Applications Of Chiral Perturbation Theory
Mohta, V
2005-01-01
Effective field theory techniques are used to describe the spectrum and interactions of hadrons. The mathematics of classical field theory and perturbative quantum field theory are reviewed. The physics of effective field theory and, in particular, of chiral perturbation theory and heavy baryon chiral perturbation theory are also reviewed. The geometry underlying heavy baryon chiral perturbation theory is described in detail. Results by Coleman et. al. in the physics literature are stated precisely and proven. A chiral perturbation theory is developed for a multiplet containing the recently- observed exotic baryons. A small coupling expansion is identified that allows the calculation of self-energy corrections to the exotic baryon masses. Opportunities in lattice calculations are discussed. Chiral perturbation theory is used to study the possibility of two multiplets of exotic baryons mixed by quark masses. A new symmetry constraint on reduced partial widths is identified. Predictions in the literature based ...
Review of chiral perturbation theory
Indian Academy of Sciences (India)
B Ananthanarayan
2003-11-01
A review of chiral perturbation theory and recent developments on the comparison of its predictions with experiment is presented. Some interesting topics with scope for further elaboration are touched upon.
Chiral Perturbation Theory and Unitarization
Ruiz-Arriola, E; Nieves, J; Peláez, J R
2000-01-01
We review our recent work on unitarization and chiral perturbation theory both in the $\\pi\\pi$ and the $\\pi N$ sectors. We pay particular attention to the Bethe-Salpeter and Inverse Amplitude unitarization methods and their recent applications to $\\pi\\pi$ and $\\pi N$ scattering.
Chiral Random Matrix Theory and Chiral Perturbation Theory
Damgaard, P H
2011-01-01
Spontaneous breaking of chiral symmetry in QCD has traditionally been inferred indirectly through low-energy theorems and comparison with experiments. Thanks to the understanding of an unexpected connection between chiral Random Matrix Theory and chiral Perturbation Theory, the spontaneous breaking of chiral symmetry in QCD can now be shown unequivocally from first principles and lattice simulations. In these lectures I give an introduction to the subject, starting with an elementary discussion of spontaneous breaking of global symmetries.
Chiral Random Matrix Theory and Chiral Perturbation Theory
Energy Technology Data Exchange (ETDEWEB)
Damgaard, Poul H, E-mail: phdamg@nbi.dk [Niels Bohr International Academy and Discovery Center, The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen (Denmark)
2011-04-01
Spontaneous breaking of chiral symmetry in QCD has traditionally been inferred indirectly through low-energy theorems and comparison with experiments. Thanks to the understanding of an unexpected connection between chiral Random Matrix Theory and chiral Perturbation Theory, the spontaneous breaking of chiral symmetry in QCD can now be shown unequivocally from first principles and lattice simulations. In these lectures I give an introduction to the subject, starting with an elementary discussion of spontaneous breaking of global symmetries.
Quenched Chiral Perturbation Theory to one loop
Colangelo, G.; Pallante, E.
1998-01-01
The divergences of the generating functional of quenched Chiral Perturbation theory (qCHPT) to one loop are computed in closed form. We show how the quenched chiral logarithms can be reabsorbed in the renormalization of the B0 parameter of the leading order Lagrangian. Finally, we do the chiral powe
Quenched chiral perturbation theory to one loop
Colangelo, Gilberto; Pallante, Elisabetta
1998-01-01
We calculate the divergences of the generating functional of quenched chiral perturbation theory at one loop, and renormalize the theory by an appropriate definition of the counterterms. We show that the quenched chiral logarithms can be accounted for by defining a renormalized B0 parameter which, a
Chiral Perturbation Theory With Lattice Regularization
Ouimet, P P A
2005-01-01
In this work, alternative methods to regularize chiral perturbation theory are discussed. First, Long Distance Regularization will be considered in the presence of the decuplet of the lightest spin 32 baryons for several different observables. This serves motivation and introduction to the use of the lattice regulator for chiral perturbation theory. The mesonic, baryonic and anomalous sectors of chiral perturbation theory will be formulated on a lattice of space time points. The consistency of the lattice as a regulator will be discussed in the context of the meson and baryon masses. Order a effects will also be discussed for the baryon masses, sigma terms and magnetic moments. The work will close with an attempt to derive an effective Wess-Zumino-Witten Lagrangian for Wilson fermions at non-zero a. Following this discussion, there will be a proposal for a phenomenologically useful WZW Lagrangian at non-zero a.
Vector Meson Masses in Chiral Perturbation Theory
Bijnens, J; Talavera, P
1997-01-01
We discuss the vector meson masses within the context of Chiral Perturbation Theory performing an expansion in terms of the momenta, quark masses and 1/Nc. We extend the previous analysis to include isospin breaking effects and also include up to order p^4. We discuss vector meson chiral perturbation theory in some detail and present a derivation from a relativistic lagrangian. The unknown coefficients are estimated in various ways. We also discuss the relevance of electromagnetic corrections and the implications of the present calculation for the determination of quark masses.
Baryon form factors in chiral perturbation theory
Kubis, B; Kubis, Bastian; Meissner, Ulf-G.
2001-01-01
We analyze the electromagnetic form factors of the ground state baryon octet to fourth order in relativistic baryon chiral perturbation theory. Predictions for the \\Sigma^- charge radius and the \\Lambda-\\Sigma^0 transition moment are found to be in excellent agreement with the available experimental information. Furthermore, the convergence behavior of the hyperon charge radii is shown to be more than satisfactory.
A primer for Chiral Perturbative Theory
Energy Technology Data Exchange (ETDEWEB)
Scherer, Stefan [Mainz Univ. (Germany). Inst. fuer Kernphysik; Schindler, Matthias R. [South Carolina Univ., Columbia, SC (United States). Dept. of Physics; George Washington Univ., Washington, DC (United States). Dept. of Physics
2012-07-01
Chiral Perturbation Theory, as effective field theory, is a commonly accepted and well established working tool, approximating quantum chromodynamics at energies well below typical hadron masses. This volume, based on a number of lectures and supplemented with additional material, provides a pedagogical introduction for graduate students and newcomers entering the field from related areas of nuclear and particle physics. Starting with the the Lagrangian of the strong interactions and general symmetry principles, the basic concepts of Chiral Perturbation Theory in the mesonic and baryonic sectors are developed. The application of these concepts is then illustrated with a number of examples. A large number of exercises (81, with complete solutions) are included to familiarize the reader with helpful calculational techniques. (orig.)
A primer for chiral perturbation theory
Scherer, Stefan
2012-01-01
Chiral Perturbation Theory, as effective field theory, is a commonly accepted and well established working tool, approximating quantum chromodynamics at energies well below typical hadron masses. This volume, based on a number of lectures and supplemented with additional material, provides a pedagogical introduction for graduate students and newcomers entering the field from related areas of nuclear and particle physics. Starting with the the Lagrangian of the strong interactions and general symmetry principles, the basic concepts of Chiral Perturbation Theory in the mesonic and baryonic sectors are developed. The application of these concepts is then illustrated with a number of examples. A large number of exercises (81, with complete solutions) are included to familiarize the reader with helpful calculational techniques.
Nonequilibrium chiral perturbation theory and disoriented chiral condensates
Nicola, A G
1999-01-01
We analyse the extension of Chiral Perturbation Theory to describe a meson gas out of thermal equilibrium. For that purpose, we let the pion decay constant be a time-dependent function and work within the Schwinger-Keldysh contour technique. A useful connection with curved space-time QFT allows to consistently renormalise the model, introducing two new low-energy constants in the chiral limit. We discuss the applicability of our approach within a Relativistic Heavy-Ion Collision environment. In particular, we investigate the formation of Disoriented Chiral Condensate domains in this model, via the parametric resonance mechanism.
Tests of Chiral perturbation theory with COMPASS
Directory of Open Access Journals (Sweden)
Friedrich Jan M.
2014-06-01
Full Text Available The COMPASS experiment at CERN accesses pion-photon reactions via the Primakoff effect., where high-energetic pions react with the quasi-real photon field surrounding the target nuclei. When a single real photon is produced, pion Compton scattering is accessed and from the measured cross-section shape, the pion polarisability is determined. The COMPASS measurement is in contradiction to the earlier dedicated measurements, and rather in agreement with the theoretical expectation from ChPT. In the same experimental data taking, reactions with neutral and charged pions in the final state are measured and analyzed in the context of chiral perturbation theory.
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.)
Properties of hyperons in chiral perturbation theory
Camalich, J Martin; Alvarez-Ruso, L; Vacas, M J Vicente
2009-01-01
The development of chiral perturbation theory in hyperon phenomenology has been troubled due to power-counting subtleties and to a possible slow convergence. Furthermore, the presence of baryon-resonances, e.g. the lowest-lying decuplet, complicates the approach, and the inclusion of their effects may become necessary. Recently, we have shown that a fairly good convergence is possible using a renormalization prescription of the loop-divergencies which recovers the power counting, is covariant and consistent with analyticity. Moreover, we have systematically incorporated the decuplet resonances taking care of both power-counting and $consistency$ problems. A model-independent understanding of diferent properties including the magnetic moments of the baryon-octet, the electromagnetic structure of the decuplet resonances and the hyperon vector coupling $f_1(0)$, has been successfully achieved within this approach. We will briefly review these developments and stress the important role they play for an accurate d...
Properties of hyperons in chiral perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Camalich, J. Martin; Geng, L.S. [Departamento de Fisica Teorica and IFIC, Universidad de Valencia-CSIC (Spain); Alvarez-Ruso, L. [Departamento de Fisica, Universidade de Coimbra (Portugal); Vacas, M.J. Vicente [Departamento de Fisica Teorica and IFIC, Universidad de Valencia-CSIC (Spain)
2010-04-01
The development of chiral perturbation theory in hyperon phenomenology has been troubled due to power-counting subtleties and to a possible slow convergence. Furthermore, the presence of baryon-resonances, e.g. the lowest-lying decuplet, complicates the approach, and the inclusion of their effects may become necessary. Recently, we have shown that a fairly good convergence is possible using a renormalization prescription of the loop-divergencies which recovers the power counting, is covariant and consistent with analyticity. Moreover, we have systematically incorporated the decuplet resonances taking care of both power-counting and consistency problems. A model-independent understanding of different properties including the magnetic moments of the baryon-octet, the electromagnetic structure of the decuplet resonances and the hyperon vector coupling f{sub 1}(0), has been successfully achieved within this approach. We will briefly review these developments and stress the important role they play for an accurate determination of the Cabibbo-Kobayashi-Maskawa matrix element V{sub us} from hyperon semileptonic decay data.
One-loop Chiral Perturbation Theory with two fermion representations
DeGrand, Thomas; Neil, Ethan T; Shamir, Yigal
2016-01-01
We develop Chiral Perturbation Theory for chirally broken theories with fermions in two different representations of the gauge group. Any such theory has a non-anomalous singlet $U(1)_A$ symmetry, yielding an additional Nambu-Goldstone boson when spontaneously broken. We calculate the next-to-leading order corrections for the pseudoscalar masses and decay constants, which include the singlet Nambu-Goldstone boson, as well as for the two condensates. The results can be generalized to more than two representations.
Hyperon decay form factors in chiral perturbation theory
Lacour, Andre; Meißner, Ulf-G
2007-01-01
We present a complete calculation of the SU(3)-breaking corrections to the hyperon vector form factors up to O(p^4) in covariant baryon chiral perturbation theory. Partial higher-order contributions are obtained, and we discuss chiral extrapolations of the vector form factor at zero momentum transfer. In addition we derive low-energy theorems for the subleading moments in hyperon decays, the weak Dirac radii and the weak anomalous magnetic moments, up to O(p^4).
Vector and Axial Currents in Wilson Chiral Perturbation Theory
Aoki, Sinya; Sharpe, Stephen R
2009-01-01
We reconsider the construction of the vector and axial-vector currents in Wilson Chiral Perturbation Theory (WChPT), the low-energy effective theory for lattice QCD with Wilson fermions. We discuss in detail the finite renormalization of the currents that has to be taken into account in order to properly match the currents. We explicitly show that imposing the chiral Ward identities on the currents does, in general, affect the axial-vector current at O(a). As an application of our results we compute the pion decay constant to one loop in the two flavor theory. Our result differs from previously published ones.
Chiral perturbation theory with tensor sources
Energy Technology Data Exchange (ETDEWEB)
Cata, Oscar; Cata, Oscar; Mateu, Vicent
2007-05-21
We construct the most general chirally-invariant Lagrangian for mesons in the presence of external sources coupled to the tensor current \\bar psi sigma_mu nu psi. In order to have only even terms in the chiral expansion, we consider the new source of O(p2). With this choice, we build the even-parity effective Lagrangian up to the p6-order (NLO). While there are only 4 new terms at the p4-order, at p6-order we find 78 terms for n_f=2 and 113 terms for n_f=3. We provide a detailed discussion on the different mechanisms that ensure that our final set of operators is complete and non-redundant. We also examine the odd-parity sector, to conclude that the first operators appear at the p8-order (NNLO).
Testing Lorentz Symmetry using Chiral Perturbation Theory
Noordmans, J P
2016-01-01
We consider the low-energy effects of a selected set of Lorentz- and CPT-violating quark and gluon operators by deriving the corresponding chiral effective lagrangian. Using this effective lagrangian, low-energy hadronic observables can be calculated. We apply this to magnetometer experiments and derive the best bounds on some of the Lorentz-violating coefficients. We point out that progress can be made by studying the nucleon-nucleon potential, and by considering storage-ring experiments for deuterons and other light nuclei.
Chiral perturbation theory of muonic hydrogen Lamb shift: polarizability contribution
Alarcón, Jose Manuel; Pascalutsa, Vladimir
2013-01-01
The proton polarizability effect in the muonic-hydrogen Lamb shift comes out as a prediction of baryon chiral perturbation theory at leading order and our calculation yields for it: $\\Delta E^{(\\mathrm{pol})} (2P-2S) = 8^{+3}_{-1}\\, \\mu$eV. This result is consistent with most of evaluations based on dispersive sum rules, but is about a factor of two smaller than the recent result obtained in {\\em heavy-baryon} chiral perturbation theory. We also find that the effect of $\\Delta(1232)$-resonance excitation on the Lamb-shift is suppressed, as is the entire contribution of the magnetic polarizability; the electric polarizability dominates. Our results reaffirm the point of view that the proton structure effects, beyond the charge radius, are too small to resolve the `proton radius puzzle'.
Radiative four-meson amplitudes in chiral perturbation theory
D'Ambrosio, G; Isidori, Gino; Neufeld, H
1996-01-01
We present a general discussion of radiative four--meson processes to O(p^4) in chiral perturbation theory. We propose a definition of ``generalized bremsstrahlung'' that takes full advantage of experimental information on the corresponding non--radiative process. We also derive general formulae for one--loop amplitudes which can be applied, for instance, to \\eta \\ra 3\\pi\\gamma, \\pi \\pi \\ra \\pi \\pi \\gamma and K \\ra 3\\pi\\gamma.
