features encountered at the one-loop level will persist. The authors are thus able to relate different hard processes and to show that suitable ratios of cross sections, being free from mass singularities, can be computed perturbatively, as usually assumed in QCD-inspired parton models. It is also possible to relate the universal leading mass singularities to leading scaling violations and to extend therefor the results of the operator product expansion method to processes outside the range of the light-cone analysis. Some delicate points caused by confinement-related singularities (e.g. narrow resonance poles) are also discussed. (Auth.)
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....
Exact mquark ≠ 0 condensates in QCD1+1(NC → ∞)
International Nuclear Information System (INIS)
Burkardt, M.
1994-01-01
In the limit of an infinite number of colors, we derive an analytic expression for the quark condensation in QCD 1+1 as a function of the quark mass and the gauge coupling constant. For zero quark mass, a nonvanishing quark condensate is obtained. Nevertheless, we prove that there is no phase transition as a function of the quark mass. It is furthermore shown that the expansion of left-angle 0|bar ψψ|0 right-angle in the gauge coupling has zero radius of convergence but that the perturbation series is Borel summable with finite radius of convergence. The nonanalytic behavior m q →0 ∼ -N C √G 2 can only be obtained by summing the perturbation series to infinite order
Meson-Baryon Scattering Lengths from Mixed-Action Lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Will Detmold, William Detmold, Konstantinos Orginos, Aaron Torok, Silas R Beane, Thomas C Luu, Assumpta Parreno, Martin Savage, Andre Walker-Loud
2010-04-01
The $\\pi^+\\Sigma^+$, $\\pi^+\\Xi^0$ , $K^+p$, $K^+n$, and $K^0 \\Xi^0$ scattering lengths are calculated in mixed-action Lattice QCD with domain-wall valence quarks on the asqtad-improved coarse MILC configurations at four light-quark masses, and at two light-quark masses on the fine MILC configurations. Heavy Baryon Chiral Perturbation Theory with two and three flavors of light quarks is used to perform the chiral extrapolations. We find no convergence for the kaon-baryon processes in the three-flavor chiral expansion. Using the two-flavor chiral expansion, we find $a_{\\pi^+\\Sigma^+} = ?0.197 ± 0.017$ fm, and $a_{\\pi^+\\Xi^0} = ?0.098 0.017$ fm, where the comprehensive error includes statistical and systematic uncertainties.
Towards the chiral limit in QCD
International Nuclear Information System (INIS)
Shailesh Chandrasekharan
2006-01-01
Computing hadronic observables by solving QCD from first principles with realistic quark masses is an important challenge in fundamental nuclear and particle physics research. Although lattice QCD provides a rigorous framework for such calculations many difficulties arise. Firstly, there are no good algorithms to solve lattice QCD with realistically light quark masses. Secondly, due to critical slowing down, Monte Carlo algorithms are able to access only small lattice sizes on coarse lattices. Finally, due to sign problems it is almost impossible to study the physics of finite baryon density. Lattice QCD contains roughly three mass scales: the cutoff (or inverse lattice spacing) a -1 , the confinement scale Λ QCD , and the pion mass m π . Most conventional Monte Carlo algorithms for QCD become inefficient in two regimes: when Λ QCD becomes small compared to a -1 and when m π becomes small compared to Λ QCD . The former can be largely controlled by perturbation theory thanks to asymptotic freedom. The latter is more difficult since chiral extrapolations are typically non-analytic and can be unreliable if the calculations are not done at sufficiently small quark masses. For this reason it has been difficult to compute quantities close to the chiral limit. The essential goal behind this proposal was to develop a new approach towards understanding QCD and QCD-like theories with sufficiently light quarks. The proposal was based on a novel cluster algorithm discovered in the strong coupling limit with staggered fermions [1]. This algorithm allowed us to explore the physics of exactly massless quarks and as well as light quarks. Thus, the hope was that this discovery would lead to the complete solution of at least a few strongly coupled QCD-like theories. The solution would be far better than those achievable through conventional methods and thus would be able to shed light on the chiral physics from a new direction. By the end of the funding period, the project led
Heterotic Pomeron: high energy hadronic collisions in QCD
International Nuclear Information System (INIS)
Chung-I Tan
1993-01-01
A unified treatment of high energy collisions in QCD is presented. Using a probabilistic approach, both perturbative (hard) and non-perturbative (soft) components are incorporated in a consistent fashion, leading to a ''Heterotic Pomeron''. As a Regge trajectory, it is non linear, approaching 1 in the limit t → -∞. 2 tabs., 9 refs
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.)
The instanton liquid model of QCD
International Nuclear Information System (INIS)
Blotz, A.
1998-01-01
Within a microscopic model for the non-perturbative vacuum of QCD, hadronic correlation functions are calculated. In the model the vacuum is a statistical, interacting ensemble of instantons and anti-instantons at the scale of Λ QCD . Hadronic two-point as well as three-point correlation functions are evaluated and compared with phenomenological information about the spectra, couplings and form factors. Especially the electro magnetic form factor of the pion is obtained and new predictions for the charm contribution to DIS structure functions are made
Exclusive hadronic and nuclear processes in QCD
International Nuclear Information System (INIS)
Brodsky, S.J.
1985-12-01
Hadronic and nuclear processes are covered, in which all final particles are measured at large invariant masses compared with each other, i.e., large momentum transfer exclusive reactions. Hadronic wave functions in QCD and QCD sum rule constraints on hadron wave functions are discussed. The question of the range of applicability of the factorization formula and perturbation theory for exclusive processes is considered. Some consequences of quark and gluon degrees of freedom in nuclei are discussed which are outside the usual domain of traditional nuclear physics. 44 refs., 7 figs
Playing with QCD I: effective field theories
International Nuclear Information System (INIS)
Fraga, Eduardo S.
2009-01-01
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)
QCD physics with the CMS experiment
Cerci, Salim
2017-01-01
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.
QCD Physics with the CMS Experiment
Cerci, S.
2017-12-01
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 αS . 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.
QCD sum rules for D mesons. In-medium effects, chiral symmetry aspects and higher orders
Energy Technology Data Exchange (ETDEWEB)
Buchheim, Thomas
2017-04-11
Heavy open flavor mesons can serve as probes of hot and dense, strongly interacting matter in heavy-ion collisions suitable to mimic the extreme conditions shortly after the big-bang or in compact stars. Thus, the thorough theoretical investigation of medium modifications of D mesons is of utmost importance for the interpretation of the experimental data. Even at finite thermodynamic parameters, such as temperature and density, the non-perturbative framework of QCD sum rules allows for the determination of hadronic properties which are not accessible in perturbative quantum chromodynamics (QCD). By virtue of the separation of scales, long-range effects of hadrons are related to quark and gluon degrees of freedom, where features of the hadron spectrum are linked to condensates parameterizing the complex QCD ground state. This thesis furnishes the conception and calculus of QCD sum rules with emphasis on in-medium effects which are inevitable when addressing such effects in higher order contributions. In this regard, the notion and implications of medium-specific condensates are elucidated. Motivated by the significant numerical impact of four-quark condensates to the ρ meson sum rule we evaluate, for the first time, the corresponding in-medium mass-dimension 6 terms for D mesons tentatively employing the factorization hypothesis. Four-quark condensates containing heavy-quark operators may be included into the sum rule analysis utilizing the in-medium heavy-quark expansion made available here. Particular quark condensates are potential order parameters of chiral symmetry breaking, which is the mass generating mechanism of QCD giving the essential mass fraction to light hadrons. The interplay of altered spectral properties with changing in-medium QCD condensates, i. e. the chiral order parameters, can be studied with chiral partner sum rules. Although, introduced for light spin-1 mesons we foster their generalization to spin-0 open charm mesons demonstrating their
QCD sum rules for D mesons. In-medium effects, chiral symmetry aspects and higher orders
International Nuclear Information System (INIS)
Buchheim, Thomas
2017-01-01
Heavy open flavor mesons can serve as probes of hot and dense, strongly interacting matter in heavy-ion collisions suitable to mimic the extreme conditions shortly after the big-bang or in compact stars. Thus, the thorough theoretical investigation of medium modifications of D mesons is of utmost importance for the interpretation of the experimental data. Even at finite thermodynamic parameters, such as temperature and density, the non-perturbative framework of QCD sum rules allows for the determination of hadronic properties which are not accessible in perturbative quantum chromodynamics (QCD). By virtue of the separation of scales, long-range effects of hadrons are related to quark and gluon degrees of freedom, where features of the hadron spectrum are linked to condensates parameterizing the complex QCD ground state. This thesis furnishes the conception and calculus of QCD sum rules with emphasis on in-medium effects which are inevitable when addressing such effects in higher order contributions. In this regard, the notion and implications of medium-specific condensates are elucidated. Motivated by the significant numerical impact of four-quark condensates to the ρ meson sum rule we evaluate, for the first time, the corresponding in-medium mass-dimension 6 terms for D mesons tentatively employing the factorization hypothesis. Four-quark condensates containing heavy-quark operators may be included into the sum rule analysis utilizing the in-medium heavy-quark expansion made available here. Particular quark condensates are potential order parameters of chiral symmetry breaking, which is the mass generating mechanism of QCD giving the essential mass fraction to light hadrons. The interplay of altered spectral properties with changing in-medium QCD condensates, i. e. the chiral order parameters, can be studied with chiral partner sum rules. Although, introduced for light spin-1 mesons we foster their generalization to spin-0 open charm mesons demonstrating their
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.)
QCD sum-rules analysis of vector (1-) heavy quarkonium meson-hybrid mixing
Palameta, A.; Ho, J.; Harnett, D.; Steele, T. G.
2018-02-01
We use QCD Laplace sum rules to study meson-hybrid mixing in vector (1-) heavy quarkonium. We compute the QCD cross-correlator between a heavy meson current and a heavy hybrid current within the operator product expansion. In addition to leading-order perturbation theory, we include four- and six-dimensional gluon condensate contributions as well as a six-dimensional quark condensate contribution. We construct several single and multiresonance models that take known hadron masses as inputs. We investigate which resonances couple to both currents and so exhibit meson-hybrid mixing. Compared to single resonance models that include only the ground state, we find that models that also include excited states lead to significantly improved agreement between QCD and experiment. In the charmonium sector, we find that meson-hybrid mixing is consistent with a two-resonance model consisting of the J /ψ and a 4.3 GeV resonance. In the bottomonium sector, we find evidence for meson-hybrid mixing in the ϒ (1 S ) , ϒ (2 S ), ϒ (3 S ), and ϒ (4 S ).
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.
International Nuclear Information System (INIS)
Brodsky, Stanley J.; de Teramond, Guy F.
2007-01-01
The AdS/CFT correspondence between string theory in AdS space and conformal .eld theories in physical spacetime leads to an analytic, semi-classical model for strongly-coupled QCD which has scale invariance and dimensional counting at short distances and color confinement at large distances. Although QCD is not conformally invariant, one can nevertheless use the mathematical representation of the conformal group in five-dimensional anti-de Sitter space to construct a first approximation to the theory. The AdS/CFT correspondence also provides insights into the inherently non-perturbative aspects of QCD, such as the orbital and radial spectra of hadrons and the form of hadronic wavefunctions. In particular, we show that there is an exact correspondence between the fifth-dimensional coordinate of AdS space z and a specific impact variable ζ which measures the separation of the quark and gluonic constituents within the hadron in ordinary space-time. This connection allows one to compute the analytic form of the frame-independent light-front wavefunctions, the fundamental entities which encode hadron properties and allow the computation of decay constants, form factors, and other exclusive scattering amplitudes. New relativistic lightfront equations in ordinary space-time are found which reproduce the results obtained using the 5-dimensional theory. The effective light-front equations possess remarkable algebraic structures and integrability properties. Since they are complete and orthonormal, the AdS/CFT model wavefunctions can also be used as a basis for the diagonalization of the full light-front QCD Hamiltonian, thus systematically improving the AdS/CFT approximation
Nucleon structure from lattice QCD
International Nuclear Information System (INIS)
Dinter, Simon
2012-01-01
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 2 ) discretization effects.
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.
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.
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.
Power corrections to exclusive processes in QCD
Energy Technology Data Exchange (ETDEWEB)
Mankiewicz, Lech
2002-02-01
In practice applicability of twist expansion crucially depends on the magnitude to power corrections to the leading-twist amplitude. I illustrate this point by considering explicit examples of two hard exclusive processes in QCD. In the case of {gamma}{sup *}{gamma} {yields} {pi}{pi} amplitude power corrections are small enough such that it should be possible to describe current experimental data by the leading-twist QCD prediction. The photon helicity-flip amplitude in DVCS on a nucleon receives large kinematical power corrections which screen the leading-twist prediction up to large values of the hard photon virtuality.
Dynamical chiral-symmetry breaking in dual QCD
International Nuclear Information System (INIS)
Krein, G.; Williams, A.G.
1991-01-01
We have extended recent studies by Baker, Ball, and Zachariasen (BBZ) of dynamical chiral-symmetry breaking in dual QCD. Specifically, we have taken dual QCD to specify the nonperturbative infrared nature of the quark-quark interaction and then we have smoothly connected onto this the known leading-log perturbative QCD interaction in the ultraviolet region. In addition, we have solved for a momentum-dependent self-energy and have used the complete lowest-order dual QCD quark-quark interaction. We calculate the quark condensate left-angle bar qq right-angle and the pion decay constant f π within this model. We find that the dual QCD parameters needed to give acceptable results are reasonably consistent with those extracted from independent physical considerations by BBZ
Problems at the interface between perturbative and nonperturbative quantum chromodynamics
International Nuclear Information System (INIS)
Brodsky, S.J.; Bodwin, G.T.; Lepage, G.P.
1983-06-01
Predictions based on perturbative QCD rest on three premises: (1) that hadronic interactions become weak in strength at small invariant separation; (2) that the perturbative expansion in α/sub s/(Q) is well-defined; and (3) factorization: all effects of collinear singularities, confinement, nonperturbative interactions, and bound state dynamics can be isolated at large momentum transfer in terms of structure functions, fragmentation functions, or in the case of exclusive processes, distribution amplitudes. The assumption that the perturbative expansion for hard scattering amplitudes converges has certainly not been demonstrated; in addition, there are serious ambiguities concerning the choice of renormalization scheme and scale choice Q 2 for the expansion in α/sub s/(Q 2 ). We will discuss a new procedure to at least partly rectify the latter problem. In the case of exclusive processes, the factorization of hadronic amplitudes at large momentum transfer in the form of distribution amplitudes convoluted with hard scattering quark-gluon subprocess amplitudes can be demonstrated systematically to all orders in α/sub s/(Q 2 ). In the case of inclusive reactions, factorization remains an ansatz; general all-orders proofs do not exist because of the complications of soft initial state interactions for hadron-induced processes; thus far factorization has only been verified to two loops beyond lowest order in a regime where the applicability of perturbation theory is in doubt. However, we shall show that a necessary condition for the validity of factorization in inclusive reactions is that the momentum transfer must be large compared to the (rest frame) length of the target. We review the present status of the factorization ansatz. 52 references
Properties of the quark gluon plasma from lattice QCD
International Nuclear Information System (INIS)
Mages, Simon Wolfgang
2015-01-01
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.
International Nuclear Information System (INIS)
Ecker, G.
1996-06-01
After a general introduction to the structure of effective field theories, the main ingredients of chiral perturbation theory are reviewed. Applications include the light quark mass ratios and pion-pion scattering to two-loop accuracy. In the pion-nucleon system, the linear σ model is contrasted with chiral perturbation theory. The heavy-nucleon expansion is used to construct the effective pion-nucleon Lagrangian to third order in the low-energy expansion, with applications to nucleon Compton scattering. (author)
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.