Automated Methods in Chiral Perturbation Theory on the Lattice
Borasoy, B; Krebs, H; Lewis, R; Borasoy, Bugra; Hippel, Georg M. von; Krebs, Hermann; Lewis, Randy
2005-01-01
We present a method to automatically derive the Feynman rules for mesonic chiral perturbation theory with a lattice regulator. The Feynman rules can be output both in a human-readable format and in a form suitable for an automated numerical evaluation of lattice Feynman diagrams. The automated method significantly simplifies working with improved or extended actions. Some applications to the study of finite-volume effects will be presented.
Heavy-Light Semileptonic Decays in Staggered Chiral Perturbation Theory
Aubin, C
2007-01-01
We calculate the form factors for the semileptonic decays of heavy-light pseudoscalar mesons in partially quenched staggered chiral perturbation theory (\\schpt), working to leading order in $1/m_Q$, where $m_Q$ is the heavy quark mass. We take the light meson in the final state to be a pseudoscalar corresponding to the exact chiral symmetry of staggered quarks. The treatment assumes the validity of the standard prescription for representing the staggered ``fourth root trick'' within \\schpt by insertions of factors of 1/4 for each sea quark loop. Our calculation is based on an existing partially quenched continuum chiral perturbation theory calculation with degenerate sea quarks by Becirevic, Prelovsek and Zupan, which we generalize to the staggered (and non-degenerate) case. As a by-product, we obtain the continuum partially quenched results with non-degenerate sea quarks. We analyze the effects of non-leading chiral terms, and find a relation among the coefficients governing the analytic valence mass depende...
Meson-Baryon Interactions in Unitarized Chiral Perturbation Theory
García-Recio, C; Ruiz-Arriola, E; Vacas, M J V
2003-01-01
Meson-Baryon Interactions can be successfully described using both Chiral Symmetry and Unitarity. The $s-$wave meson-baryon scattering amplitude is analyzed in a Bethe-Salpeter coupled channel formalism incorporating Chiral Symmetry in the potential. Two body coupled channel unitarity is exactly preserved. The needed two particle irreducible matrix amplitude is taken from lowest order Chiral Perturbation Theory in a relativistic formalism. Off-shell behavior is parameterized in terms of low energy constants. The relation to the heavy baryon limit is discussed. The position of the complex poles in the second Riemann sheet of the scattering amplitude determine masses and widths baryonic resonances of the N(1535), N(1670), $\\Lambda (1405)$ and $\\Lambda(1670)$ resonances which compare well with accepted numbers.
Chiral Perturbation Theory with Virtual Photons and Leptons
Knecht, M; Rupertsberger, H W; Talavera, P
2000-01-01
We construct a low-energy effective field theory which allows the full treatment of isospin-breaking effects in semileptonic weak interactions. To this end, we enlarge the particle spectrum of chiral perturbation theory with virtual photons by including also the light leptons as dynamical degrees of freedom. Using super-heat-kernel techniques, we determine the additional one-loop divergences generated by the presence of virtual leptons and give the full list of associated local counterterms. We illustrate the use of our effective theory by applying it to the decays pi -> l nu_{l} and K -> l nu_{l}.
\\pi N scattering in relativistic baryon chiral perturbation theory revisited
Alarcon, J M; Oller, J A; Alvarez-Ruso, L
2011-01-01
We have analyzed pion-nucleon scattering using the manifestly relativistic covariant framework of Infrared Regularization up to {\\cal O}(q^3) in the chiral expansion, where q is a generic small momentum. We describe the low-energy phase shifts with a similar quality as previously achieved with Heavy Baryon Chiral Perturbation Theory, \\sqrt{s}\\lesssim1.14 GeV. New values are provided for the {\\cal O}(q^2) and {\\cal O}(q^3) low-energy constants, which are compared with previous determinations. This is also the case for the scattering lengths and volumes. Finally, we have unitarized the previous amplitudes and as a result the energy range where data are reproduced increases significantly.
Generalized polarizabilities of the nucleon in baryon chiral perturbation theory
Lensky, Vadim; Pascalutsa, Vladimir; Vanderhaeghen, Marc
2017-02-01
The nucleon generalized polarizabilities (GPs), probed in virtual Compton scattering (VCS), describe the spatial distribution of the polarization density in a nucleon. They are accessed experimentally via the process of electron-proton bremsstrahlung (ep→ epγ ) at electron-beam facilities, such as MIT-Bates, CEBAF (Jefferson Lab), and MAMI (Mainz). We present the calculation of the nucleon GPs and VCS observables at next-to-leading order in baryon chiral perturbation theory (Bχ PT), and confront the results with the empirical information. At this order our results are predictions, in the sense that all the parameters are well known from elsewhere. Within the relatively large uncertainties of our calculation we find good agreement with the experimental observations of VCS and the empirical extractions of the GPs. We find large discrepancies with previous chiral calculations - all done in heavy-baryon χ PT (HBχ PT) - and discuss the differences between Bχ PT and HBχ PT responsible for these discrepancies.
Masses and Sigma Terms of Pentaquarks in Chiral Perturbation Theory
Institute of Scientific and Technical Information of China (English)
LI Xiao-Ya; L(U) Xiao-Fu
2006-01-01
Assuming that the recently θ+ and other exotic resonances belong to the pentaquark (-1-0) of SU(3)f with JP= 1/2, we constructed a relativistic effective lagrangian in the frame work of baryon chiral perturbation theory.The masses of pentaquarks under isospin symmetry is determined by calculating the propagator to one loop, where the extended on-mass-shell renormalization scheme is applied. Using the experimental data for masses of θ+, (I) and N, we estimated the mass of Σ. And the σ terms.
$K_{\\ell3}$ decays in Chiral Perturbation Theory
Bijnens, J; Bijnens, Johan; Talavera, Pere
2003-01-01
The process $K_{\\ell3}$ is calculated to two-loop order ($p^6$) in Chiral Perturbation Theory (ChPT) in the isospin conserved case. We use expressions suitable for use with previous work in two-loop CHPT where the order $p^4$ parameters ($L_i^r$) were determined from experiment. We point out that all the order $p^6$ parameters ($C_i^r$) that appear in the value of $f_+(0)$ relevant for the determination of $|V_{us}|$ can be determined from $K_{\\ell3}$ measurements via the slope and the curvature of the scalar form-factor.
Applications Of Chiral Perturbation Theory To Lattice Qcd
Van de Water, R S
2005-01-01
Quantum chromodynamics (QCD) is the fundamental theory that describes the interaction of quarks and gluons. Thus, in principle, one should be able to calculate all properties of hadrons from the QCD Lagrangian. It turns out, however, that such calculations can only be performed numerically on a computer using the nonperturbative method of lattice QCD, in which QCD is simulated on a discrete spacetime grid. Because lattice simulations use unphysically heavy quark masses (for computational reasons), lattice results must be connected to the real world using expressions calculated in chiral perturbation theory (χPT), the low-energy effective theory of QCD. Moreover, because real spacetime is continuous, they must be extrapolated to the continuum using an extension of χPT that includes lattice discretization effects, such as staggered χPT. This thesis is organized as follows. We motivate the need for lattice QCD and present the basic methodology in Chapter 1. We describe a common approximat...
A Review of Heavy-Quark and Chiral Perturbation Theory
Naboulsi, R
2003-01-01
In this paper we discuss the relations between various decays that can be obtained by combining heavy-quark perturbation theory and chiral perturbation theory for the emission of soft pseudoscalar particles. In the heavy-quark limit of QCD the interactions of the heavy quark Q are simplified because of a new set of symmetries not manifestly present in the full QCD. This fact is usually used in the construction of the new effective theory where the heavy-quark mass goes to infinity $(m_Q\\gg \\Lambda_{QCD})$ with its four-velocity fixed. The spin-flavor symmetry group of this new theory with N heavy quarks is SU(2N) because the interactions of the heavy quarks are independent of their spins and flavors. This fact is widely used in the description of the semileptonic decays of $B$ mesons to $D$ and $D^\\ast$ mesons where heavy-quark symmetry allows a parameterization of the decay amplitudes in terms of the single Isgur-Wise function [1].
SIMP model at NNLO in chiral perturbation theory
DEFF Research Database (Denmark)
Hansen, Martin Rasmus Lundquist; Langaeble, K.; Sannino, F.
2015-01-01
We investigate the phenomenological viability of a recently proposed class of composite dark matter models where the relic density is determined by 3 to 2 number-changing processes in the dark sector. Here the pions of the strongly interacting field theory constitute the dark matter particles....... By performing a consistent next-to-leading and next-to-next-to-leading order chiral perturbative investigation we demonstrate that the leading order analysis cannot be used to draw conclusions about the viability of the model. We further show that higher order corrections substantially increase the tension...... with phenomenological constraints challenging the viability of the simplest realisation of the strongly interacting massive particle (SIMP) paradigm....
Chiral perturbation theory analysis of baryon temperature mass shifts
Bedaque, P F
1995-01-01
We compute the finite temperature pole mass shifts of the octet and decuplet baryons using heavy baryon chiral perturbation theory and the 1/N_c expansion, where N_c is the number of QCD colors. We consider the temperatures of the order of the pion mass m_\\pi, and expand truncate the chiral and 1/N_c expansions assuming that m_\\pi \\sim 1/N_c. There are three scales in the problem: the temperature T, the pion mass m_\\pi, and the octet--decuplet mass difference. Therefore, the result is not simply a power series in T. We find that the nucleon and \\Delta temperature mass shifts are opposite in sign, and that their mass difference changes by 20% in the temperature range 90 MeV < T < 130 MeV, that is the range where the freeze out in relativistic heavy ion collisions is expected to occur. We argue that our results are insensitive to the neglect of 1/N_c- supressed effects; the main purpose of the 1/N_c expansion in this work is to justify our treatment of the decuplet states.
Topics on heavy baryon chiral perturbation theory in the large N_c limit
Flores-Mendieta, R
2002-01-01
We compute nonanalytical pion-loop corrections to baryon masses in a combined expansion in chiral symmetry breaking and 1/N_c, where N_c is the number of colors. Specifically, we compute flavor-27 baryon mass splittings at leading order in chiral perturbation theory. Our results, at the physical value N_c=3, are compared with the expressions obtained in heavy baryon chiral perturbation theory with no 1/N_c expansion.
Ultraviolet finiteness of Chiral Perturbation Theory for two-dimensional Quantum Electrodynamics
Paston, S A; Franke, V A
2003-01-01
We consider the perturbation theory in the fermion mass (chiral perturbation theory) for the two-dimensional quantum electrodynamics. With this aim, we rewrite the theory in the equivalent bosonic form in which the interaction is exponential and the fermion mass becomes the coupling constant. We reformulate the bosonic perturbation theory in the superpropagator language and analyze its ultraviolet behavior. We show that the boson Green's functions without vacuum loops remain finite in all orders of the perturbation theory in the fermion mass.
Chiral-scale perturbation theory about an infrared fixed point
Directory of Open Access Journals (Sweden)
Crewther R.J.
2014-06-01
Full Text Available We review the failure of lowest order chiral SU(3L ×SU(3R perturbation theory χPT3 to account for amplitudes involving the f0(500 resonance and O(mK extrapolations in momenta. We summarize our proposal to replace χPT3 with a new effective theory χPTσ based on a low-energy expansion about an infrared fixed point in 3-flavour QCD. At the fixed point, the quark condensate ⟨q̅q⟩vac ≠ 0 induces nine Nambu-Goldstone bosons: π,K,η and a QCD dilaton σ which we identify with the f0(500 resonance. We discuss the construction of the χPTσ Lagrangian and its implications for meson phenomenology at low-energies. Our main results include a simple explanation for the ΔI = 1/2 rule in K-decays and an estimate for the Drell-Yan ratio in the infrared limit.
Chiral perturbation theory approach to hadronic weak amplitudes
Energy Technology Data Exchange (ETDEWEB)
Rafael, E. de (Centre National de la Recherche Scientifique, 13 - Marseille (France). Centre de Physique Theorique 2)
1989-07-01
We are concerned with applications to the non-leptonic weak interactions in the sector of light quark flavors: u, d and s. Both strangeness changing {Delta}S=1 and {Delta}S=2 non-leptonic transitions can be described as weak perturbations to the strong effective chiral Lagrangian; the chiral structure of the weak effective Lagrangian being dictated by the transformation properties of the weak non-leptonic Hamiltonian of the Standard Model under global SU(3){sub Left}xSU(3){sub Right} rotations of the quark-fields. These lectures are organized as follows. Section 2 gives a review of the basic properties of chiral symmetry. Section 3 explains the effective chiral realization of the non-leptonic weak Hamiltonian of the Standard Model to lowest order in derivatives and masses. Section 4 deals with non-leptonic weak transitions in the presence of electromagnetism. Some recent applications to radiative kaon decays are reviewed and the effect of the so called electromagnetic penguin like diagrams is also discussed. Section 5 explains the basic ideas of the QCD-hadronic duality approach to the evaluation of coupling constants of the non-leptonic chiral weak Lagrangian. (orig./HSI).
Sigma Terms and Strangeness Contents of Baryon Octet in Modified Chiral Perturbation Theory
Institute of Scientific and Technical Information of China (English)
LI Xiao-Ya; L(U) Xiao-Fu
2006-01-01
In the frame work of chiral perturbation theory, a modified effective Lagrangian for meson-baryon system is constructed, where the SU(3) breaking effect for meson is considered. The difference between physical and chiral limit decay constants is taken into account. Calculated to one loop at O(p3), the sigma terms and strangeness contents of baryon octet are obtained.
SU(3)-breaking corrections to the baryon-octet magnetic moments in chiral perturbation theory
Camalich, J Martin; Geng, L S; Vacas, M J Vicente
2009-01-01
We report a calculation of the baryon magnetic moments using covariant chiral perturbation theory within the extended-on-mass-shell renormalization scheme including intermediate octet and decuplet contributions. By fitting the two available low-energy constants, we improve the Coleman-Glashow description of the data when we include the leading SU(3) breaking effects coming from the lowest-order loops. We compare with previous attempts at the same order using heavy-baryon and covariant infrared chiral perturbation theory, and discuss the source of the differences.
Gold-plated moments of nucleon structure functions in baryon chiral perturbation theory
Lensky, Vadim; Pascalutsa, Vladimir
2014-01-01
We obtain leading- and next-to-leading order predictions of chiral perturbation theory for several prominent moments of nucleon structure functions. These free-parameter free results turn out to be in overall agreement with the available empirical information on all of the considered moments, in the region of low-momentum transfer ($Q^2 < 0.3$ GeV$^2$). Especially surprising is the situation for the $\\delta_{LT}$ moment, which thus far was not reproducible for proton and neutron simultaneously in chiral perturbation theory. This problem, known as the "$\\delta_{LT}$ puzzle," is not seen in the present calculation.
The epsilon regime of chiral perturbation theory with Wilson-type fermions
Energy Technology Data Exchange (ETDEWEB)
Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Shindler, A. [Liverpool Univ. (United Kingdom). Theoretical Physics Division
2009-11-15
In this proceeding contribution we report on the ongoing effort to simulate Wilson-type fermions in the so called epsilon regime of chiral perturbation theory (cPT).We present results for the chiral condensate and the pseudoscalar decay constant obtained with Wilson twisted mass fermions employing two lattice spacings, two different physical volumes and several quark masses. With this set of simulations we make a first attempt to estimate the systematic uncertainties. (orig.)