Nonperturbative QCD and elastic processes at CEBAF energies
International Nuclear Information System (INIS)
Radyushkin, A.V.
1994-01-01
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 knownclose quotes) short-distance effects and nonperturbative (open-quotes unknownclose 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 2 closer to 10 GeV 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
Hadronic and nuclear interactions in QCD
International Nuclear Information System (INIS)
1982-01-01
Despite the evidence that QCD - or something close to it - gives a correct description of the structure of hadrons and their interactions, it seems paradoxical that the theory has thus far had very little impact in nuclear physics. One reason for this is that the application of QCD to distances larger than 1 fm involves coherent, non-perturbative dynamics which is beyond present calculational techniques. For example, in QCD the nuclear force can evidently be ascribed to quark interchange and gluon exchange processes. These, however, are as complicated to analyze from a fundamental point of view as is the analogous covalent bond in molecular physics. Since a detailed description of quark-quark interactions and the structure of hadronic wavefunctions is not yet well-understood in QCD, it is evident that a quantitative first-principle description of the nuclear force will require a great deal of theoretical effort. Another reason for the limited impact of QCD in nuclear physics has been the conventional assumption that nuclear interactions can for the most part be analyzed in terms of an effective meson-nucleon field theory or potential model in isolation from the details of short distance quark and gluon structure of hadrons. These lectures, argue that this view is untenable: in fact, there is no correspondence principle which yields traditional nuclear physics as a rigorous large-distance or non-relativistic limit of QCD dynamics. On the other hand, the distinctions between standard nuclear physics dynamics and QCD at nuclear dimensions are extremely interesting and illuminating for both particle and nuclear physics
International Nuclear Information System (INIS)
Ali, A.
1981-04-01
The promise of e + e - annihilation as an ideal laboratory to test Quantum Chromodynamics, QCD, has been the dominating theme in elementary particle physics during the last several years. An attempt is made to partially survey the subject in deep perturbative region in e + e - annihilation where theoretical ambiguities are minimal. Topics discussed include a review of the renormalization group methods relevant for e + e - annihilation, total hadronic cross section, jets and large-psub(T) phenomena, non-perturbative quark and gluon fragmentation effects and analysis of the jet distributions measured at DORIS, SPEAR and PETRA. My hope is to review realistic tests of QCD in e + e - annihilation - as opposed to the ultimate tests, which abound in literature. (orig.)
The multiparton distribution equations in QCD
International Nuclear Information System (INIS)
Shelest, V.P.; Snigirev, A.M.; Zinovjev, G.M.
1982-01-01
The equations for multiparton distribution functions of deep-inelastic lepton-hadron scattering and fragmentation functions of e + e - annihilation are obtained by using parton interpretation of the leading logarithm diagrams of perturbative QCD theory. These equations have essentially different structute but the solutions are the same on the definite initial conditions and coincide with the jet calculus rules. The difference is crucial when these equations for hadron jets description are generalized [ru
High momentum transfer processes in QCD
International Nuclear Information System (INIS)
Efremov, A.V.; Radyushkin, A.V.
1978-01-01
A unified approach to the investigation of inclusive high momentum transfer processes in the QCD framework is proposed. A modified parton model (with parton distribution functions depending on an additional renormalization parameter) is shown to be valid in all orders of perturbation theory. The approach is also applicable for studying wide-angle elastic scattering processes of colourless bound states of quarks (the hadrons). The asymptotic behaviour of pion electromagnetic form factor is calculated as an example
Large x Behaviour and the Non-Perturbative Structure of Hadronic Systems
Energy Technology Data Exchange (ETDEWEB)
Anthony W. Thomas
2005-02-01
While the traditional interest in structure functions has been the confirmation of the predictions of perturbative QCD, this data also contains a wealth of information on how QCD works in the infrared, or confinement, region. As the challenge of the strong force now turns to the study of QCD in the non-perturbative region, such information is extremely valuable.We outline some of the key issues for both nucleon and nuclear structure functions.
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...
The effective QCD theory at low energy; La theorie effective de QCD a basse energie
Energy Technology Data Exchange (ETDEWEB)
Knecht, M. [Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire
1995-12-31
Quantum chromodynamics is studied here in the range of low energies. The Chiral perturbation theory is presented, this theory is based on a thorough study of QCD symmetry, of general field theory principles and of S-matrices. Ward identities are defined within the scope of current algebras and by using functional method. Their consequences on Chiral structure of QCD emptiness and on strong interaction at low energies are studied. The pion-pion diffusion at low energies is treated as an example. (A.C.) 70 refs.
Studying the perturbative Reggeon
International Nuclear Information System (INIS)
Griffiths, S.; Ross, D.A.
2000-01-01
We consider the flavour non-singlet Reggeon within the context of perturbative QCD. This consists of ladders built out of ''reggeized'' quarks. We propose a method for the numerical solution of the integro-differential equation for the amplitude describing the exchange of such a Reggeon. The solution is known to have a sharp rise at low values of Bjorken-x when applied to non-singlet quantities in deep-inelastic scattering. We show that when the running of the coupling is taken into account this sharp rise is further enhanced, although the Q 2 dependence is suppressed by the introduction of the running coupling. We also investigate the effects of simulating non-perturbative physics by introducing a constituent mass for the soft quarks and an effective mass for the soft gluons exchanged in the t-channel. (orig.)
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.
Perturbation of an exact strong gravity solution
International Nuclear Information System (INIS)
Baran, S.A.
1982-10-01
Perturbations of an exact strong gravity solution are investigated. It is shown, by using the new multipole expansions previously presented, that this exact and static spherically symmetric solution is stable under odd parity perturbations. (author)
The Asymptotic Expansion of Lattice Loop Integrals Around the Continuum Limit
International Nuclear Information System (INIS)
Becher, Thomas G
2002-01-01
We present a method of computing any one-loop integral in lattice perturbation theory by systematically expanding around its continuum limit. At any order in the expansion in the lattice spacing, the result can be written as a sum of continuum loop integrals in analytic regularization and a few genuine lattice integrals (''master integrals''). These lattice master integrals are independent of external momenta and masses and can be computed numerically. At the one-loop level, there are four master integrals in a theory with only bosonic fields, seven in HQET and sixteen in QED or QCD with Wilson fermions
Freezing of the QCD coupling constant and the pion form factor
International Nuclear Information System (INIS)
Aguilar, A.C.; Mihara, A.; Natale, A.A.
2003-01-01
The possibility that the QCD coupling constant (α s ) has an infrared finite behavior (freezing) has been extensively studied in recent years. We compare phenomenological values of the 'frozen' the QCD running coupling between different classes of solutions obtained through non-perturbative Schwinger-Dyson Equations. With these solutions were computed QCD predictions for the asymptotic pion form factor which, in turn, were compared with experiment. (author)
QCD Factorizations in Exclusive γ*γ*→ρL0ρL0
International Nuclear Information System (INIS)
Pire, B.; Segond, M.; Szymanowski, L.; Wallon, S.
2008-01-01
The exclusive process e + e - →e + e - ρ L 0 ρ L 0 allows to study various dynamics and factorization properties of perturbative QCD. At moderate energy, we demonstrate how collinearQCD 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
Probing QCD in low energy anti pp collisions
International Nuclear Information System (INIS)
Brodsky, S.J.
1986-06-01
A number of exclusive and inclusive antiproton reactions are discussed which could provide useful constraints or test novel features of quantum chromodynamics in the intermediate momentum transfer domain involving both perturbative and non-perturbative dynamics. High momentum transfer reactions are briefly reviewed. Inclusive antiproton reactions and the QCD critical length, QCD predictions for proton-antiproton exclusive processes, and studies of the Compton amplitude in proton-antiproton annihilation are covered. Testing hadron helicity conservation in heavy quark resonance is discussed. Also covered are heavy hadron pair production in proton-antiproton exclusive interactions, exclusive nuclear reactions, and quasi-exclusive nuclear processes
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
Large Nc QCD at nonzero chemical potential
International Nuclear Information System (INIS)
Cohen, Thomas D.
2004-01-01
The general issue of large N c QCD at nonzero chemical potential is considered with a focus on understanding the difference between large N c QCD with an isospin chemical potential and large N c QCD with a baryon chemical potential. A simple diagrammatic analysis analogous to 't Hooft's analysis at μ=0 implies that the free energy with a given baryon chemical potential is equal to the free energy with an isospin chemical potential of the same value plus 1/N c corrections. Phenomenologically, these two systems behave quite differently. A scenario to explain this difference in light of the diagrammatic analysis is explored. This scenario is based on a phase transition associated with pion condensation when the isospin chemical potential exceeds m π /2; associated with this transition there is breakdown of the 1/N c expansion--in the pion condensed phase there is a distinct 1/N c expansion including a larger set of diagrams. While this scenario is natural, there are a number of theoretical issues which at least superficially challenge it. Most of these can be accommodated. However, the behavior of quenched QCD which raises a number of apparently analogous issues cannot be easily understood completely in terms of an analogous scenario. Thus, the overall issue remains open
CPsup(N-1) model: a toy model for QCD
International Nuclear Information System (INIS)
Cant, R.J.; Davis, A.C.
1979-01-01
The authors examine the CP 2 sup(N-1) models and discuss their relevance as toy models for QCD 4 . Specifically, they study the role of instantons, theta vacua, and confinement in the 1/N expansion. The results, and comparisons with other two-dimensional models, suggest that most of the interesting features of these models are peculiarities of two-dimensional space-time and cannot be expected to reappear in QCD 4 . (Auth.)
Energy Technology Data Exchange (ETDEWEB)
Anon.
1979-10-15
Is quantum chromodynamics (QCD) the ultimate theory of hadronic phenomena? Or, put more sceptically, can one tell QCD from a hole in the ground? This is the title of a new theory roadshow, which after a successful premiere at CERN went on to attract a large audience at Erice, Sicily, during the recent international school of subnuclear physics.
International Nuclear Information System (INIS)
Simonov, Yu.A.
1989-01-01
To apply QCD to nuclear physics one needs methods of long-distance QCD. A new method, method of Confining Background Fields, CBF, which incorporates confinement, is presented with applications to heavy and light quarks, both in mesons and baryons. Spin-dependent forces are calculated for light and heavy quarks. The quark potential model in some limiting case is derived. 25 refs
International Nuclear Information System (INIS)
Anon.
1979-01-01
Is quantum chromodynamics (QCD) the ultimate theory of hadronic phenomena? Or, put more sceptically, can one tell QCD from a hole in the ground? This is the title of a new theory roadshow, which after a successful premiere at CERN went on to attract a large audience at Erice, Sicily, during the recent international school of subnuclear physics
High energy asymptotics of multi-colour QCD and two-dimensional conformal field theories
International Nuclear Information System (INIS)
Lipatov, L.N.; Deutsches Elektronen-Synchrotron
1993-04-01
In the multi-colour limit of perturbative QCD the holomorphic factorization of wave functions of compound states of n reggeized gluons in the impact parameter space is shown. The conformally invariant Hamiltonian for each holomorphic factor has a nontrivial integral of motion. The odderon in QCD is the simplest example of the composite system with these properties. (orig.)
Perturbation theory of quantum resonances
Czech Academy of Sciences Publication Activity Database
Durand, P.; Paidarová, Ivana
2016-01-01
Roč. 135, č. 7 (2016), s. 159 ISSN 1432-2234 Institutional support: RVO:61388955 Keywords : Partitioning technique * Analytic continuation * Perturbative expansion Subject RIV: CF - Physical ; Theoretical Chemistry
Generalized perturbation series
International Nuclear Information System (INIS)
Baird, L.C.; Stinchcomb, G.
1973-01-01
An approximate solution of the Green's function equation may be used to generate an exact solution of the Schroedinger equation. This is accomplished through an iterative procedure. The procedure is equivalent to a perturbation expansion if the approximate Green's function is exact with respect to some reference potential
International Nuclear Information System (INIS)
Suslov, I.M.
2005-01-01
Various perturbation series are factorially divergent. The behavior of their high-order terms can be determined by Lipatov's method, which involves the use of instanton configurations of appropriate functional integrals. When the Lipatov asymptotic form is known and several lowest order terms of the perturbation series are found by direct calculation of diagrams, one can gain insight into the behavior of the remaining terms of the series, which can be resummed to solve various strong-coupling problems in a certain approximation. This approach is demonstrated by determining the Gell-Mann-Low functions in φ 4 theory, QED, and QCD with arbitrary coupling constants. An overview of the mathematical theory of divergent series is presented, and interpretation of perturbation series is discussed. Explicit derivations of the Lipatov asymptotic form are presented for some basic problems in theoretical physics. A solution is proposed to the problem of renormalon contributions, which hampered progress in this field in the late 1970s. Practical perturbation-series summation schemes are described both for a coupling constant of order unity and in the strong-coupling limit. An interpretation of the Borel integral is given for 'non-Borel-summable' series. Higher order corrections to the Lipatov asymptotic form are discussed
Effective string theory and QCD scattering amplitudes
International Nuclear Information System (INIS)
Makeenko, Yuri
2011-01-01
QCD string is formed at distances larger than the confinement scale and can be described by the Polchinski-Strominger effective string theory with a nonpolynomial action, which has nevertheless a well-defined semiclassical expansion around a long-string ground state. We utilize modern ideas about the Wilson-loop/scattering-amplitude duality to calculate scattering amplitudes and show that the expansion parameter in the effective string theory is small in the Regge kinematical regime. For the amplitudes we obtain the Regge behavior with a linear trajectory of the intercept (d-2)/24 in d dimensions, which is computed semiclassically as a momentum-space Luescher term, and discuss an application to meson scattering amplitudes in QCD.
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
International Nuclear Information System (INIS)
Smith, W.H.
1997-01-01
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 2 , which is used to determine the gluon momentum distribution. Both low and high Q 2 regimes are discussed. The low Q 2 transition from perturbative QCD to soft hadronic physics is examined. Jet production in deep inelastic scattering to measure α 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
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.
Resummation and the gluon damping rate in hot QCD
International Nuclear Information System (INIS)
Pisarski, R.D.
1990-08-01
At high temperature a consistent perturbative expansion requires the resummation of an infinite subset of loop corrections into an effective expansion. This effective exansion is used to compute the gluon damping rate at leading order. 25 refs
Finite volume QCD at fixed topological charge
Aoki, Sinya; Fukaya, Hidenori; Hashimoto, Shoji; Onogi, Tetsuya
2007-01-01
In finite volume the partition function of QCD with a given $\\theta$ is a sum of different topological sectors with a weight primarily determined by the topological susceptibility. If a physical observable is evaluated only in a fixed topological sector, the result deviates from the true expectation value by an amount proportional to the inverse space-time volume 1/V. Using the saddle point expansion, we derive formulas to express the correction due to the fixed topological charge in terms of...
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.
Energy Technology Data Exchange (ETDEWEB)
Curci, G [European Organization for Nuclear Research, Geneva (Switzerland); Greco, M; Srivastava, Y [Istituto Nazionale di Fisica Nucleare, Frascati (Italy). Lab. Nazionale di Frascati
1979-11-19
A recently proposed approach to the problem of infrared and mass singularities in QCD based on the formalism of coherent states, is extended to discuss massless quark and gluon jets. The present results include all leading (ln delta) terms as well as finite terms in the energy loss epsilon, in addition to the usual ln epsilon associated with ln delta. The formulae agree with explicit perturbative calculations, whenever available. Explicit expressions for the total Ksub(T) distributions are given which take into account transverse-momentum conservation. Predictions are also made for the Q/sup 2/ dependence of the mean Ksub(T)/sup 2/ for quark and gluon jets. The jet ksub(T) distributions are extrapolated for low ksub(T) and shown to describe with good accuracy the data for eanti e..-->..qanti q..-->.. hadrons. Numerical predictions are also presented for the forthcoming PETRA, PEP and LEP machines.