Li, Hao-Song; Chen, Xiao-Lin; Deng, Wei-Zhen; Zhu, Shi-Lin
2016-01-01
We have systematically investigated the magnetic moments and magnetic form factors of the decuplet baryons to the next-to-next-leading order in the framework of the heavy baryon chiral perturbation theory. Our calculation includes the contributions from both the intermediate decuplet and octet baryon states in the loops. We also calculate the charge and magnetic dipole form factors of the decuplet baryons. Our results may be useful to the chiral extrapolation of the lattice simulations of the decuplet electromagnetic properties.
$\\gamma\\gamma$ \\to $\\pi\\pi\\pi$ to one loop in chiral perturbation theory
Talavera, P; Bijnens, J; Bramon, A; Cornet, F
1995-01-01
The \\gamma\\gamma \\to \\pi^0 \\pi^0 \\pi^0 and \\gamma\\gamma \\to \\pi^+ \\pi^- \\pi^0 amplitudes are discussed in the general context of Chiral Perturbation Theory (ChPT) to O(p^6). Chiral loops are found to play a major role. This makes these processes a good test of ChPT, mainly in its anomalous sector. We correct earlier numerical results at tree level and determine the one-loop results as well.
Improved Unitarized Heavy Baryon Chiral Perturbation Theory for $\\pi N $ Scattering
Nicola, A G; Peláez, J R; Ruiz-Arriola, E
2000-01-01
We show how the unitarized description of pion nucleon scattering within Heavy Baryon Chiral Perturbation Theory can be considerably improved, by a suitable reordering of the expansion over the nucleon mass. Within this framework, the $\\Delta$ resonance and its associated pole can be recovered from the chiral parameters obtained from low-energy determinations. In addition, we can obtain a good description of the six $S$ and $P$ wave phase shifts in terms of chiral parameters with a natural size and compatible with the Resonance Saturation Hypothesis.
Extending Chiral Perturbation Theory with an Isosinglet Scalar
DEFF Research Database (Denmark)
Hansen, Martin; Langaeble, Kasper; Sannino, Francesco
2017-01-01
We augment the chiral Lagrangian by an isosinglet scalar and compute the one-loop radiative corrections to the pion mass and decay constant, as well as the scalar mass. The calculations are carried out for different patterns of chiral symmetry breaking of immediate relevance for phenomenology...
The electric dipole form factor of the nucleon in chiral perturbation theory to subleading order
Mereghetti, E; de Vries, Jordy; Hockings, W.H.; Maekawa, C.M.; van Kolck, U
2011-01-01
The electric dipole form factor (EDFF) of the nucleon stemming from the QCD ¯ term and from the quark color-electric dipole moments is calculated in chiral perturbation theory to sub-leading order. This is the lowest order in which the isoscalar EDFF receives a calculable, non-analytic contribution
Chiral perturbation theory study of the axial $N\\to\\Delta(1232)$ transition
Geng, L S; Alvarez-Ruso, L; Vacas, M J Vicente
2008-01-01
We have performed a theoretical study of the axial Nucleon to Delta(1232) ($N\\to\\Delta$) transition form factors up to one-loop order in covariant baryon chiral perturbation theory within a formalism in which the unphysical spin-1/2 components of the $\\Delta$ fields are decoupled.
Extending Chiral Perturbation Theory with an Isosinglet Scalar
Hansen, Martin; Sannino, Francesco
2016-01-01
We augment the chiral Lagrangian by an isosinglet scalar and compute the one-loop radiative corrections to the pion mass and decay constant, as well as the scalar mass. The calculations are carried out for different patterns of chiral symmetry breaking of immediate relevance for phenomenology and lattice investigations. By construction our results encompass several interesting limits, ranging from the dilaton to the linear sigma model.
Extending chiral perturbation theory with an isosinglet scalar
Hansen, Martin; Langæble, Kasper; Sannino, Francesco
2017-02-01
We augment the chiral Lagrangian by an isosinglet scalar and compute the one-loop radiative corrections to the pion mass and decay constant, as well as the scalar mass. The calculations are carried out for different patterns of chiral symmetry breaking of immediate relevance for phenomenology and lattice investigations. By construction our results encompass several interesting limits, ranging from the dilaton to the linear sigma model.
Matching Pion-Nucleon Roy-Steiner Equations to Chiral Perturbation Theory
Hoferichter, Martin; Ruiz de Elvira, Jacobo; Kubis, Bastian; Meißner, Ulf-G.
2015-11-01
We match the results for the subthreshold parameters of pion-nucleon scattering obtained from a solution of Roy-Steiner equations to chiral perturbation theory up to next-to-next-to-next-to-leading order, to extract the pertinent low-energy constants including a comprehensive analysis of systematic uncertainties and correlations. We study the convergence of the chiral series by investigating the chiral expansion of threshold parameters up to the same order and discuss the role of the Δ (1232 ) resonance in this context. Results for the low-energy constants are also presented in the counting scheme usually applied in chiral nuclear effective field theory, where they serve as crucial input to determine the long-range part of the nucleon-nucleon potential as well as three-nucleon forces.
Matching pion-nucleon Roy-Steiner equations to chiral perturbation theory
Hoferichter, Martin; Kubis, Bastian; Meißner, Ulf-G
2015-01-01
We match the results for the subthreshold parameters of pion-nucleon scattering obtained from a solution of Roy-Steiner equations to chiral perturbation theory up to next-to-next-to-next-to-leading order, to extract the pertinent low-energy constants including a comprehensive analysis of systematic uncertainties and correlations. We study the convergence of the chiral series by investigating the chiral expansion of threshold parameters up to the same order and discuss the role of the \\Delta(1232) resonance in this context. Results for the low-energy constants are also presented in the counting scheme usually applied in chiral nuclear effective field theory, where they serve as crucial input to determine the long-range part of the nucleon-nucleon potential as well as three-nucleon forces.
Hyperon forward spin polarizability gamma0 in baryon chiral perturbation theory
Blin, Astrid Hiller; Ledwig, Tim; Lyubovitskij, Valery E
2015-01-01
We present the calculation of the hyperon forward spin polarizability gamma0 using manifestly Lorentz covariant baryon chiral perturbation theory including the intermediate contribution of the spin 3/2 states. As at the considered order the extraction of gamma0 is a pure prediction of chiral perturbation theory, the obtained values are a good test for this theory. After including explicitly the decuplet states, our SU(2) results have a very good agreement with the experimental data and we extend our framework to SU(3) to give predictions to the hyperons' gamma0 values. Prominent are the Sigma^- and Xi^- baryons as their photon transition to the decuplet is forbidden in SU(3) symmetry and therefore they are not sensitive to the explicit inclusion of the decuplet in the theory.
Aspects of meson-baryon scattering in three- and two-flavor chiral perturbation theory
Mai, Maxim; Kubis, Bastian; Meißner, Ulf-G
2009-01-01
We analyze meson-baryon scattering lengths in the framework of covariant baryon chiral perturbation theory at leading one-loop order. We compute the complete set of matching relations between the dimension-two low-energy constants in the two- and three-flavor formulations of the theory. We derive new two-flavor low-energy theorems for pion-hyperon and pion-cascade scattering that can be tested in lattice simulations.
Subtraction of power counting breaking terms in chiral perturbation theory: spinless matter fields
Du, Meng-Lin; Meißner, Ulf-G
2016-01-01
When matter fields are included in chiral perturbation theory, the nonvanishing mass in the chiral limit introduces a new energy scale so that the loop diagrams including such matter field propagators spoil the usual power counting. However, the power counting breaking terms can be absorbed into counterterms in the chiral Lagrangian. In this paper, we systematically derive these terms to leading one-loop order (next-to-next-to leading order in the chiral expansion) at once by calculating the generating functional using the path integral. They are then absorbed by counterterms in the next-to-leading order Lagrangian. The method can be extended to calculating power counting breaking terms for other matter fields.
Elastic Pion-Nucleon Scattering to $O(p^{3})$ in Heavy Baryon Chiral Perturbation Theory
Mojzis, M
1997-01-01
The elastic pi-N scattering amplitude in the isospin limit is calculated in the framework of heavy baryon chiral perturbation theory, up to the third order. Threshold parameters like scattering lengths, volumes, effective ranges, etc. are compared with data. All relevant low energy constants are fixed from the available pion-nucleon data. A clear improvement in the description of data is observed, when going from the first two orders in the chiral expansion to the third one. The importance of even higher orders is suggested by the result.
Properties of the ground-state baryons in chiral perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Martin Camalich, J., E-mail: camalich@ific.uv.e [Departamento de Fisica Teorica and IFIC, Universidad de Valencia-CSIC (Spain); Geng, L.S., E-mail: lisheng.geng@ph.tum.d [School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191 (China); Physik Department, Technische Universitaet Muenchen, D-85747 Garching (Germany); Vicente Vacas, J.M., E-mail: vicente@ific.uv.e [Departamento de Fisica Teorica and IFIC, Universidad de Valencia-CSIC (Spain)
2010-10-15
We review recent progress in the understanding of low-energy baryon structure by means of chiral perturbation theory. In particular, we discuss the application of this formalism to the description of various properties such as the baryon-octet magnetic moments, the electromagnetic structure of decuplet resonances and the hyperon vector coupling f{sub 1}(0). Moreover, we present the results on the chiral extrapolation of recent lattice QCD results on the lowest-lying baryon masses and we predict the corresponding baryonic sigma-terms.
Properties of the ground-state baryons in chiral perturbation theory
Martin-Camalich, J; Vacas, M J Vicente
2010-01-01
We review recent progress in the understanding of low-energy baryon structure by means of chiral perturbation theory. In particular, we discuss the application of this formalism to the description of various properties such as the baryon-octet magnetic moments, the electromagnetic structure of decuplet resonances and the hyperon vector coupling $f_1(0)$. Moreover, we present the results on the chiral extrapolation of recent lattice QCD results on the lowest-lying baryon masses and we predict the corresponding baryonic sigma-terms.
Forward virtual Compton scattering and the Lamb shift in chiral perturbation theory
Nevado, David
2007-01-01
We compute the spin-independent structure functions of the forward virtual-photon Compton tensor of the proton at one loop using heavy baryon chiral perturbation theory and dispersion relations. We study the relation between both approaches. We use these results to generalize some sum rules to virtual photon transfer momentum and relate them with sum rules in deep inelastic scattering. We then compute the leading chiral term of the polarizability correction to the Lamb shift of the hydrogen and muonic hydrogen. We obtain -87.05/n^3 Hz and -0.148/n^3 meV for the correction to the hydrogen and muonic hydrogen Lamb shift respectively.
Correlators of left charges and weak operators in finite volume chiral perturbation theory
Hernández, Pilar; Laine, Mikko
2003-01-01
We compute the two-point correlator between left-handed flavour charges, and the three-point correlator between two left-handed charges and one strangeness violating DeltaI = 3/2 weak operator, at next-to-leading order in finite volume SU(3)L × SU(3)R chiral perturbation theory, in the so-called epsilon-regime. Matching these results with the corresponding lattice measurements would in principle allow to extract the pion decay constant F, and the effective chiral theory parameter g27, which determines the Delta I = 3/2 amplitude of the weak decays K to pipi as well as the kaon mixing parameter BK in the chiral limit. We repeat the calculations in the replica formulation of quenched chiral perturbation theory, finding only mild modifications. In particular, a properly chosen ratio of the three-point and two-point functions is shown to be identical in the full and quenched theories at this order.
Baryon chiral perturbation theory extended beyond the low-energy region
Epelbaum, E; Meißner, Ulf-G; Yao, De-Liang
2015-01-01
We consider an extension of the one-nucleon sector of baryon chiral perturbation theory beyond the low-energy region. The applicability of this approach for higher energies is restricted to small scattering angles, i.e. the kinematical region, where the quark structure of hadrons cannot be resolved. The main idea is to re-arrange the low-energy effective Lagrangian according to a new power counting and to exploit the freedom of the choice of the renormalization condition for loop diagrams. We generalize the extended on-mass-shell scheme for the one-nucleon sector of baryon chiral perturbation theory by choosing a sliding scale, that is we expand the physical amplitudes around kinematical points beyond the threshold. This requires the introduction of complex-valued renormalized coupling constants which can be either extracted from experimental data, or calculated using the renormalization group evolution of coupling constants fixed in threshold region.
The lowest-lying baryon masses in covariant SU(3)-flavor chiral perturbation theory
Martin-Camalich, J; Vacas, M J Vicente
2010-01-01
We present an analysis of the baryon-octet and -decuplet masses using covariant SU(3)-flavor chiral perturbation theory up to next-to-leading order. Besides the description of the physical masses we address the problem of the lattice QCD extrapolation. Using the PACS-CS collaboration data we show that a good description of the lattice points can be achieved at next-to-leading order with the covariant loop amplitudes and phenomenologically determined values for the meson-baryon couplings. Moreover, the extrapolation to the physical point up to this order is found to be better than the linear one given at leading-order by the Gell-Mann-Okubo approach. The importance that a reliable combination of lattice QCD and chiral perturbation theory may have for hadron phenomenology is emphasized with the prediction of the pion-baryon and strange-baryon sigma terms.
Electromagnetic structure of the low-lying baryons in covariant chiral perturbation theory
Camalich, J Martin; Geng, L S; Vacas, M J Vicente
2009-01-01
We report a calculation of the low-lying baryon magnetic moments using covariant chiral perturbation theory within the extended-on-mass-shell renormalization scheme including intermediate octet and decuplet contributions. For the case of the baryon octet, we succeed to improve the Coleman-Glashow description by including the leading SU(3)$_F$-breaking effects coming from the lowest-order loops. We compare with previous attempts at the same order using heavy-baryon and covariant infrared chiral perturbation theory, and discuss the source of the differences. For the case of the decuplet-baryons we fix the only unknown LEC with the well measured magnetic dipole moment of the $\\Omega^-$ and predict the corresponding ones of the $\\Delta(1232)$ isospin multiplet. In particular we obtain $\\mu_{\\Delta^{++}}=6.0(6) \\mu_N$ and $\\mu_{\\Delta^{+}}=2.84(34) \\mu_N$ that compare well with the current experimental information.
Chiral perturbation theory of muonic-hydrogen Lamb shift: polarizability contribution
Energy Technology Data Exchange (ETDEWEB)
Alarcon, Jose Manuel; Pascalutsa, Vladimir [Johannes Gutenberg-Universitaet, Cluster of Excellence PRISMA Institut fuer Kernphysik, Mainz (Germany); Lensky, Vadim [University of Manchester, Theoretical Physics Group, School of Physics and Astronomy, Manchester (United Kingdom); Institute for Theoretical and Experimental Physics, Moscow (Russian Federation)
2014-04-15
The proton polarizability effect in the muonic-hydrogen Lamb shift comes out as a prediction of baryon chiral perturbation theory at leading order and our calculation yields ΔE{sup (pol)}(2P - 2S) = 8{sub -1}{sup +3}μeV. This result is consistent with most of evaluations based on dispersive sum rules, but it is about a factor of 2 smaller than the recent result obtained in heavy-baryon chiral perturbation theory.We also find that the effect of Δ(1232)-resonance excitation on the Lamb shift is suppressed, as is the entire contribution of the magnetic polarizability; the electric polarizability dominates. Our results reaffirm the point of view that the proton structure effects, beyond the charge radius, are too small to resolve the 'proton radius puzzle'. (orig.)