2017-01-01
This edition is the ninth in a series of workshops that had been previously organised in Poland (2009), Slovakia (2010 and 2015), France (2011), Portugal (2012 and 2016) and Bosnia and Herzegovina (2013 and 2014). In the year 2017 the workshop goes to the beautiful Sintra near Lisbon, Portugal. The workshop covers diverse aspects of QCD: (i) QCD at low energies: excited hadrons, new resonances, glueballs, multiquarks. (ii) QCD at high temperatures and large densities: heavy-ion collisions, jets, diffraction, hadronisation, quark-gluon plasma, holography, colour-glass condensate, compact stars, applications to astrophysics.
International Nuclear Information System (INIS)
Kronfeld, Andreas
2005-01-01
Quantum chromodynamics (QCD) is the quantum field theory describing the strong interactions of quarks bound inside hadrons. It is marvelous theory, which works (mathematically) at all distance scales. Indeed, for thirty years, theorists have known how to calculate short-distance properties of QCD, thanks to the (Nobel-worthy) idea of asymptotic freedom. More recently, numerical techniques applied to the strong-coupling regime of QCD have enabled us to compute long-distance bound-state properties. In this colloquium, we review these achievements and show how the new-found methods of calculation will influence high-energy physics.
International Nuclear Information System (INIS)
Ingelman, Gunnar
1994-01-01
The traditional annual DESY Theory Workshop highlights a topical theory sector. The most recent was under the motto 'Quantum Chromo-Dynamics' - QCD, the field theory of quarks and gluons. The organizers had arranged a programme covering most aspects of current QCD research. This time the workshop was followed by a topical meeting on 'QCD at HERA' to look at the electron-proton scattering experiments now in operation at DESY's new HERA collider
Aurenche , P; Guillet , J.-Ph; Pilon , E
2016-01-01
3rd cycle; Ces notes sont une introduction à l'application de l'électrodynamique quantique (QED) et de la chromodynamiques quantique (QCD) aux réactions de diffusion à hautes énergies. Le premier thème abordé est celui des divergences ultraviolettes et de la renormalisation à une boucle, avec comme conséquence pour QCD la liberté asymptotique. Le deuxième thème est celui des divergences infrarouges et colinéaires qui dans QCD sont traitées dans le cadre du modèle des partons avec l'introducti...
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...
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.
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.
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.
Higher order corrections in perturbative quantum chromodynamics
Indian Academy of Sciences (India)
Since the discovery of asymptotic freedom in non-abelian gauge field theories, like quan- tum chromodynamics (QCD), many perturbative calculations have been performed to ..... The integral above appears in the partial integration with respect to the momentum. &½ of the expression below (see figure 2). ¼. Т&½. ґѕπµТ.
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.
The power of perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Serone, Marco [SISSA International School for Advanced Studies and INFN Trieste, Via Bonomea 265, 34136, Trieste (Italy); Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste (Italy); Spada, Gabriele [SISSA International School for Advanced Studies and INFN Trieste, Via Bonomea 265, 34136, Trieste (Italy); Villadoro, Giovanni [Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste (Italy)
2017-05-10
We study quantum mechanical systems with a discrete spectrum. We show that the asymptotic series associated to certain paths of steepest-descent (Lefschetz thimbles) are Borel resummable to the full result. Using a geometrical approach based on the Picard-Lefschetz theory we characterize the conditions under which perturbative expansions lead to exact results. Even when such conditions are not met, we explain how to define a different perturbative expansion that reproduces the full answer without the need of transseries, i.e. non-perturbative effects, such as real (or complex) instantons. Applications to several quantum mechanical systems are presented.
QCD in gauge-boson production at the LHC
Schott, Matthias; The ATLAS collaboration
2018-01-01
Measurements of the Drell-Yan production of W and Z/gamma* bosons at the LHC provide a benchmark of our understanding of perturbative QCD and probe the proton structure in a unique way. The ATLAS and CMS collaborations have performed several high precision measurements at different center-of-mass energies, ranging from single to triple differential cross sections. These measurements are the key in improving physics modelling uncertainties of electroweak precision measurements at the LHC. Moreover, perturbative QCD can be tested further in a multi-scale environment, when studying the production of jets in association with single and di-bosons final states. In this talk, we review the latest measurements, discuss the compatibility between the experiments and compare the results to the state-of-the-art QCD calculations and Monte Carlo simulations, as well their potential impact on improving our understanding PDFs.
The strong coupling constant of QCD with four flavors
International Nuclear Information System (INIS)
Tekin, Fatih
2010-01-01
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 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 Λ parameter is determined in units of a technical scale L max which is an unambiguously defined length in the hadronic regime. The coupling α 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.)
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.)
International Nuclear Information System (INIS)
Kaplan, D.B.
1995-01-01
I give a brief and selective overview of QCD as it pertains to determining hadron structure, and the relevant directions in this field for nuclear theory. This document is intended to start discussion about priorities, not end it
Sykora, Tomas; The ATLAS collaboration
2018-01-01
Recent results of soft QCD measurements performed by the ATLAS collaboration are reported. The measurements include total, elastic and inelastic cross sections, inclusive spectra, underlying event and particle correlations in p-p and p-Pb collisions.
International Nuclear Information System (INIS)
Dominguez, C.A.
1987-02-01
The scalar (0 ++ ) and the tensor (2 ++ ) gluonium spectrum is analyzed in the framework of QCD sum rules. Stable eigenvalue solutions, consistent with duality and low energy theorems, are obtained for the mass and width of these glueballs. (orig.)
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.
International Nuclear Information System (INIS)
Christ, Norman H
2000-01-01
The architecture and capabilities of the computers currently in use for large-scale lattice QCD calculations are described and compared. Based on this present experience, possible future directions are discussed
International Nuclear Information System (INIS)
Kalashnikova, Yu.S.; Nefediev, A.V.
1997-01-01
The QCD-motivated constituent string model is extended to consider the baryon. The system of three quarks propagating in the confining background field is studied in the Wilson loop approach, and the effective action is obtained. The resulting Lagrangian at large interquark distances corresponds to the Mercedes Benz string configuration. Assuming the quarks to be heavy enough to allow the adiabatic separation of quark and string junction motion and using the hyperspherical expansion for the quark subsystem we write out and solve the classical equation of motion for the junction. We quantize the motion of the junction and demonstrate that the account of these modes leads to the effective swelling of baryon in comparison with standard potential picture. The effects of finite gluonic correlation length which do not affect the excited states but appear to be substantial for the baryonic ground state, reducing the swelling considerably is discussed
International Nuclear Information System (INIS)
Neubert, Matthias
2001-01-01
The QCD factorization approach provides the theoretical basis for a systematic analysis of nonleptonic decay amplitudes of B mesons in the heavy-quark limit. After recalling the basic ideas underlying this formalism, several tests of QCD factorization in the decays B→D (*) L, B→K * γ, and B→πK, ππ are discussed. It is then illustrated how factorization can be used to obtain new constraints on the parameters of the unitarity triangle
Schuster, Theodor
2013-01-01
We derive color decompositions of arbitrary tree and one-loop QCD amplitudes into color ordered objects called primitive amplitudes. Furthermore, we derive general fermion flip and reversion identities spanning the null space among the primitive amplitudes and use them to prove that all color ordered tree amplitudes of massless QCD can be written as linear combinations of color ordered tree amplitudes of $\\mathcal{N}=4$ super Yang-Mills theory.
Masses and couplings of open beauty states in QCD
International Nuclear Information System (INIS)
Rubinstein, H.R.; Reinders, L.J.; Yazaki, S.