Determination of low-energy constants of Wilson chiral perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Herdoiza, Gregorio [Mainz Univ. (Germany). Inst fuer Kernphysik, PRISMA Cluster of Excellence; Univ. Autonoma de Madrid, Contoblanco (Spain). Dept. de Fisica Teorica; Univ. Autonoma de Madrid (Spain). Inst. de Fisica Teorica UAM/CSIC; Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Univ. Cyprus, Nicosia (Cyprus). Dept. of Physics; Michael, Chris [Liverpool Univ. (United Kingdom). Theoretical Physics Division; Ottnad, Konstantin; Urbach, Carsten [Bonn Univ. (Germany). Helmholtz-Institut fuer Strahlen und Kernphysik; Univ. Bonn (Germany). Bethe Center for Theoretical Physics; Collaboration: European Twisted Mass Collaboration
2013-03-15
By matching Wilson twisted mass lattice QCD determinations of pseudoscalar meson masses to Wilson Chiral Perturbation Theory we determine the low-energy constants W{sub 6}{sup '}, W{sub 8}{sup '} and their linear combination c{sub 2}. We explore the dependence of these low-energy constants on the choice of the lattice action and on the number of dynamical flavours.
Masses and magnetic moments of ground-state baryons in covariant baryon chiral perturbation theory
Geng, L S; Alvarez-Ruso, L; Vicente-Vacas, M J
2012-01-01
We report on some recent developments in our understanding of the light-quark mass dependence and the SU(3) flavor symmetry breaking corrections to the magnetic moments of the ground-state baryons in a covariant formulation of baryon chiral perturbation theory, the so-called EOMS formulation. We show that this covariant ChPT exhibits some promising features compared to its heavy-baryon and infrared counterparts.
Nucleon-to-Delta axial transition form factors in relativistic baryon chiral perturbation theory
Geng, L S; Alvarez-Ruso, L; Vacas, M J Vicente
2008-01-01
We report a theoretical study of the axial Nucleon to Delta(1232) ($N\\to\\Delta$) transition form factors up to one-loop order in relativistic baryon chiral perturbation theory. We adopt a formalism in which the $\\Delta$ couplings obey the spin-3/2 gauge symmetry and, therefore, decouple the unphysical spin-1/2 fields. We compare the results with phenomenological form factors obtained from neutrino bubble chamber data and in quark models.
Chiral Perturbation Theory and the $pp \\to pp \\pi^0$ Reaction Near Threshold
Sato, T; Myhrer, F; Kubodera, K
1997-01-01
A chiral-perturbative consideration of the near-threshold pp -> pp pi0 reaction indicates that the pion-rescattering term has a substantial energy and momentum dependence. The existing calculations that incorporate this dependence give pion rescattering contributions significantly larger than those of the conventional treatment, and this enhanced rescattering term interferes destructively with the one-body impulse term, leading to theoretical cross sections that are much smaller than the observed values. However, since the existing calculations are based on coordinate-space representation, they involve a number of simplifying assumptions about the energy-momentum flow in the rescattering diagram, even though the delicate interplay between the one-body and two-body terms makes it desirable to avoid these kinematical assumptions. We carry out here a momentum-space calculation that retains the energy-momentum dependence of the vertices as predicted by chiral perturbation theory. Our improved treatment increases ...
Large $N_{c}$ in chiral perturbation theory
Kaiser, R
2000-01-01
The construction of the effective Lagrangian relevant for the mesonic sector of QCD in the large N_c limit meets with a few rather subtle problems. We thoroughly examine these and show that, if the variables of the effective theory are chosen suitably, the known large N_c counting rules of QCD can unambiguously be translated into corresponding counting rules for the effective coupling constants. As an application, we demonstrate that the Kaplan-Manohar transformation is in conflict with these rules and is suppressed to all orders in 1/N_c. The anomalous dimension of the axial singlet current generates an additional complication: The corresponding external field undergoes nonmultiplicative renormalization. As a consequence, the Wess-Zumino-Witten term, which accounts for the U(3)_R x U(3)_L anomalies in the framework of the effective theory, contains pieces that depend on the running scale of QCD. The effect only shows up at nonleading order in 1/N_c, but requires specific unnatural parity contributions in the...
Energy Technology Data Exchange (ETDEWEB)
Hehl, H.
2002-07-01
This thesis has studied the range of validity of the chiral random matrix theory in QCD on the example of the quenched staggered Dirac operator. The eigenvalues of this operator in the neighbourhood of zero are essential for the understanding of the spontaneous breaking of the chiral symmetry and the phase transition connected with this. The phase transition cannot be understood in the framework of perturbation theory, so that the formulation of QCD on the lattice has been chosen as the only non-perturbative approach. In order to circumvent both the problem of the fermion doubling and to study chiral properties on the lattice with acceptable numerical effort, quenched Kogut-Susskind fermions have been applied. The corresponding Dirac operator can be completely diagonalized by the Lanczos procedure of Cullum and Willoughby. Monte carlo simulations on hypercubic lattice have been performed and the Dirac operators of very much configurations diagonalized at different lattice lengths and coupling constants. The eigenvalue correlations on the microscopic scale are completely described by the chiral random matrix theory for the topological sector zero, which has been studied by means of the distribution of the smallest eigenvalue, the microscopic spectral density and the corresponding 2-point correlation function. The found universal behaviour shows, that on the scale of the lowest eigenvalue only completely general properties of the theory are important, but not the full dynamics. In order to determine the energy scale, from which the chiral random matrix theory losses its validity, - the Thouless energy - with the scalar susceptibilities observables have been analyzed, which are because of their spectral mass dependence sensitive on this. For each combination of the lattice parameter so the deviation point has been identified.
Yao, De-Liang; Siemens, D.; Bernard, V.; Epelbaum, E.; Gasparyan, A. M.; Gegelia, J.; Krebs, H.; Meißner, Ulf-G.
2016-05-01
We present the results of a third order calculation of the pion-nucleon scattering amplitude in a chiral effective field theory with pions, nucleons and delta resonances as explicit degrees of freedom. We work in a manifestly Lorentz invariant formulation of baryon chiral perturbation theory using dimensional regularization and the extended on-mass-shell renormalization scheme. In the delta resonance sector, the on mass-shell renormalization is realized as a complex-mass scheme. By fitting the low-energy constants of the effective Lagrangian to the S- and P -partial waves a satisfactory description of the phase shifts from the analysis of the Roy-Steiner equations is obtained. We predict the phase shifts for the D and F waves and compare them with the results of the analysis of the George Washington University group. The threshold parameters are calculated both in the delta-less and delta-full cases. Based on the determined low-energy constants, we discuss the pion-nucleon sigma term. Additionally, in order to determine the strangeness content of the nucleon, we calculate the octet baryon masses in the presence of decuplet resonances up to next-to-next-to-leading order in SU(3) baryon chiral perturbation theory. The octet baryon sigma terms are predicted as a byproduct of this calculation.
Baryon chiral perturbation theory up to next-to-leading order
Bos, J W; Lee, S C; Lin, Y C; Shih, H H; Bos, J W; Chang, D W; Lee, S C; Lin, Y C; Shih, H H
1995-01-01
We examine the general lagrangian for baryon chiral perturbation theory with SU(3) flavor symmetry, up to the next-to-leading order. We consider both the strong and the weak interaction. The inverse of the baryon mass is treated as an additional small expansion parameter, and heavy fermion effective field theory techniques are employed to provide a consistent expansion scheme. A detailed account is given on the restrictions imposed on the lagrangian by the various symmetries. Corrections due to the finite baryon mass are also discussed.
Li, Xiao-ya; Wang, Bin; Sun, Win-min; Zong, Hong-shi
2008-01-01
The thermal properties of cold dense nuclear matter are investigated with chiral perturbation theory. The evolution curves for the baryon number density, baryon number susceptibility, pressure and the equation of state are obtained. The chiral condensate is calculated and our result shows that when the baryon chemical potential goes beyond $1150 \\mathrm{MeV}$, the absolute value of the quark condensate decreases rapidly, which indicates a tendency of chiral restoration.
S=--1 Meson-Baryon Scattering in Coupled Channel Unitarized Chiral Perturbation Theory
García-Recio, C; Ruiz-Arriola, E; Vacas, M J V
2003-01-01
The $s-$wave meson-baryon scattering amplitude is analyzed for the strangeness $S=-1$ and isospin I=0 sector in a Bethe-Salpeter coupled channel formalism incorporating Chiral Symmetry. Four two-body channels have been considered: $\\bar K N$, $\\pi \\Sigma $, $\\eta \\Lambda $, $ K \\Xi$. The needed two particle irreducible matrix amplitude is taken from lowest order Chiral Perturbation Theory in a relativistic formalism. Off-shell behaviour is parameterized in terms of low energy constants, which outnumber those assumed in previous works and provide a better fit to the data. The position of the complex poles in the second Riemann sheet of the scattering amplitude determine masses and widths of the $\\Lambda (1405)$ and $\\Lambda(1670)$ resonances which compare well with accepted numbers.
S=-1 meson-baryon scattering in coupled-channel unitarized Chiral Perturbation Theory
Energy Technology Data Exchange (ETDEWEB)
Garcia-Recio, C.; Nieves, J.; Ruiz Arriola, E. [Departamento de Fisica Moderna, Universidad de Granada, E-18071, Granada (Spain); Vicente Vacas, M. [Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Ap. Correos 22085, E-46071, Valencia (Spain)
2003-11-01
The s-wave meson-baryon scattering amplitude is analyzed for the strangeness S=-1 and isospin I=0 sector in a Bethe-Salpeter coupled-channel formalism incorporating Chiral Symmetry. Four two-body channels have been considered: anti K N, {pi}{sigma}, {eta}{lambda}, K {xi}. The needed two-particle irreducible matrix amplitude is taken from lowest-order Chiral Perturbation Theory in a relativistic formalism. Off-shell behaviour is parameterized in terms of low-energy constants, which outnumber those assumed in previous works and provide a better fit to the data. The position of the complex poles in the second Riemann sheet of the scattering amplitude determines masses and widths of the {lambda}(1405) and {lambda}(1670) resonances which compare well with accepted numbers. (orig.)
Chiral Perturbation Theory and the $\\bar B \\bar B$ Strong Interaction
Liu, Zhan-Wei; Zhu, Shi-Lin
2012-01-01
We have calculated the potentials of the heavy (charmed or bottomed) pseudoscalar mesons up to $O(\\epsilon^2)$ with the heavy meson chiral perturbation theory. We take into account the contributions from the football, triangle, box, and crossed diagrams with the 2$\\phi$ exchange and one-loop corrections to the contact terms. We notice that the total 2$\\phi$-exchange potential alone is attractive in the small momentum region in the channel ${\\bar B \\bar B}^{I=1}$, ${\\bar B_s \\bar B_s}^{I=0}$, or ${\\bar B \\bar B_s}^{I=1/2}$, while repulsive in the channel ${\\bar B \\bar B}^{I=0}$. Hopefully the analytical chiral structures of the potentials may be useful in the extrapolation of the heavy meson interaction from lattice QCD simulation.
Equation of state of imbalanced cold matter from chiral perturbation theory
Carignano, Stefano; Mannarelli, Massimo
2016-01-01
We study the thermodynamic properties of matter at vanishing temperature for non-extreme values of the isospin chemical potential and of the strange quark chemical potential. From the leading order pressure obtained by maximizing the static chiral Lagrangian density we derive a simple expression for the equation of state in the pion condensed phase and in the kaon condensed phase. We find an analytical expression for the maximum of the ratio between the chiral perturbation energy density and the Stefan-Boltzmann energy density as well as for the isospin chemical potential at the peak in good agreement with lattice simulations of quantum chromodynamics. We speculate on the location of the crossover from the Bose-Einstein condensate state to the Bardeen-Cooper-Schrieffer state by a simple analysis of the thermodynamic properties of the system. For $\\mu_I \\gtrsim 2 m_\\pi$ the leading order chiral perturbation theory breaks down; as an example it underestimates the energy density of the system and leads to a wron...
Pion-nucleon scattering in chiral perturbation theory II: Fourth order calculation
Fettes, N
2000-01-01
We analyze elastic pion-nucleon scattering to fourth order in heavy-baryon chiral perturbation theory, extending the third-order study published in Nucl. Phys. A 640 (1998) 199. We use various partial-wave analyses to pin down the low-energy constants from data in the physical region. The S-wave scattering lengths are consistent with recent determinations from pionic hydrogen and deuterium. We find an improved description of the P-waves. We also discuss the pion-nucleon sigma term and problems related to the prediction of the subthreshold parameters.
Proton radius from electron-proton scattering and chiral perturbation theory
Horbatsch, Marko; Pineda, Antonio
2016-01-01
We determine the root-mean-square proton charge radius, $R_{\\rm p}$, from a fit to low-$Q^2$ electron-proton elastic scattering cross section data with the higher moments fixed (within uncertainties) to the values predicted by chiral perturbation theory. We obtain $R_{\\rm p}=0.844(12)$ fm. This number is perfectly consistent with the value obtained from muonic hydrogen analyses and disagrees with the CODATA value (based upon atomic hydrogen spectroscopy and electron-proton scattering determinations) by more than two standard deviations.
Leading-order decuplet contributions to the baryon magnetic moments in chiral perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Geng, L.S. [Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Institutos de Investigacion de Paterna, 46071-Valencia (Spain); Camalich, J. Martin [Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Institutos de Investigacion de Paterna, 46071-Valencia (Spain)], E-mail: camalich@ific.uv.es; Vacas, M.J. Vicente [Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Institutos de Investigacion de Paterna, 46071-Valencia (Spain)
2009-06-01
We extend an earlier study of the baryon magnetic moments in chiral perturbation theory by the explicit inclusion of the spin-3/2 decuplet resonances. We find that the corrections induced by these heavier degrees of freedom are relatively small in a covariant framework where unphysical spin-1/2 modes are removed. Consequently, implementing the leading SU(3)-breaking corrections given by both the baryon and decuplet contributions, we obtain a description of the baryon-octet magnetic moments that is better than the Coleman-Glashow relations. Finally, we discuss the uncertainties and compare between heavy baryon and covariant approaches.
Leading SU(3)-breaking corrections to the baryon magnetic moments in chiral perturbation theory.
Geng, L S; Camalich, J Martin; Alvarez-Ruso, L; Vacas, M J Vicente
2008-11-28
We calculate the baryon magnetic moments using covariant chiral perturbation theory (chiPT) within the extended-on-mass-shell renormalization scheme. By fitting the two available low-energy constants, we improve the Coleman-Glashow description of the data when we include the leading SU(3)-breaking effects coming from the lowest-order loops. This success is in dramatic contrast with previous attempts at the same order using heavy-baryon chiPT and covariant infrared chiPT. We also analyze the source of this improvement with particular attention to the comparison between the covariant results.
Leading-order decuplet contributions to the baryon magnetic moments in Chiral Perturbation Theory
Geng, L S; Vacas, M J Vicente
2009-01-01
We extend an earlier study of the baryon magnetic moments in chiral perturbation theory by the explicit inclusion of the spin-3/2 decuplet resonances. We find that the corrections induced by these heavier degrees of freedom are relatively small in a covariant framework where unphysical spin-1/2 modes are removed. Consequently, implementing the leading SU(3)-breaking corrections given by both the baryon and decuplet contributions, we obtain a description of the baryon-octet magnetic moments that is better than the Coleman-Glashow relations. Finally, we discuss the uncertainties and compare between heavy baryon and covariant approaches.
The Inverse Amplitude Method in $\\pi\\pi$ Scattering in Chiral Perturbation Theory to Two Loops
Nieves, J; Ruiz-Arriola, E
2002-01-01
The inverse amplitude method is used to unitarize the two loop $\\pi\\pi$ scattering amplitudes of SU(2) Chiral Perturbation Theory in the $I=0,J=0$, $I=1,J=1$ and $I=2,J=0$ channels. An error analysis in terms of the low energy one-loop parameters $\\bar l_{1,2,3,4,}$ and existing experimental data is undertaken. A comparison to standard resonance saturation values for the two loop coefficients $\\bar b_{1,2,3,4,5,6} $ is also carried out. Crossing violations are quantified and the convergence of the expansion is discussed.
Two-point Functions at Two Loops in Three Flavour Chiral Perturbation Theory
Amorós, G; Talavera, P; Amoros, Gabriel; Bijnens, Johan; Talavera, Pere
2000-01-01
The vector and axial-vector two-point functions are calculated to next-to-next-to-leading order in Chiral Perturbation Theory for three light flavours. We also obtain expressions at the same order for the masses, $m_\\pi^2$, $m_K^2$ and $m_\\eta^2$, and the decay constants, $F_\\pi$, $F_K$ and $F_\\eta$. We present some numerical results after a simple resonance estimate of some of the new ${\\cal O}(p^6)$ constants.
T-odd correlations in radiative K_l3^+ decays and Chiral Perturbation Theory
Müller, E H; Meißner, Ulf G; Kubis, Bastian; Müller, Eike H; Mei{\\ss}ner, Ulf-G.
2006-01-01
The charged kaon decay channel K_l3gamma^+ allows for studies of direct CP violation, possibly due to non-standard mechanisms, with the help of T-odd correlation variables. In order to be able to extract a CP-violating signal from experiment, it is necessary to understand all possible Standard Model phases that also produce T-odd asymmetries. We complement earlier studies by considering strong interaction phases in hadronic structure functions that appear at higher orders in Chiral Perturbation Theory, and compare our findings to other potential sources of asymmetries.
The baryon axial current in large $N_c$ chiral perturbation theory
Hernandez-Ruiz, Maria A
2014-01-01
In this thesis we calculate the baryon axial current within the combined framework of the $1/N_c$ expansion and chiral perturbation theory, where $N_c$ is the number of colors. This calculation shall consider Feynman diagrams to order of one-loop, octet and decuplet intermediaries states. We obtain corrections due to one-loop and perturbative SU(3) symmetry breaking. The first corrections come from Feynman diagrams, then talk about a broken chiral symmetry in the implicit limit $m_q \\rightarrow 0$, where $m_q$ is the quark mass and the second corrections are obtained by ignoring isospin breaking and in that case the SU(3) symmetry breaking a first-order perturbation is included, leading an explicit break symmetry. The matrix elements of the spatial components of the axial operator between the states of the spin flavor symmetry, give the typical values of the axial vector coupling. For the baryon octet, links axial vector are $g_A$, just as they are defined in experiments of baryon semileptonic decays, where $...
Elastic pion-nucleon scattering in chiral perturbation theory: A fresh look
Siemens, D.; Bernard, V.; Epelbaum, E.; Gasparyan, A.; Krebs, H.; Meißner, Ulf-G.
2016-07-01
Elastic pion-nucleon scattering is analyzed in the framework of chiral perturbation theory up to fourth order within the heavy-baryon expansion and a covariant approach based on an extended on-mass-shell renormalization scheme. We discuss in detail the renormalization of the various low-energy constants and provide explicit expressions for the relevant β functions and the finite subtractions of the power-counting breaking terms within the covariant formulation. To estimate the theoretical uncertainty from the truncation of the chiral expansion, we employ an approach which has been successfully applied in the most recent analysis of the nuclear forces. This allows us to reliably extract the relevant low-energy constants from the available scattering data at low energy. The obtained results provide clear evidence that the breakdown scale of the chiral expansion for this reaction is related to the Δ resonance. The explicit inclusion of the leading contributions of the Δ isobar is demonstrated to substantially increase the range of applicability of the effective field theory. The resulting predictions for the phase shifts are in an excellent agreement with the predictions from the recent Roy-Steiner-equation analysis of pion-nucleon scattering.
Consistency between SU(3) and SU(2) covariant baryon chiral perturbation theory for the nucleon mass
Ren, Xiu-Lei; Alvarez-Ruso, L.; Geng, Li-Sheng; Ledwig, Tim; Meng, Jie; Vicente Vacas, M. J.
2017-03-01
Treating the strange quark mass as a heavy scale compared to the light quark mass, we perform a matching of the nucleon mass in the SU(3) sector to the two-flavor case in covariant baryon chiral perturbation theory. The validity of the 19 low-energy constants appearing in the octet baryon masses up to next-to-next-to-next-to-leading order [1] is supported by comparing the effective parameters (the combinations of the 19 couplings) with the corresponding low-energy constants in the SU(2) sector [2]. In addition, it is shown that the dependence of the effective parameters and the pion-nucleon sigma term on the strange quark mass is relatively weak around its physical value, thus providing support to the assumption made in Ref. [2] that the SU(2) baryon chiral perturbation theory can be applied to study nf = 2 + 1 lattice QCD simulations as long as the strange quark mass is close to its physical value.
Geng, L S; Vacas, M J Vicente
2009-01-01
We present a calculation of the leading SU(3)-breaking $\\mathcal{O}(p^3)$-corrections to the electromagnetic moments and charge radius (CR) of the lowest-lying decuplet resonances in covariant chiral perturbation theory. In particular, the magnetic dipole moment (MDM) of the members of the decuplet is predicted fixing the only low-energy constant (LEC) present up to this order with the well measured MDM of the $\\Omega^-$. We predict $\\mu_\\Delta^{++}=6.04(13)$ and $\\mu_\\Delta^+=2.84(2)$ which agree well with the current experimental information. For the electric quadrupole moment (EQM) and the CR we use state-of-the-art lattice QCD results to determine the corresponding LECs, whereas for the magnetic octupole moment (MOM) there is no unknown LEC up to the order considered here and we obtain a pure prediction. We compare our results with those reported in large $N_c$, lattice QCD, heavy-baryon chiral perturbation theory and other models.
Upper Energy Limit of Heavy Baryon Chiral Perturbation Theory in Neutral Pion Photoproduction
Fernandez-Ramirez, C
2013-01-01
We assess the energy limit up to which Heavy Baryon Chiral Perturbation Theory can be accurately applied to the process of neutral pion photoproduction from the proton by analyzing the latest data from the A2 and CB-TAPS collaborations at Mainz. We find that, within the current experimental status, the theory works up to $\\sim$170 MeV. Above this energy the data call for further improvement in the theory such as the explicit inclusion of the $\\Delta$(1232). We also find that data and multipoles can be well described up to $\\sim$185 MeV with Taylor expansions in the partial waves up to first order in pion energy.
Ananthanarayan, B.; Das, Diganta; Sentitemsu Imsong, I.
2012-10-01
Ampcalculator (AMPC) is a Mathematica © based program that was made publicly available some time ago by Unterdorfer and Ecker. It enables the user to compute several processes at one loop (upto O( p 4) in SU(3) chiral perturbation theory. They include computing matrix elements and form factors for strong and non-leptonic weak processes with at most six external states. It was used to compute some novel processes and was tested against well-known results by the original authors. Here we present the results of several thorough checks of the package. Exhaustive checks performed by the original authors are not publicly available, and hence the present effort. Some new results are obtained from the software especially in the kaon odd-intrinsic parity non-leptonic decay sector involving the coupling G 27. Another illustrative set of amplitudes at tree level we provide is in the context of τ-decays with several mesons including quark mass effects, of use to the BELLE experiment. All eight meson-meson scattering amplitudes have been checked. The Kaon-Compton amplitude has been checked and a minor error in the published results has been pointed out. This exercise is a tutorial-based one, wherein several input and output notebooks are also being made available as ancillary files on the arXiv. Some of the additional notebooks we provide contain explicit expressions that we have used for comparison with established results. The purpose is to encourage users to apply the software to suit their specific needs. An automatic amplitude generator of this type can provide error-free outputs that could be used as inputs for further simplification, and in varied scenarios such as applications of chiral perturbation theory at finite temperature, density and volume. This can also be used by students as a learning aid in low-energy hadron dynamics.
Energy Technology Data Exchange (ETDEWEB)
Ananthanarayan, B.; Sentitemsu Imsong, I. [Indian Institute of Science, Centre for High Energy Physics, Bangalore (India); Das, Diganta [The Institute of Mathematical Sciences Taramani, Chennai (India)
2012-10-15
Ampcalculator (AMPC) is a Mathematica {sup copyright} based program that was made publicly available some time ago by Unterdorfer and Ecker. It enables the user to compute several processes at one loop (upto O(p {sup 4})) in SU(3) chiral perturbation theory. They include computing matrix elements and form factors for strong and non-leptonic weak processes with at most six external states. It was used to compute some novel processes and was tested against well-known results by the original authors. Here we present the results of several thorough checks of the package. Exhaustive checks performed by the original authors are not publicly available, and hence the present effort. Some new results are obtained from the software especially in the kaon odd-intrinsic parity non-leptonic decay sector involving the coupling G{sub 27}. Another illustrative set of amplitudes at tree level we provide is in the context of {tau}-decays with several mesons including quark mass effects, of use to the BELLE experiment. All eight meson-meson scattering amplitudes have been checked. The Kaon-Compton amplitude has been checked and a minor error in the published results has been pointed out. This exercise is a tutorial-based one, wherein several input and output notebooks are also being made available as ancillary files on the arXiv. Some of the additional notebooks we provide contain explicit expressions that we have used for comparison with established results. The purpose is to encourage users to apply the software to suit their specific needs. An automatic amplitude generator of this type can provide error-free outputs that could be used as inputs for further simplification, and in varied scenarios such as applications of chiral perturbation theory at finite temperature, density and volume. This can also be used by students as a learning aid in low-energy hadron dynamics. (orig.)
New lessons from the nucleon mass, lattice QCD and heavy baryon chiral perturbation theory
Walker-Loud, A
2008-01-01
I will review heavy baryon chiral perturbation theory for the nucleon delta degrees of freedom and then examine the recent dynamical lattice calculations of the nucleon mass from the BMW, ETM, JLQCD, LHP, MILC, NPLQCD, PACS-CS, QCDSF/UKQCD and RBC/UKQCD Collaborations. Performing the chiral extrapolations of these results, one finds remarkable agreement with the physical nucleon mass, from each lattice data set. However, a careful examination of the lattice data and the resulting extrapolation functions reveals some unexpected results, serving to highlight the significant challenges in performing chiral extrapolations of baryon quantities. All the N_f=2+1 dynamical results can be quantitatively described by theoretically unmotivated fit function linear in the pion mass with m_pi ~ 750 -190 MeV. When extrapolated to the physical point, the results are in striking agreement with the physical nucleon mass. I will argue that knowledge of each lattice datum of the nucleon mass is required at the 1-2% level, includ...
Elastic pion-nucleon scattering in chiral perturbation theory: A fresh look
Siemens, D; Epelbaum, E; Gasparyan, A; Krebs, H; Meißner, Ulf-G
2016-01-01
Elastic pion-nucleon scattering is analyzed in the framework of chiral perturbation theory up to fourth order within the heavy-baryon expansion and a covariant approach based on an extended on-mass-shell renormalization scheme. We discuss in detail the renormalization of the various low-energy constants and provide explicit expressions for the relevant $\\beta$-functions and the finite subtractions of the power-counting breaking terms within the covariant formulation. To estimate the theoretical uncertainty from the truncation of the chiral expansion, we employ an approach which has been successfully applied in the most recent analysis of the nuclear forces. This allows us to reliably extract the relevant low-energy constants from the available scattering data at low energy. The obtained results provide a clear evidence that the breakdown scale of the chiral expansion for this reaction is related to the $\\Delta$-resonance. The explicit inclusion of the leading contributions of the $\\Delta$-isobar is demonstrat...
Bernard, V; Meißner, Ulf G; Kubis, Bastian; Mei{\\ss}ner, Ulf-G.
2005-01-01
We analyze the Fubini-Furlan-Rosetti sum rule in the framework of covariant baryon chiral perturbation theory to leading one-loop accuracy and including next-to-leading order polynomial contributions. We discuss the relation between the subtraction constants in the invariant amplitudes and certain low-energy constants employed in earlier chiral perturbation theory studies of threshold neutral pion photoproduction off nucleons. In particular, we consider the corrections to the sum rule due to the finite pion mass and show that below the threshold they agree well with determinations based on fixed-t dispersion relations. We also discuss the energy dependence of the electric dipole amplitude E_{0+}.
Yao, De-Liang; Bernard, V; Epelbaum, E; Gasparyan, A M; Gegelia, J; Krebs, H; Meißner, Ulf-G
2016-01-01
We present the results of a third order calculation of the pion-nucleon scattering amplitude in a chiral effective field theory with pions, nucleons and delta resonances as explicit degrees of freedom. We work in a manifestly Lorentz invariant formulation of baryon chiral perturbation theory using dimensional regularization and the extended on-mass-shell renormalization scheme. In the delta resonance sector, the on mass-shell renormalization is realized as a complex-mass scheme. By fitting the low-energy constants of the effective Lagrangian to the $S$- and $P$-partial waves a satisfactory description of the phase shifts from the analysis of the Roy-Steiner equations is obtained. We predict the phase shifts for the $D$ and $F$ waves and compare them with the results of the analysis of the George Washington University group. The threshold parameters are calculated both in the delta-less and delta-full cases. Based on the determined low-energy constants, we discuss the pion-nucleon sigma term. Additionally, in ...
Mass Spectra of Heavy-Light Mesons in Heavy Hadron Chiral Perturbation Theory
Alhakami, Mohammad H
2016-01-01
We study the masses of the low-lying charm and bottom mesons within the framework of heavy- hadron chiral perturbation theory. We work to third order in the chiral expansion, where meson loops contribute. In contrast to previous approaches, we use physical meson masses in evaluating these loops. This ensures that their imaginary parts are consistent with the observed widths of the D-mesons. The lowest odd- and even-parity, strange and nonstrange charm mesons provide enough constraints to determine only certain linear combinations of the low-energy constants (LECs) in the effective Lagrangian. We comment on how lattice QCD could provide further information to disentangle these constants. Then we use the results from the charm sector to predict the spectrum of odd- and even-parity of the bottom mesons. The predicted masses from our theory are in good agreement with experimentally measured masses for the case of the odd-parity sector. For the even-parity sector, the B-meson states have not yet been observed; thu...