1981-05-01
Masses and couplings of open beauty states (strange and non-strange) with Jsup(PC) = 0 ++ , 0 -+ , 1 -- . and 1 ++ are calculated using the QCD sum rule formalism. Non-perturbative effects due to quark and gluon condensate operators are shown to be important, confirming earlier calculations for equal quark mass systems. (author)
Gazing into the multiparton distribution equations in QCD
International Nuclear Information System (INIS)
Shelest, V.P.; Sinigirev, A.M.; Zinovjev, G.M.
1982-01-01
Using a parton interpretation of the leading logarithm diagrams of perturbative QCD theory we obtain the equations for the multiparton distribution and fragmentation functions. These equations are not identical but the solutions are the same on the definite initial conditions and coincide with the jet calculus rules. The difference is crucial when we generalize these equations for a hardron-jet description. (orig.)
Why QCD lattice theory is important to spin physicists
International Nuclear Information System (INIS)
Rebbi, C.
1982-01-01
The lattice formulation of a quantum field theory allows calculations in the regime of strong coupling, by expansion techniques, and for intermediate coupling, by Monte Carlo simulations. These computations are especially valuable in the case of Quantum Chromodynamics (QCD), where several of the most important problems are not amenable to a perturbative analysis. Monte carlo simulations, in particular, have recently emerged as a very powerful tool and have been used to evaluate a variety of important physical quantities, such as the string tension, the deconfinement temperature, the scale of the interquark potential, glueball masses and masses in the quark model spectrum. If we consider those problems of strong interactions where spin plays an important role, it is unlikely, for the moment at least, that the lattice formulation may be of relevance where the phenomena being investigated involve propagations over extended domains of space-time; thus, for instance, it is impossible to perform a meaningful simulation of a scattering experiment on the lattice. But we are at the stage where Monte Carlo calculations begin to provide relevant information on spectroscopic properties related to spin. These are briefly discussed
Factorization and pion form factor in QCD
International Nuclear Information System (INIS)
Efremov, A.V.; Radyushkin, A.V.
1979-01-01
The behaviour of the pion electromagnetic form factor (EMFF) in the framework of quantum chromodynamics (QCD) is discussed. Pion is considered to be a quark-antiquark bound state. It is proposed to use an OPE description of the bound state structure by matrix elements of certain local gauge-invariant operators. Short-distance quark interactions is proved using a direct analysis of perturbation theory in the α-parametric representation of the Feynman diagrams. It is shown that the short-distance parton picture privides a self-consistent description of the large Q 2 momentum behaviour of the pion EMFF in QCD. Pion EMFF asymptotics is expressed in terms of fu fundamental constants of the theory
Probing QCD and new physics with dijets
CERN. Geneva
2014-01-01
Dijets are the most abundant final state in hadron collisions. During the last 30 years dijets have been used to probe QCD and also search for new phenomena beyond the Standard Model. Recent results from Tevatron and LHC are discussed that reveal the full physics potential of dijets. Precise measurements of cross sections and angular observables, made possible thanks to the excellent understanding of the jet objects, confront the perturbative QCD predictions at the multi-TeV regime and constrain the PDFs. At the same time, the dijet invariant mass spectrum is used as a means of searching for resonances and for contact interactions between the quarks. Following the success of the LHC Run I physics program, dijets will once again play a central role in the quest for exciting discoveries at Run II, and we are prepared to exploit this powerful final state.
Compositeness and QCD at the SSC
International Nuclear Information System (INIS)
Barnes, V.; Blumenfeld, B.; Cahn, R.
1987-01-01
Compositeness may be signaled by an increase in the production of high transverse momentum hadronic jet pairs or lepton pairs. The hadronic jet signal competes with the QCD production of jets, a subject of interest in its own right. Tests of perturbative QCD at the SSC will be of special interest because the calculations are expected to be quite reliable. Studies show that compositeness up to a scale of 20 to 35 TeV would be detected in hadronic jets at the SSC. Leptonic evidence would be discovered for scales up to 10 to 20 TeV. The charge asymmetry for leptons would provide information on the nature of the compositeness interaction. Calorimetry will play a crucial role in the detection of compositeness in the hadronic jet signal. Deviations from an e/h response of 1 could mask the effect. The backgrounds for lepton pair production seem manageable. 30 refs., 19 figs., 10 tabs
Exactly soluble QCD and confinement of quarks
International Nuclear Information System (INIS)
Rusakov, B.
1997-01-01
An exactly soluble non-perturbative model of the pure gauge QCD is derived as a weak coupling limit of the lattice theory in plaquette formulation [B. Rusakov, Phys. Lett. B 398 (1997) 331]. The model represents QCD as a theory of the weakly interacting field strength fluxes. The area law behavior of the Wilson loop average is a direct result of this representation: the total flux through macroscopic loop is the additive (due to the weakness of the interaction) function of the elementary fluxes. The compactness of the gauge group is shown to be the factor which prevents the elementary fluxes contributions from cancellation. There is no area law in the non-compact theory. (orig.)
Singular perturbation of simple eigenvalues
International Nuclear Information System (INIS)
Greenlee, W.M.
1976-01-01
Two operator theoretic theorems which generalize those of asymptotic regular perturbation theory and which apply to singular perturbation problems are proved. Application of these theorems to concrete problems is involved, but the perturbation expansions for eigenvalues and eigenvectors are developed in terms of solutions of linear operator equations. The method of correctors, as well as traditional boundary layer techniques, can be used to apply these theorems. The current formulation should be applicable to highly singular ''hard core'' potential perturbations of the radial equation of quantum mechanics. The theorems are applied to a comparatively simple model problem whose analysis is basic to that of the quantum mechanical problem
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
Light-cone quantization and QCD phenomenology
International Nuclear Information System (INIS)
Brodsky, S.J.; Robertson, D.G.
1995-01-01
In principle, quantum chromodynamics provides a fundamental description of hadronic and nuclear structure and dynamics in terms of their elementary quark and gluon degrees of freedom. In practice, the direct application of QCD to reactions involving the structure of hadrons is extremely complex because of the interplay of nonperturbative effects such as color confinement and multi-quark coherence. A crucial tool in analyzing such phenomena is the use of relativistic light-cone quantum mechanics and Fock state methods to provide tractable and consistent treatments of relativistic many-body systems. In this article we present an overview of this formalism applied to QCD, focusing in particular on applications to the final states in deep inelastic lepton scattering that will be relevant for the proposed European Laboratory for Electrons (ELFE), HERMES, HERA, SLAC, and CEBAF. We begin with a brief introduction to light-cone field theory, stressing how it many allow the derivation of a constituent picture, analogous to the constituent quark model, from QCD. We then discuss several applications of the light-cone Fock state formalism to QCD phenomenology. The Fock state representation includes all quantum fluctuations of the hadron wavefunction, including far off-shell configurations such as intrinsic charm and, in the case of nuclei, hidden color. In some applications, such as exclusive processes at large momentum transfer, one can make first-principle predictions using factorization theorems which separate the hard perturbative dynamics from the nonpertubative physics associated with hadron binding. The Fock state components of the hadron with small transverse size, which dominate hard exclusive reactions, have small color dipole moments and thus diminished hadronic interactions. Thus QCD predicts minimal absorptive corrections, i.e., color transparency for quasi-elastic exclusive reactions in nuclear targets at large momentum transfer
Local-duality QCD sum rules for strong isospin breaking in the decay constants of heavy-light mesons
Energy Technology Data Exchange (ETDEWEB)
Lucha, Wolfgang [Austrian Academy of Sciences, Institute for High Energy Physics, Vienna (Austria); Melikhov, Dmitri [Austrian Academy of Sciences, Institute for High Energy Physics, Vienna (Austria); M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of Nuclear Physics, Moscow (Russian Federation); University of Vienna, Faculty of Physics, Vienna (Austria); Simula, Silvano [Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tre, Rome (Italy)
2018-02-15
We discuss the leptonic decay constants of heavy-light mesons by means of Borel QCD sum rules in the local-duality (LD) limit of infinitely large Borel mass parameter. In this limit, for an appropriate choice of the invariant structures in the QCD correlation functions, all vacuum-condensate contributions vanish and all nonperturbative effects are contained in only one quantity, the effective threshold. We study properties of the LD effective thresholds in the limits of large heavy-quark mass m{sub Q} and small light-quark mass m{sub q}. In the heavy-quark limit, we clarify the role played by the radiative corrections in the effective threshold for reproducing the pQCD expansion of the decay constants of pseudoscalar and vector mesons. We show that the dependence of the meson decay constants on m{sub q} arises predominantly (at the level of 70-80%) from the calculable m{sub q}-dependence of the perturbative spectral densities. Making use of the lattice QCD results for the decay constants of nonstrange and strange pseudoscalar and vector heavy mesons, we obtain solid predictions for the decay constants of heavy-light mesons as functions of m{sub q} in the range from a few to 100 MeV and evaluate the corresponding strong isospin-breaking effects: f{sub D{sup +}} - f{sub D{sup 0}} = (0.96 ± 0.09) MeV, f{sub D}{sup {sub *}{sub +}} - f{sub D}{sup {sub *}{sub 0}} = (1.18 ± 0.35) MeV, f{sub B{sup 0}} - f{sub B{sup +}} = (1.01 ± 0.10) MeV, f{sub B}{sup {sub *}{sub 0}} - f{sub B}{sup {sub *}{sub +}} = (0.89 ± 0.30) MeV. (orig.)