Consistency between SU(3) and SU(2) chiral perturbation theory for the nucleon mass
Ren, Xiu-Lei; Geng, Li-Sheng; Ledwig, T; Meng, Jie; Vacas, M J Vicente
2016-01-01
Treating the strange quark mass as a heavy scale compared to the light quark mass, we perform a matching of the nucleon mass in the SU(3) sector to the two-flavor case in covariant baryon chiral perturbation theory. The validity of the $19$ low-energy constants appearing in the octet baryon masses up to next-to-next-to-next-to-leading order~\\cite{Ren:2014vea} is supported by comparing the effective parameters (the combinations of the $19$ couplings) with the corresponding low-energy constants in the SU(2) sector~\\cite{Alvarez-Ruso:2013fza}. In addition, it is shown that the dependence of the effective parameters and the pion-nucleon sigma term on the strange quark mass is relatively weak around its physical value, thus providing support to the assumption made in Ref.~\\cite{Alvarez-Ruso:2013fza}.
Leading SU(3)-breaking corrections to the baryon magnetic moments in Chiral Perturbation Theory
Geng, L S; Alvarez-Ruso, L; Vacas, M J Vicente
2008-01-01
We calculate the baryon magnetic moments using covariant Chiral Perturbation Theory ($\\chi$PT) within the Extended-on-mass-shell (EOMS) renormalization scheme. By fitting the two available low-energy constants, we improve the Coleman-Glashow description of the data when we include the leading SU(3) breaking effects coming from the lowest-order loops. This success is in dramatic contrast with previous attempts at the same order using Heavy Baryon (HB) $\\chi$PT and covariant Infrared (IR) $\\chi$PT. We also analyze the source of this improvement with particular attention on the comparison between the covariant results, and conclude that SU(3) baryon $\\chi$PT coverges better within the EOMS renormalization scheme.
One-loop divergences in chiral perturbation theory and right-invariant metrics on SU(3)
Energy Technology Data Exchange (ETDEWEB)
Esposito-Farese, G. (Centre National de la Recherche Scientifique, 13 - Marseille (France). Centre de Physique Theorique)
1991-04-01
In the framework of chiral perturbation theory, we compute the one-loop divergences of the effective Lagrangian describing strong and non-leptonic weak interactions of pseudoscalar mesons. We use the background field method and the heat-kernel expansion, and underline the geometrical meaning of the different terms, showing how the right-invariance of the metrics on SU(3) allows to clarify and simplify the calculations. Our results are given in terms of a minimal set of independent counterterms, and shorten previous ones of the literature, in the particular case where the electromagnetic field is the only external source which is considered. We also show that a geometrical construction of the effective Lagrangian at order O(p{sup 4}) allows to derive some relations between the finite parts of the coupling constants. These relations do not depend on the scale {mu} used to renormalize. (orig.).
The electric dipole form factor of the nucleon in chiral perturbation theory to sub-leading order
Mereghetti, E.; de Vries, J.; Hockings, W. H.; Maekawa, C. M.; van Kolck, U.
2011-01-01
The electric dipole form factor (EDFF) of the nucleon stemming from the QCD (theta) over bar term and from the quark color-electric dipole moments is calculated in chiral perturbation theory to sub-leading order. This is the lowest order in which the isoscalar EDFF receives a calculable, non-analyti
Convergence properties of η → 3π decays in chiral perturbation theory
Kolesár, Marián; Novotný, Jiří
2017-01-01
The convergence of the decay widths and some of the Dalitz plot parameters of the decay η → 3π seems problematic in low energy QCD. In the framework of resummed chiral perturbation theory, we explore the question of compatibility of experimental data with a reasonable convergence of a carefully defined chiral series. By treating the uncertainties in the higher orders statistically, we numerically generate a large set of theoretical predictions, which are then confronted with experimental information. In the case of the decay widths, the experimental values can be reconstructed for a reasonable range of the free parameters and thus no tension is observed, in spite of what some of the traditional calculations suggest. The Dalitz plot parameters a and d can be described very well too. When the parameters b and α are concerned, we find a mild tension for the whole range of the free parameters, at less than 2σ C.L. This can be interpreted in two ways - either some of the higher order corrections are indeed unexpectedly large or there is a specific configuration of the remainders, which is, however, not completely improbable.
Equation of state of imbalanced cold matter from chiral perturbation theory
Carignano, Stefano; Mammarella, Andrea; Mannarelli, Massimo
2016-03-01
We study the thermodynamic properties of matter at vanishing temperature for nonextreme values of the isospin chemical potential and of the strange quark chemical potential. From the leading-order pressure obtained by maximizing the static chiral Lagrangian density, we derive a simple expression for the equation of state in the pion condensed phase and in the kaon condensed phase. We find an analytical expression for the maximum of the ratio between the energy density and the Stefan-Boltzmann energy density and for the isospin chemical potential at the peak, both in good agreement with lattice simulations of quantum chromodynamics. We speculate on the location of the crossover from the Bose-Einstein condensate state to the Bardeen-Cooper-Schrieffer state by a simple analysis of the thermodynamic properties of the system. For μI≳2 mπ, the leading-order chiral perturbation theory breaks down; for example, it underestimates the energy density of the system and leads to a wrong asymptotic behavior.
The Kaon B-parameter in Mixed Action Chiral Perturbation Theory
Aubin, C; De van Water, R S; Laiho, Jack; Water, Ruth S. Van de
2006-01-01
We calculate the kaon B-parameter, B_K, in chiral perturbation theory for a partially quenched, mixed action theory with Ginsparg-Wilson valence quarks and staggered sea quarks. We find that the resulting expression is similar to that in the continuum, and in fact has only two additional unknown parameters. At one-loop order, taste-symmetry violations in the staggered sea sector only contribute to flavor-disconnected diagrams by generating an O(a^2) shift to the masses of taste-singlet sea-sea mesons. Lattice discretization errors also give rise to an analytic term which shifts the tree-level value of B_K by an amount of O(a^2). This term, however, is not strictly due to taste-breaking, and is therefore also present in the expression for B_K for pure G-W lattice fermions. We also present a numerical study of the mixed B_K expression in order to demonstrate that both discretization errors and finite volume effects are small and under control on the MILC improved staggered lattices.
The Kaon B-parameter in mixed action chiral perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Aubin, C.; /Columbia U.; Laiho, Jack; Van de Water, Ruth S.; /Fermilab
2006-09-01
We calculate the kaon B-parameter, B{sub K}, in chiral perturbation theory for a partially quenched, mixed action theory with Ginsparg-Wilson valence quarks and staggered sea quarks. We find that the resulting expression is similar to that in the continuum, and in fact has only two additional unknown parameters. At one-loop order, taste-symmetry violations in the staggered sea sector only contribute to flavor-disconnected diagrams by generating an {Omicron}(a{sup 2}) shift to the masses of taste-singlet sea-sea mesons. Lattice discretization errors also give rise to an analytic term which shifts the tree-level value of B{sub K} by an amount of {Omicron}(a{sup 2}). This term, however, is not strictly due to taste-breaking, and is therefore also present in the expression for B{sub K} for pure G-W lattice fermions. We also present a numerical study of the mixed B{sub K} expression in order to demonstrate that both discretization errors and finite volume effects are small and under control on the MILC improved staggered lattices.
Geng, L S; Vacas, M J Vicente
2009-01-01
We calculate the SU(3)-breaking corrections to the hyperon vector coupling $f_1(0)$ up to $\\mathcal{O}(p^4)$ in covariant baryon chiral perturbation theory with dynamical octet and decuplet contributions. We find that the decuplet contributions are of similar or even larger size than the octet ones. Combining both, we predict positive SU(3)-breaking corrections to all the four independent $f_1(0)$'s (assuming isospin symmetry), which are consistent, within uncertainties, with the latest results form large $N_c$ fits, chiral quark models, and quenched lattice QCD calculations.
The lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments in chiral perturbation theory
Geng, L S; Alvarez-Ruso, L; Vicente-Vacas, M J
2010-01-01
We review some recent progress in our understanding of the lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments (MMs) in terms of Chiral Perturbation Theory (ChPT). In particular, we show that at next-to-leading-order ChPT can describe the MMs of the octet baryons quite well. We also make predictions for the decuplet MMs at the same chiral order. Among them, the MMs of the $\\Delta^{++}$ and $\\Delta^+$ are found to agree well with data within the experimental uncertainties.
Kimura, Daiji; Umeeda, Hiroyuki
2016-01-01
Transition form factors and partial decay widths are investigated for Dalitz decays of $V\\to Pl^+l^-$ and $P\\to \\gamma l^+l^-$ $(V=1^-, P=0^-)$ in a model of resonance chiral perturbation theory. The differential decay width of $P\\to\\pi^+\\pi^-\\gamma$ and the partial widths of $V\\to 3P, V\\to P\\gamma, \\eta^\\prime\\to V\\gamma, \\phi\\to\\omega\\pi^0$ and $P\\to2\\gamma$ are also analyzed. The model contains octet and singlet fields as representation of SU(3). 1-loop order counter terms are introduced, based on the discussion of superficial degree of divergence. Intrinsic parity violating interactions are considered with singlet fields. We give the result of numerical analysis, and find a parameter region consistent with experimental data of transition form factors for $V\\to Pl^+l^-$. Predictions of the model are presented for transition form factors of $P\\to\\gamma l^+l^-$, differential decay width of $P\\to\\pi^+\\pi^-\\gamma$ and so forth. Furthermore, in the vicinity of resonance regions, the transition form factors of $...
Energy Technology Data Exchange (ETDEWEB)
Pelaez, J. R. [Univ. Complutense Madrid (Spain); Pennington, Michael R. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); de Elvira, J. Ruiz [Univ. Complutense Madrid (Spain); Wilson, D. J. [Argonne National Lab. (ANL), Argonne, IL (United States)
2011-11-01
The leading 1/N{sub c} behavior of Unitarized Chiral Perturbation Theory distinguishes the nature of the {rho} and the {sigma}. At one loop order the {rho} is a {bar q}q meson, while the {sigma} is not. However, semi-local duality between resonances and Regge behaviour cannot be satisfied for larger N{sub c}, if such a distinction holds. While the {sigma} at N{sub c}= 3 is inevitably dominated by its di-pion component, Unitarised Chiral Perturbation Theory beyond one loop order reveals that as N{sub c} increases above 6-8, the {sigma} has a sub-dominant {bar q}q fraction up at 1.2 GeV. Remarkably this ensures semi-local duality is fulfilled for the range of N{sub c} {approx}< 15-30, where the unitarization procedure adopted applies.
Energy Technology Data Exchange (ETDEWEB)
Navratil, P; Caurier, E
2003-10-14
The authors calculate properties of A = 6 system using the accurate charge-dependent nucleon-nucleon (NN) potential at fourth order of chiral perturbation theory. By application of the ab initio no-core shell model (NCSM) and a variational calculation in the harmonic oscillator basis with basis size up to 16 {h_bar}{Omega} they obtain the {sup 6}Li binding energy of 28.5(5) MeV and a converged excitation spectrum. Also, they calculate properties of {sup 10}B using the same NN potential in a basis space of up to 8 {h_bar}{Omega}. The results are consistent with results obtained by standard accurate NN potentials and demonstrate a deficiency of Hamiltonians consisting of only two-body terms. At this order of chiral perturbation theory three-body terms appear. It is expected that inclusion of such terms in the Hamiltonian will improve agreement with experiment.
Low-energy pi-pi and pi-K scatterings revisited in three-flavour resummed chiral perturbation theory
Descotes-Genon, S
2007-01-01
Chiral symmetry breaking may exhibit significantly different patterns in two chiral limits: N_f=2 massless flavours (m_u=m_d=0, m_s physical) and N_f=3 massless flavours (m_u=m_d=0=m_s=0). Such a difference may arise due to vacuum fluctuations of s-bar{s} pairs related to the violation of the Zweig rule in the scalar sector, and could yield a numerical competition between contributions counted as leading order and next-to-leading in the chiral expansions of observables. We recall and extend Resummed Chiral Perturbation Theory (ReChPT), a framework that we introduced previously to deal with such instabilities: it requires a more careful definition of the relevant observables and their one-loop chiral expansions. We analyse the amplitudes for low-energy pi-pi and pi-K scatterings within ReChPT, which we match in subthreshold regions with dispersive representations obtained from the solutions Roy and Roy-Steiner equations. Using a frequentist approach, we constrain the quark mass ratio as well as the quark conde...
Peripheral nucleon-nucleon scattering at fifth order of chiral perturbation theory
Entem, D R; Machleidt, R; Nosyk, Y
2014-01-01
We present the two- and three-pion exchange contributions to the nucleon-nucleon interaction which occur at next-to-next-to-next-to-next-to-leading order (N4LO, fifth order) of chiral effective field theory, and calculate nucleon-nucleon scattering in peripheral partial waves with L>=3 using low-energy constants that were extracted from pi-N analysis at fourth order. While the net three-pion exchange contribution is moderate, the two-pion exchanges turn out to be sizeable and prevailingly repulsive, thus, compensating the excessive attraction characteristic for NNLO and N3LO. As a result, the N4LO predictions for the phase shifts of peripheral partial waves are in very good agreement with the data (with the only exception of the 1F3 wave). We also discuss the issue of the order-by-order convergence of the chiral expansion for the NN interaction.
Geng, L S; Vacas, M J Vicente
2009-01-01
We report on a recent study of the SU(3)-breaking corrections to the hyperon vector coupling $f_1(0)$ up to $\\mathcal{O}(p^4)$ in covariant baryon chiral perturbation theory with dynamical octet and decuplet contributions. The decuplet contributions are taken into account for the first time in a covariant ChPT study and are found of similar or even larger size than the octet ones. We predict positive SU(3)-breaking corrections to all the four independent $f_1(0)$'s (assuming isospin symmetry), which are consistent, within uncertainties, with the latest results from large $N_c$ fits, chiral quark models, and quenched lattice QCD calculations. We also discuss briefly the implications of our results for the extraction of $V_{us}$ from hyperon decay data.
Birse, Michael C
2012-01-01
We calculate the amplitude T_1 for forward doubly-virtual Compton scattering in heavy-baryon chiral perturbation theory, to fourth order in the chiral expansion and with the leading contribution of the gammaNDelta form factor. This provides a model-independent expression for the amplitude in the low-momentum region, which is the dominant one for its contribution to the Lamb shift. It allows us to significantly reduce the theoretical uncertainty in the proton polarisability contributions to the Lamb shift in muonic hydrogen. We also stress the importance of consistency between the definitions of the Born and structure parts of the amplitude. Our result leaves no room for any effect large enough to explain the discrepancy between proton charge radii as determined from muonic and normal hydrogen.
Energy Technology Data Exchange (ETDEWEB)
Birse, M.C.; McGovern, J.A. [University of Manchester, Theoretical Physics Division, School of Physics and Astronomy, Manchester (United Kingdom)
2012-09-15
We calculate the amplitude T{sub 1} for forward doubly virtual Compton scattering in heavy-baryon chiral perturbation theory, to fourth order in the chiral expansion and with the leading contribution of the {gamma}N{Delta} form factor. This provides a model-independent expression for the amplitude in the low-momentum region, which is the dominant one for its contribution to the Lamb shift. It allows us to significantly reduce the theoretical uncertainty in the proton polarisability contributions to the Lamb shift in muonic hydrogen. We also stress the importance of consistency between the definitions of the Born and structure parts of the amplitude. Our result leaves no room for any effect large enough to explain the discrepancy between proton charge radii as determined from muonic and normal hydrogen. (orig.)
Institute of Scientific and Technical Information of China (English)
WANG Peng-Zhou; ZHANG Hong-Hao; ZHANG Shun-Li; YAN Wen-Bin; LI Xue-Song
2008-01-01
By using combinatorics, we give a new proof for the recurrence relations of the characteristic polynomial coefficients, and we further obtain an explicit expression for the generic term of the coefficient sequence, which yields the trace formulae of the Cayley-Hamilton's theorem with all coefficients explicitly given. This implies a byproduct, a complete expression for the determinant of any finite-dimensional matrix in terms of the traces of its successive powers.And we discuss some of their applications to chiral perturbation theory and general relativity.
Peripheral nucleon-nucleon scattering at fifth order of chiral perturbation theory
Entem, D. R.; Kaiser, N.; Machleidt, R.; Nosyk, Y.
2015-01-01
We present the two- and three-pion-exchange contributions to the nucleon-nucleon interaction which occur at next-to-next-to-next-to-next-to-leading order (N4LO , fifth order) of chiral effective field theory and calculate nucleon-nucleon scattering in peripheral partial waves with L ≥3 by using low-energy constants that were extracted from π N analysis at fourth order. While the net three-pion-exchange contribution is moderate, the two-pion exchanges turn out to be sizable and prevailingly repulsive, thus compensating the excessive attraction characteristic for next-to-next-to-leading order and N3LO . As a result, the N4LO predictions for the phase shifts of peripheral partial waves are in very good agreement with the data (with the only exception being the 1F3 wave). We also discuss the issue of the order-by-order convergence of the chiral expansion for the N N interaction.
Energy Technology Data Exchange (ETDEWEB)
Lehnhart, B.C.
2007-05-15
This thesis is concerned with electromagnetic pion production within manifestly Lorentz-invariant chiral perturbation theory using the assumption of isospin symmetry. In a one-loop calculation up to the chiral order O(q{sup 4}), 105 Feynman diagrams contribute, consisting of 20 tree graphs and 85 loop diagrams. The tree graphs are classified as 16 pole diagrams and 4 contact graphs. Of the 85 loop diagrams, 50 diagrams are of order three and 35 diagrams are of fourth order. To calculate the pion production amplitude algorithms are developed on the basis of the Mathematica package FeynCalc. The one-photon-exchange approximation allows one to parametrise the pion production amplitude as the product of the polarisation vector of the (virtual) photon and the matrix element of the transition current. The polarisation vector is related to the leptonic vertex and the photon propagator and is well-known from QED. The dependence of the amplitude on the strong interaction is contained in the matrix element of the transition current, and we use chiral perturbation theory to describe this matrix element. The transition current can be expressed in terms of six gauge invariant amplitudes, each of which can again be decomposed into three isospin amplitudes. Linear combinations of these amplitudes allow us to describe the physical amplitudes. The one-loop integrals appearing within this calculation are determined numerically by the program LoopTools. In the case of tensorial integrals it is required to perform the method of Passarino and Veltman first. Furthermore, we apply the reformulated infrared regularisation which ensures that the results fulfill the chiral power counting. For this purpose algorithms are developed which determine the subtraction terms automatically. The obtained isospin amplitudes are integrated in the program MAID. As tests the s-wave multipoles E{sub 0+} and L{sub 0+} (using results up to chiral order O(q{sup 3})) are calculated in the threshold region
Pion-nucleon scattering in chiral perturbation theory; 2, Fourth order calculation
Fettes, N; Fettes, Nadia; Meissner, Ulf-G.
2000-01-01
We analyse elastic-pion nucleon scattering to fourth order in heavy baryonchiral perturbation theory, extending the third order study published in Nucl.Phys. A640 (1998) 199. We use various partial wave analyses to pin down thelow-energy constants from data in the physical region. The S-wave scatteringlengths are consistent with recent determinations from pionic hydrogen anddeuterium. We find an improved description of the P-waves. We also discuss thepion-nucleon sigma term and problems related to the prediction of thesubthreshold parameters.
Results from the MILC collaboration's SU(3) chiral perturbation theory analysis
Bazavov, A; DeTar, C; Du, X; Freeman, W; Gottlieb, Steven; Heller, Urs M; Hetrick, J E; Laiho, J; Levkova, L; Oktay, M B; Osborn, J; Sugar, R; Toussaint, D; Van de Water, R S
2009-01-01
We present the status of the MILC collaboration's analysis of the light pseudoscalar meson sector with SU(3) chiral fits. The analysis includes data from new ensembles with smaller lattice spacing, smaller light quark masses and lighter than physical strange quark masses. Our fits include the NNLO chiral logarithms. We present results for decay constants, quark masses, Gasser-Leutwyler low energy constants, and condensates in the two- and three-flavor chiral limits.
{Delta}I = 3/2 and {Delta}S = 2 Hyperon decays in chiral perturbation theory
Energy Technology Data Exchange (ETDEWEB)
He, X.G. [University of Melbourne, Parkville, VIC (Australia). School of Physics; Valencia, G. [Iowa State University, Ames, Iowa (United States). Department of Physics and Astronomy
1997-05-01
We study the| {Delta}I| = 3/2 and |{Delta}S| = 2 amplitudes for hyperon decays of the form B {yields} B`{pi} at lowest order in chiral perturbation theory. At this order, the {Delta}I = 3/2 amplitudes depend on only one constant. We extract the value of this constant from experiment and find a reasonable description of these processes within experimental errors. The same constant determines the {Delta}S = 2 transitions which, in the standard model, are too small to be observed. We find that new physics with parity odd {Delta}S = 2 interactions can produce observable rates in hyperon decays while evading the bounds from K{sup 0} - K-bar{sup 0} mixing. (authors) 10 refs., 3 tabs.
Pion-nucleon scattering: from chiral perturbation theory to Roy-Steiner equations
Kubis, Bastian; Hoferichter, Martin; de Elvira, Jacobo Ruiz; Meißner, Ulf-G.
2016-11-01
Ever since Weinberg's seminal predictions of the pion-nucleon scattering amplitudes at threshold, this process has been of central interest for the study of chiral dynamics involving nucleons. The scattering lengths or the pion-nucleon σ-term are fundamental quantities characterizing the explicit breaking of chiral symmetry by means of the light quark masses. On the other hand, pion-nucleon dynamics also strongly affects the long-range part of nucleon-nucleon potentials, and hence has a far-reaching impact on nuclear physics. We discuss the fruitful combination of dispersion-theoretical methods, in the form of Roy-Steiner equations, with chiral dynamics to determine pion-nucleon scattering amplitudes at low energies with high precision.*
Low-Energy Photon-Photon Fusion into Three Pions in Generalized Chiral Perturbation Theory
Ametller, L; Knecht, M; Talavera, P
1999-01-01
The processes $\\gamma\\gamma\\to\\pi^0\\pi^0\\pi^0$ and $\\gamma\\gamma\\to \\pi^+ of their potential sensitivity to the mechanism of spontaneous breaking of chiral symmetry and to various counterterms. The amplitudes are computed up to order ${\\cal O}(p^6)$. The event production rates are estimated for the Daphne
Compton scattering on the proton, neutron, and deuteron in chiral perturbation theory to O(Q{sup 4})
Energy Technology Data Exchange (ETDEWEB)
S.R. Beane; M. Malheiro; J.A. McGovern; D.R. Phillips; U. van Kolck
2004-03-01
We study Compton scattering in systems with A=1 and 2 using chiral perturbation theory up to fourth order. For the proton we fit the two undetermined parameters in the O(Q{sup 4}) {gamma}p amplitude of McGovern to experimental data in the region {omega}, {radical}|t| {le} 180 MeV, obtaining a {chi}{sup 2}/d.o.f. of 133/113. This yields a model-independent extraction of proton polarizabilities based solely on low-energy data: {alpha}{sub p} = (12.1 {+-} 1.1 (stat.)){sub -0.5}{sup +0.5} (theory) and {beta}{sub p} = (3.4 {+-} 1.1 (stat.)){sub -0.1}{sup +0.1} (theory), both in units of 10{sup -4} fm{sup 3}. We also compute Compton scattering on deuterium to O(Q{sup 4}). The {gamma}d amplitude is a sum of one- and two-nucleon mechanisms, and contains two undetermined parameters, which are related to the isoscalar nucleon polarizabilities. We fit data points from three recent {gamma}d scattering experiments with a {chi}{sup 2}/d.o.f. = 26.3/20, and find {alpha}{sub N} = 8.9 {+-} 1.5 (stat.){sub -0.9}{sup +4.7} (theory) and {beta}{sub N} = 2.2 {+-} 1.5 (stat.){sub -0.9}{sup +1.2} (theory), again in units of 10{sup -4} fm{sup 3}.
Chiral dynamics of baryons in the perturbative chiral quark model
Energy Technology Data Exchange (ETDEWEB)
Pumsa-ard, K.
2006-07-01
In this work we develop and apply variants of a perturbative chiral quark model (PCQM) to the study of baryonic properties dominantly in the low-energy region. In a first step we consider a noncovariant form of the PCQM, where confinement is modelled by a static, effective potential and chiral corrections are treated to second order, in line with similar chiral quark models. We apply the PCQM to the study of the electromagnetic form factors of the baryon octet. We focus in particular on the low-energy observables such as the magnetic moments, the charge and magnetic radii. In addition, the electromagnetic N-delta transition is also studied in the framework of the PCQM. In the chiral loop calculations we consider a quark propagator, which is restricted to the quark ground state, or in hadronic language to nucleon and delta intermediate states, for simplicity. We furthermore include the low-lying excited states to the quark propagator. In particular, the charge radius of the neutron and the transverse helicity amplitudes of the N-delta transition are considerably improved by this additional effect. In a next step we develop a manifestly Lorentz covariant version of the PCQM, where in addition higher order chiral corrections are included. The full chiral quark Lagrangian is motivated by and in analogy to the one of Chiral Perturbation Theory (ChPT). This Lagrangian contains a set of low energy constants (LECs), which are parameters encoding short distance effects and heavy degrees of freedom. We evaluate the chiral Lagrangian to order O(p{sup 4}) and to one loop to generate the dressing of the bare quark operators by pseudoscalar mesons. In addition we include the vector meson degrees of freedom in our study. Projection of the dressed quark operators on the baryonic level serves to calculate the relevant matrix elements. In a first application of this scheme, we resort to a parameterization of the valence quark form factors in the electromagnetic sector. Constraints
Resumming QCD vacuum fluctuations in three-flavour Chiral Perturbation Theory
Descotes-Genon, S; Girlanda, L; Stern, J
2003-01-01
Due to its light mass of order Lambda_QCD, the strange quark can play a special role in Chiral Symmetry Breaking (ChSB): differences in the pattern of ChSB in the limits N_f=2 (m_u,m_d->0, m_s physical) and N_f=3 (m_u,m_d,m_s->0) may arise due to vacuum fluctuations of s-bar s pairs, related to the violation of the Zweig rule in the scalar sector and encoded in particular in the O(p^4) low-energy constants L_4 and L_6. In case of large fluctuations, we show that the customary treatment of SU(3)xSU(3) chiral expansions generate instabilities upsetting their convergence. We develop a systematic program to cure these instabilities by resumming nonperturbatively vacuum fluctuations of s-bar s pairs, in order to extract information about ChSB from experimental observations even in the presence of large fluctuations. We advocate a Bayesian framework for treating the uncertainties due to the higher orders. As an application, we present a three-flavour analysis of the low-energy pi-pi scattering and show that the rec...
Nieves, J
2001-01-01
Heavy Baryon Chiral Perturbation Theory (HBChPT) to leading order provides a kernel to solve the Bethe-Salpeter equation for the $P_{33}$ ($\\Delta(1232)$-channel) $\\pi-N$ system, in the infinite nucleon mass limit. Crossed Born terms include, when iterated within the Bethe-Salpeter equation, both {\\it all} one- and {\\it some} two-pion intermediate states, hence preserving elastic unitarity below the two-pion production threshold. This suggests searching for a solution with the help of dispersion relations and suitable subtraction constants, when all in-elasticities are explicitly neglected. The solution allows for a successful description of the experimental phase shift from threshold up to $\\sqrt{s}=1500$ MeV in terms of four subtraction constants. Next-to-leading order HBChPT calculations are also used to estimate the unknown subtraction constants which appear in the solution. Large discrepancies are encountered which can be traced to the slow convergence rate of HBChPT.
Convergence properties of $\\eta\\to 3\\pi$ decays in chiral perturbation theory
Kolesar, Marian
2016-01-01
Theoretical efforts to describe and explain the $\\eta\\to 3\\pi$ decays reach far back in time. Even today, the convergence of the decay widths and some of the Dalitz plot parameters seems problematic in low energy QCD. In the framework of resummed CHPT, we explore the question of compatibility of experimental data with a reasonable convergence of a carefully defined chiral series, where NNLO remainders are assumed to be small. By treating the uncertainties in the higher orders statistically, we numerically generate a large set of theoretical predictions, which are then confronted with experimental information. In the case of the decay widths, the experimental values can be reconstructed for a reasonable range of the free parameters and thus no tension is observed, in spite of what some of the traditional calculations suggest. The Dalitz plot parameters $a$ and $d$ can be described very well too. When the parameters $b$ and $\\alpha$ are concerned, we find a mild tension for the whole range of the free parameter...
The two-photon exchange contribution to muonic hydrogen from chiral perturbation theory
Peset, Clara
2014-01-01
We compute the spin-dependent and spin-independent structure functions of the forward virtual-photon Compton tensor of the proton at one loop using heavy baryon effective theory including the Delta particle. We compare with previous results when existing. Using these results we obtain the leading hadronic contributions, associated to the pion and Delta particles, to the Wilson coefficients of the lepton-proton four fermion operators in NRQED. The spin-independent coefficient yields a pure prediction for the two-photon exchange contribution to the muonic hydrogen Lamb shift, $\\Delta E_{\\rm TPE}(\\pi\\&\\Delta)=34(13)$ $\\mu$eV. We also compute the charge, $\\langle r^n \\rangle$, and Zemach, $\\langle r^n \\rangle_{(2)}$, moments for $n \\geq 3$. Finally, we discuss the spin-dependent case, for which we compute the difference between the four-fermion Wilson coefficients relevant for hydrogen and muonic hydrogen.
Kubis, B
2001-01-01
We analyze the electromagnetic form factors of the nucleon to fourth order in relativistic baryon chiral perturbation theory. We employ the recently proposed infrared regularization scheme and show that the convergence of the chiral expansion is improved as compared to the heavy-fermion approach. We also discuss the inclusion of vector mesons and obtain an accurate description of all four-nucleon form factors for momentum transfer squared up to Q sup 2 approx =0.4 GeV sup 2.
Automated Lattice Perturbation Theory
Energy Technology Data Exchange (ETDEWEB)
Monahan, Christopher
2014-11-01
I review recent developments in automated lattice perturbation theory. Starting with an overview of lattice perturbation theory, I focus on the three automation packages currently "on the market": HiPPy/HPsrc, Pastor and PhySyCAl. I highlight some recent applications of these methods, particularly in B physics. In the final section I briefly discuss the related, but distinct, approach of numerical stochastic perturbation theory.
Generalized Supersymmetric Perturbation Theory
Institute of Scientific and Technical Information of China (English)
B. G(o)n(ǖ)l
2004-01-01
@@ Using the basic ingredient of supersymmetry, a simple alternative approach is developed to perturbation theory in one-dimensional non-relativistic quantum mechanics. The formulae for the energy shifts and wavefunctions do not involve tedious calculations which appear in the available perturbation theories. The model applicable in the same form to both the ground state and excited bound states, unlike the recently introduced supersymmetric perturbation technique which, together with other approaches based on logarithmic perturbation theory, are involved within the more general framework of the present formalism.