Heavy-light mesons in lattice HQET and QCD
International Nuclear Information System (INIS)
Guazzini, D.
2007-12-01
We present a study of a combination of HQET and relativistic QCD to extract the b-quark mass and the B 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 0 and the experimental B s and K masses, we get the final results for the renormalization group invariant mass M b =6.88(10) GeV, translating into anti m b (anti m b )=4.42(6) GeV in the MS scheme, and f B 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.)
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.)
Probing the perturbative NLO parton evolution in the small-x region
International Nuclear Information System (INIS)
Glueck, M.; Pisano, C.; Reya, E.
2005-01-01
A dedicated test of the perturbative QCD NLO parton evolution in the very small-x region is performed. We find a good agreement with recent precision HERA data for F 2 p (x,Q 2 ), as well as with the present determination of the curvature of F 2 p . Characteristically, perturbative QCD evolutions result in a positive curvature which increases as xdecreases. Future precision measurements in the very small x-region, x -4 , could provide a sensitive test of the range of validity of perturbative QCD. (orig.)
International Nuclear Information System (INIS)
Bartlett, R.; Kirtman, B.; Davidson, E.R.
1978-01-01
After noting some advantages of using perturbation theory some of the various types are related on a chart and described, including many-body nonlinear summations, quartic force-field fit for geometry, fourth-order correlation approximations, and a survey of some recent work. Alternative initial approximations in perturbation theory are also discussed. 25 references
Conformal window in QCD for large numbers of colors and flavors
International Nuclear Information System (INIS)
Zhitnitsky, Ariel R.
2014-01-01
We conjecture that the phase transitions in QCD at large number of colors N≫1 is triggered by the drastic change in the instanton density. As a result of it, all physical observables also experience some sharp modification in the θ behavior. This conjecture is motivated by the holographic model of QCD where confinement–deconfinement phase transition indeed happens precisely at temperature T=T c where θ-dependence of the vacuum energy experiences a sudden change in behavior: from N 2 cos(θ/N) at T c to cosθexp(−N) at T>T c . This conjecture is also supported by recent lattice studies. We employ this conjecture to study a possible phase transition as a function of κ≡N f /N from confinement to conformal phase in the Veneziano limit N f ∼N when number of flavors and colors are large, but the ratio κ is finite. Technically, we consider an operator which gets its expectation value solely from non-perturbative instanton effects. When κ exceeds some critical value κ>κ c the integral over instanton size is dominated by small-size instantons, making the instanton computations reliable with expected exp(−N) behavior. However, when κ c , the integral over instanton size is dominated by large-size instantons, and the instanton expansion breaks down. This regime with κ c corresponds to the confinement phase. We also compute the variation of the critical κ c (T,μ) when the temperature and chemical potential T,μ≪Λ QCD slightly vary. We also discuss the scaling (x i −x j ) −γ det in the conformal phase
Introduction to finite temperature and finite density QCD
International Nuclear Information System (INIS)
Kitazawa, Masakiyo
2014-01-01
It has been pointed out that QCD (Quantum Chromodynamics) in the circumstances of medium at finite temperature and density shows numbers of phenomena similar to the characteristics of solid state physics, e.g. phase transitions. In the past ten years, the very high temperature and density matter came to be observed experimentally at the heavy ion collisions. At the same time, the numerical QCD analysis at finite temperature and density attained quantitative level analysis possible owing to the remarkable progress of computers. In this summer school lecture, it has been set out to give not only the recent results, but also the spontaneous breaking of the chiral symmetry, the fundamental theory of finite temperature and further expositions as in the following four sections. The first section is titled as 'Introduction to Finite Temperature and Density QCD' with subsections of 1.1 standard model and QCD, 1.2 phase transition and phase structure of QCD, 1.3 lattice QCD and thermodynamic quantity, 1.4 heavy ion collision experiments, and 1.5 neutron stars. The second one is 'Equilibrium State' with subsections of 2.1 chiral symmetry, 2.2 vacuum state: BCS theory, 2.3 NJL (Nambu-Jona-Lasinio) model, and 2.4 color superconductivity. The third one is 'Static fluctuations' with subsections of 3.1 fluctuations, 3.2 moment and cumulant, 3.3 increase of fluctuations at critical points, 3.4 analysis of fluctuations by lattice QCD and Taylor expansion, and 3.5 experimental exploration of QCD phase structure. The fourth one is 'Dynamical Structure' with 4.1 linear response theory, 4.2 spectral functions, 4.3 Matsubara function, and 4.4 analyses of dynamical structure by lattice QCD. (S. Funahashi)
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.)
International Nuclear Information System (INIS)
Roessner, Simon
2009-01-01
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.)
QCD machines - present and future
International Nuclear Information System (INIS)
Christ, N.H.
1991-01-01
The present status of the currently working and nearly working dedicated QCD machines is reviewed and proposals for future machines are discussed with particular emphasis on the QCD Teraflop Project in the US. (orig.)
International Nuclear Information System (INIS)
Bolzoni, P.
2007-09-01
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.)
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.)
Study of QCD medium by sum rules
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Mallik, S [Saha Institute of Nuclear Physics, Calcutta (India)
1998-08-01
Though it has no analogue in condensed matter physics, the thermal QCD sum rules can, nevertheless, answer questions of condensed matter type about the QCD medium. The ingredients needed to write such sum rules, viz. the operator product expansion and the spectral representation at finite temperature, are reviewed in detail. The sum rules are then actually written for the case of correlation function of two vector currents. Collecting information on the thermal average of the higher dimension operators from other sources, we evaluate these sum rules for the temperature dependent {rho}-meson parameters. Possibility of extracting more information from the combined set of all sum rules from different correlation functions is also discussed. (author) 30 refs., 2 figs.
QCD and panti p collider physics
International Nuclear Information System (INIS)
Altarelli, G.
1983-01-01
The relevance for QCD of experiments at the SPS collider rests on the possibility they offer of testing parton dynamics in a new and highly non trivial configuration. For example, hadron-hadron interactions in the deep inelastic, large Psub(perpendicular to), region are non linear in parton densities. Also the relevant predictions cannot be derived by less committed formulations than the explicit QCD improved parton model, as for example light cone dominance and operator expansion. This complexity, which is important for providing qualitatively new testing grounds is however paid for by a loss of precision in predictive power. In addition to that, panti p collisions are also important as jet sources with an energy scale comparable to that of an e + e - ring with beam energy up to 50 GeV and more. (orig./HSI)
Twisting perturbed parafermions
Directory of Open Access Journals (Sweden)
A.V. Belitsky
2017-07-01
Full Text Available The near-collinear expansion of scattering amplitudes in maximally supersymmetric Yang–Mills theory at strong coupling is governed by the dynamics of stings propagating on the five sphere. The pentagon transitions in the operator product expansion which systematize the series get reformulated in terms of matrix elements of branch-point twist operators in the two-dimensional O(6 nonlinear sigma model. The facts that the latter is an asymptotically free field theory and that there exists no local realization of twist fields prevents one from explicit calculation of their scaling dimensions and operator product expansion coefficients. This complication is bypassed making use of the equivalence of the sigma model to the infinite-level limit of WZNW models perturbed by current–current interactions, such that one can use conformal symmetry and conformal perturbation theory for systematic calculations. Presently, to set up the formalism, we consider the O(3 sigma model which is reformulated as perturbed parafermions.
Threshold resummation and higher order effects in QCD
International Nuclear Information System (INIS)
Ringer, Felix Maximilian
2015-01-01
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.
The renormalization group and lattice QCD
International Nuclear Information System (INIS)
Gupta, R.
1989-01-01
This report discusses the following topics: scaling of thermodynamic quantities and critical exponents; scaling relations; block spin idea of Kadanoff; exact RG solution of the 1-d Ising model; Wilson's formulation of the renormalization group; linearized transformation matrix and classification of exponents; derivation of exponents from the eigenvalues of Τ αβ ; simple field theory: the gaussian model; linear renormalization group transformations; numerical methods: MCRG; block transformations for 4-d SU(N) LGT; asymptotic freedom makes QCD simple; non-perturbative β-function and scaling; and the holy grail: the renormalized trajectory
International Nuclear Information System (INIS)
Borsanyi, Sz.; Kampert, K.H.; Fodor, Z.; Forschungszentrum Juelich; Eoetvoes Univ., Budapest
2016-06-01
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 the MeV scale 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 (χ) up to the few GeV temperature region. These two results, EoS and χ, 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.
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.
International Nuclear Information System (INIS)
Zou, L.P.; Zhang, P.M.; 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. 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
QCD analysis of structure functions in terms of Jacobi polynomials
International Nuclear Information System (INIS)
Krivokhizhin, V.G.; Kurlovich, S.P.; Savin, I.A.; Sidorov, A.V.; Skachkov, N.B.; Sanadze, V.V.
1987-01-01
A new method of QCD-analysis of singlet and nonsinglet structure functions based on their expansion in orthogonal Jacobi polynomials is proposed. An accuracy of the method is studied and its application is demonstrated using the structure function F 2 (x,Q 2 ) obtained by the EMC Collaboration from measurements with an iron target. (orig.)
International Nuclear Information System (INIS)
Brodsky, Stanley J.; SLAC
2007-01-01
I discuss a number of novel topics in QCD, including the use of the AdS/CFT correspondence between Anti-de Sitter space and conformal gauge theories to obtain an analytically tractable approximation to QCD in the regime where the QCD coupling is large and constant. In particular, there is an exact correspondence between the fifth-dimension coordinate z of AdS space and a specific impact variable ζ which measures the separation of the quark constituents within the hadron in ordinary space-time. This connection allows one to compute the analytic form of the frame-independent light-front wavefunctions of mesons and baryons, the fundamental entities which encode hadron properties and allow the computation of exclusive scattering amplitudes. I also discuss a number of novel phenomenological features of QCD. Initial- and final-state interactions from gluon-exchange, normally neglected in the parton model, have a profound effect in QCD hard-scattering reactions, leading to leading-twist single-spin asymmetries, diffractive deep inelastic scattering, diffractive hard hadronic reactions, the breakdown of the Lam Tung relation in Drell-Yan reactions, and nuclear shadowing and non-universal antishadowing--leading-twist physics not incorporated in the light-front wavefunctions of the target computed in isolation. I also discuss tests of hidden color in nuclear wavefunctions, the use of diffraction to materialize the Fock states of a hadronic projectile and test QCD color transparency, and anomalous heavy quark effects. The presence of direct higher-twist processes where a proton is produced in the hard subprocess can explain the large proton-to-pion ratio seen in high centrality heavy ion collisions
Baryon interactions in lattice QCD: the direct method vs. the HAL QCD potential method
Iritani, T.; HAL QCD Collaboration
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 be clarified by a few low-lying eigenfunctions and eigenvalues on the finite volume derived from the HAL QCD potential, which implies that the ground state saturation of $\\Xi\\Xi$($^1$S$_0$) requires $t \\sim 10$ fm in the direct method for the smeared source on $(4.3 \\ \\mathrm{fm})^3$ lattice, while the HAL QCD method does not suffer from such a problem.
International Nuclear Information System (INIS)
Anisovich, V.V.
1989-06-01
Using the language of the quarks and gluons for description of the soft hadron physics it is necessary to take into account two characteristic phenomena which prevent one from usage of QCD Lagrangian in the straightforward way, chiral symmetry breaking, and confinement of colour particles. The topics discussed in this context are: QCD in the domain of soft processes, phenomenological Lagrangian for soft processes and exotic mesons, spectroscopy of low-lying hadrons (mesons, baryons and mesons with heavy quarks - c,b -), confinement forces, spectral integration over quark masses. (author) 3 refs.; 19 figs.; 3 tabs
International Nuclear Information System (INIS)
Shindler, A.
2007-07-01
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.)
International Nuclear Information System (INIS)
Hansl-Kozanecka, T.
1992-01-01
The phenomenological aspects of Quantum Chromodynamics (QCD) are examined which are relevant for lepton-hadron, electron-positron and hadron-hadron collisions. In deep inelastic scattering the virtual γ or W/Z is used as a probe of the nucleon structure. The strong coupling constant (α s ) measurements via deep inelastic scattering and e + e - annihilation are discussed. Parton-parton collisions (e.g., hard hadron-hadron collisions) are examined as the third regime for QCD tests. (K.A.) 122 refs., 84 figs., 4 tabs
International Nuclear Information System (INIS)
Lippert, Matthew
2009-01-01
We investigated the Sakai-Sugimoto model of large N QCD at nonzero temperature and baryon chemical potential and in the presence of background electric and magnetic fields. We studied the holographic representation of baryons and the deconfinement, chiral-symmetry breaking, and nuclear matter phase transitions. In a background electric field, chiral-symmetry breaking corresponds to an insulator-conductor transition. A magnetic field both catalyzes chiral-symmetry breaking and generates, in the confined phase, a pseudo-scalar gradient or, in the deconfined phase, an axial current. The resulting phase diagram is in qualitative agreement with studies of hot, dense QCD.
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.)
$\\delta$-Expansion at Finite Temperature
Ramos, Rudnei O.
1996-01-01
We apply the $\\delta$-expansion perturbation scheme to the $\\lambda \\phi^{4}$ self-interacting scalar field theory in 3+1 D at finite temperature. In the $\\delta$-expansion the interaction term is written as $\\lambda (\\phi^{2})^{ 1 + \\delta}$ and $\\delta$ is considered as the perturbation parameter. We compute within this perturbative approach the renormalized mass at finite temperature at a finite order in $\\delta$. The results are compared with the usual loop-expansion at finite temperature.
QCD effects on the event structure in leptoproduction
International Nuclear Information System (INIS)
Bengtsson, M.; Sjoestrand, T.
1988-01-01
Perturbative QCD corrections to leptoproduction events can be introduced either in the form of matrix elements or of parton showers. Each of these approaches has its advantages and disadvantages, making a comparison of the two interesting. At present energies, both methods can be made to agree reasonably well with data, whereas differences appear at higher energies. The influence of these QCD effects on the expected event structure at ep colliders, HERA in particular, is investigated in detail. This includes multiplicity and momentum distributions transverse momentum flow and correlations, as well as jet properties. (orig.)
Suppressing the QCD axion abundance by hidden monopoles
International Nuclear Information System (INIS)
Kawasaki, Masahiro
2015-11-01
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 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.