Perturbative Topological Field Theory
Dijkgraaf, Robbert
We give a review of the application of perturbative techniques to topological quantum field theories, in particular three-dimensional Chern-Simons-Witten theory and its various generalizations. To this end we give an introduction to graph homology and homotopy algebras and the work of Vassiliev and Kontsevich on perturbative knot invariants.
Density matrix perturbation theory.
Niklasson, Anders M N; Challacombe, Matt
2004-05-14
An orbital-free quantum perturbation theory is proposed. It gives the response of the density matrix upon variation of the Hamiltonian by quadratically convergent recursions based on perturbed projections. The technique allows treatment of embedded quantum subsystems with a computational cost scaling linearly with the size of the perturbed region, O(N(pert.)), and as O(1) with the total system size. The method allows efficient high order perturbation expansions, as demonstrated with an example involving a 10th order expansion. Density matrix analogs of Wigner's 2n+1 rule are also presented.
Instantaneous stochastic perturbation theory
Lüscher, Martin
2015-01-01
A form of stochastic perturbation theory is described, where the representative stochastic fields are generated instantaneously rather than through a Markov process. The correctness of the procedure is established to all orders of the expansion and for a wide class of field theories that includes all common formulations of lattice QCD.
Nucleon and Delta axial-vector couplings in 1/N{sub c}-Baryon Chiral Perturbation Theory
Energy Technology Data Exchange (ETDEWEB)
Goity, Jose Luis [JLAB; Calle Cordon, Alvaro [JLAB
2013-08-01
In this contribution, baryon axial-vector couplings are studied in the framework of the combined 1/N{sub c} and chiral expansions. This framework is implemented on the basis of the emergent spin-flavor symmetry in baryons at large N{sub c} and HBChPT, and linking both expansions ({xi}-expansion), where 1/N{sub c} is taken to be a quantity order p. The study is carried out including one-loop contributions, which corresponds to order xi to the third for baryon masses and order {xi} square for the axial couplings.
Large Spin Perturbation Theory
Alday, Luis F
2016-01-01
We consider conformal field theories around points of large twist degeneracy. Examples of this are theories with weakly broken higher spin symmetry and perturbations around generalised free fields. At the degenerate point we introduce twist conformal blocks. These are eigenfunctions of certain quartic operators and encode the contribution, to a given four-point correlator, of the whole tower of intermediate operators with a given twist. As we perturb around the degenerate point, the twist degeneracy is lifted. In many situations this breaking is controlled by inverse powers of the spin. In such cases the twist conformal blocks can be decomposed into a sequence of functions which we systematically construct. Decomposing the four-point correlator in this basis turns crossing symmetry into an algebraic problem. Our method can be applied to a wide spectrum of conformal field theories in any number of dimensions and at any order in the breaking parameter. As an example, we compute the spectrum of various theories ...
Ooguri, H; Ooguri, Hirosi; Yin, Zheng
1996-01-01
These lecture notes are based on a course on string theories given by Hirosi Ooguri in the first week of TASI 96 Summer School at Boulder, Colorado. It is an introductory course designed to provide students with minimum knowledge before they attend more advanced courses on non-perturbative aspects of string theories in the School. The course consists of five lectures: 1. Bosonic String, 2. Toroidal Compactifications, 3. Superstrings, 4. Heterotic Strings, and 5. Orbifold Compactifications.
Renormalized Cosmological Perturbation Theory
Crocce, M
2006-01-01
We develop a new formalism to study nonlinear evolution in the growth of large-scale structure, by following the dynamics of gravitational clustering as it builds up in time. This approach is conveniently represented by Feynman diagrams constructed in terms of three objects: the initial conditions (e.g. perturbation spectrum), the vertex (describing non-linearities) and the propagator (describing linear evolution). We show that loop corrections to the linear power spectrum organize themselves into two classes of diagrams: one corresponding to mode-coupling effects, the other to a renormalization of the propagator. Resummation of the latter gives rise to a quantity that measures the memory of perturbations to initial conditions as a function of scale. As a result of this, we show that a well-defined (renormalized) perturbation theory follows, in the sense that each term in the remaining mode-coupling series dominates at some characteristic scale and is subdominant otherwise. This is unlike standard perturbatio...
Degenerate density perturbation theory
Palenik, Mark C.; Dunlap, Brett I.
2016-09-01
Fractional occupation numbers can be used in density functional theory to create a symmetric Kohn-Sham potential, resulting in orbitals with degenerate eigenvalues. We develop the corresponding perturbation theory and apply it to a system of Nd degenerate electrons in a harmonic oscillator potential. The order-by-order expansions of both the fractional occupation numbers and unitary transformations within the degenerate subspace are determined by the requirement that a differentiable map exists connecting the initial and perturbed states. Using the X α exchange-correlation (XC) functional, we find an analytic solution for the first-order density and first- through third-order energies as a function of α , with and without a self-interaction correction. The fact that the XC Hessian is not positive definite plays an important role in the behavior of the occupation numbers.
Degenerate Density Perturbation Theory
Palenik, Mark C
2016-01-01
Fractional occupation numbers can be used in density functional theory to create a symmetric Kohn-Sham potential, resulting in orbitals with degenerate eigenvalues. We develop the corresponding perturbation theory and apply it to a system of $N_d$ degenerate electrons in a harmonic oscillator potential. The order-by-order expansions of both the fractional occupation numbers and unitary transformations within the degenerate subspace are determined by the requirement that a differentiable map exists connecting the initial and perturbed states. Using the X$\\alpha$ exchange-correlation (XC) functional, we find an analytic solution for the first-order density and first through third-order energies as a function of $\\alpha$, with and without a self-interaction correction. The fact that the XC Hessian is not positive definite plays an important role in the behavior of the occupation numbers.
Chiral deformations of conformal field theories
Dijkgraaf, Robbert
1997-02-01
We study general perturbations of two-dimensional conformal field theories by holomorphic fields. It is shown that the genus one partition function is controlled by a contact term (pre-Lie) algebra given in terms of the operator product expansion. These models have applications to vertex operator algebras, two-dimensional QCD, topological strings, holomorphic anomaly equations and modular properties of generalized characters of chiral algebras such as the W1+∞ algebra, that is treated in detail.
Chiral Deformations of Conformal Field Theories
Dijkgraaf, R
1996-01-01
We study general perturbations of two-dimensional conformal field theories by holomorphic fields. It is shown that the genus one partition function is controlled by a contact term (pre-Lie) algebra given in terms of the operator product expansion. These models have applications to vertex operator algebras, two-dimensional QCD, topological strings, holomorphic anomaly equations and modular properties of generalized characters of chiral algebras such as the $W_{1+\\infty}$ algebra, that is treated in detail.
Chiral deformations of conformal field theories
Energy Technology Data Exchange (ETDEWEB)
Dijkgraaf, R. [Amsterdam Univ. (Netherlands). Dept. of Math.
1997-06-02
We study general perturbations of two-dimensional conformal field theories by holomorphic fields. It is shown that the genus one partition function is controlled by a contact term (pre-Lie) algebra given in terms of the operator product expansion. These models have applications to vertex operator algebras, two-dimensional QCD, topological strings, holomorphic anomaly equations and modular properties of generalized characters of chiral algebras such as the W{sub 1+{infinity}} algebra, that is treated in detail. (orig.).
Chiral Deformations of Conformal Field Theories
Dijkgraaf, R.
1996-01-01
We study general perturbations of two-dimensional conformal field theories by holomorphic fields. It is shown that the genus one partition function is controlled by a contact term (pre-Lie) algebra given in terms of the operator product expansion. These models have applications to vertex operator algebras, two-dimensional QCD, topological strings, holomorphic anomaly equations and modular properties of generalized characters of chiral algebras such as the $W_{1+\\infty}$ algebra, that is treat...
Chiral unitary theory: Application to nuclear problems
Indian Academy of Sciences (India)
E Oset; D Cabrera; H C Chiang; C Garcia Recio; S Hirenzaki; S S Kamalov; J Nieves; Y Okumura; A Ramos; H Toki; M J Vicente Vacas
2001-08-01
In this talk we brieﬂy describe some basic elements of chiral perturbation theory, , and how the implementation of unitarity and other novel elements lead to a better expansion of the -matrix for meson–meson and meson–baryon interactions. Applications are then done to the interaction in nuclear matter in the scalar and vector channels, antikaons in nuclei and - atoms, and how the meson properties are changed in a nuclear medium.
The chirally rotated Schroedinger functional. Theoretical expectations and perturbative tests
Energy Technology Data Exchange (ETDEWEB)
Dalla Brida, Mattia [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Sint, Stefan [Trinity College Dublin (Ireland). School of Mathematics; Vilaseca, Pol [Istituto Nazionale di Fisica Nucleare, Sezione di Roma (Italy)
2016-03-15
The chirally rotated Schroedinger functional (χSF) with massless Wilson-type fermions provides an alternative lattice regularization of the Schroedinger functional (SF), with different lattice symmetries and a common continuum limit expected from universality. The explicit breaking of flavour and parity symmetries needs to be repaired by tuning the bare fermion mass and the coefficient of a dimension 3 boundary counterterm. Once this is achieved one expects the mechanism of automatic O(a) improvement to be operational in the χSF, in contrast to the standard formulation of the SF. This is expected to significantly improve the attainable precision for step-scaling functions of some composite operators. Furthermore, the χSF offers new strategies to determine finite renormalization constants which are traditionally obtained from chiral Ward identities. In this paper we consider a complete set of fermion bilinear operators, define corresponding correlation functions and explain the relation to their standard SF counterparts. We discuss renormalization and O(a) improvement and then use this set-up to formulate the theoretical expectations which follow from universality. Expanding the correlation functions to one-loop order of perturbation theory we then perform a number of non-trivial checks. In the process we obtain the action counterterm coefficients to one-loop order and reproduce some known perturbative results for renormalization constants of fermion bilinears. By confirming the theoretical expectations, this perturbative study lends further support to the soundness of the χSF framework and prepares the ground for non-perturbative applications.
Applications of Cosmological Perturbation Theory
Christopherson, Adam J
2011-01-01
Cosmological perturbation theory is crucial for our understanding of the universe. The linear theory has been well understood for some time, however developing and applying the theory beyond linear order is currently at the forefront of research in theoretical cosmology. This thesis studies the applications of perturbation theory to cosmology and, specifically, to the early universe. Starting with some background material introducing the well-tested 'standard model' of cosmology, we move on to develop the formalism for perturbation theory up to second order giving evolution equations for all types of scalar, vector and tensor perturbations, both in gauge dependent and gauge invariant form. We then move on to the main result of the thesis, showing that, at second order in perturbation theory, vorticity is sourced by a coupling term quadratic in energy density and entropy perturbations. This source term implies a qualitative difference to linear order. Thus, while at linear order vorticity decays with the expan...
Invariant regularization of anomaly-free chiral theories
Chang, L N; Chang, Lay Nam; Soo, Chopin
1997-01-01
We present a generalization of the Frolov-Slavnov invariant regularization scheme for chiral fermion theories in curved spacetimes. The Lagrangian level regularization is explicitly invariant under all the local gauge symmetries of the theory, including local Lorentz invariance. The perturbative scheme works for {\\it arbitrary} representations which satisfy the chiral gauge anomaly and mixed Lorentz-gauge anomaly cancellation conditions. Anomalous theories on the other hand manifest themselves by having divergent fermion loops which remain unregularized by the scheme. Since the invariant scheme is promoted to also include local Lorentz invariance, spectator fields which do not couple to gravity cannot be, and are not, introduced. Furthermore, the scheme is truly Weyl(chiral) in that {\\it all} fields, including the regulators, are left-handed; and {\\it only the left-handed spin connection} is needed. The scheme is therefore well-suited for the perturbative study of all four known forces in a completely chiral ...
Phases of (Asymptotically) Safe Chiral Theories with(out) Scalars
Molgaard, Esben
2016-01-01
We unveil the dynamics of four dimensional chiral gauge-Yukawa theories featuring several scalar degrees of freedom transforming according to distinct representations of the underlying gauge group. We consider generalized Georgi-Glashow and Bars-Yankielowicz theories. We determine, to the maximum known order in perturbation theory, the phase diagram of these theories and further disentangle their ultraviolet asymptotic nature according to whether they are asymptotically free or safe. We therefore extend the number of theories that are known to be fundamental in the Wilsonian sense to the case of chiral gauge theories with scalars.
Nucleon polarizabilities in the perturbative chiral quark model
Dong, Y; Gutsche, T; Kuckei, J; Lyubovitskij, V E; Pumsa-ard, K; Shen, P; Faessler, Amand; Gutsche, Th.
2006-01-01
The nucleon polarizabilities alpha(E) and beta(M) are studied in the context of the perturbative chiral quark model. We demonstrate that meson cloud effects are sufficient to explain the electric polarizability of nucleon. Contributions of excite quark states to the paramagnetic polarizability are dominant and cancel the diamagnetic polarizability arising from the chiral field. The obtained results are compared to data and other theoretical predictions.
Perturbation Theory of Embedded Eigenvalues
DEFF Research Database (Denmark)
Engelmann, Matthias
We study problems connected to perturbation theory of embedded eigenvalues in two different setups. The first part deals with second order perturbation theory of mass shells in massive translation invariant Nelson type models. To this end an expansion of the eigenvalues w.r.t. fiber parameter up...... project gives a general and systematic approach to analytic perturbation theory of embedded eigenvalues. The spectral deformation technique originally developed in the theory of dilation analytic potentials in the context of Schrödinger operators is systematized by the use of Mourre theory. The group...
Collisions in Chiral Kinetic Theory
Chen, Jing-Yuan; Stephanov, Mikhail A
2015-01-01
Using a covariant formalism, we construct a chiral kinetic theory Lorentz invariant to order $\\mathcal O(\\hbar)$ which includes collisions. We find a new contribution to the particle number current due to the side jumps required by the conservation of angular momentum during collisions. We also find a conserved symmetric stress-energy tensor as well as the $H$-function obeying Boltzmann's $H$-theorem. We demonstrate their use by finding a general equilibrium solution and the values of the anomalous transport coefficients characterizing chiral vortical effect.
Institute of Scientific and Technical Information of China (English)
PENG Jin-Song; ZHOU Li-Juan; MENG Cheng-Ju; PAN Ji-Huan; MA Wei-Xing; YUAN Tong-Quan
2013-01-01
Based on the fully dressed quark propagator and chiral perturbation theory,we study the ratio of the strange quark mass ms to up or down quark mass mu,d.The ratio is related to the determination of quark masses which are fundamental input parameters of QCD Lagrangian in the Standard Model of particle physics and can not be directly measured since the quark is confined within a hadron.An accurate determination of these QCD free parameters is extremely important for both phenomenological and theoretical applications.We begin with a brief introduction to the non-perturbation QCD theory,and then study the mass ratio in the framework of the chiral perturbation theory (xPT) with a parameterized fully dressed quark propagator which describes confining fully dressed quark propagation and is analytic everywhere in the finite complex p2-plane and has no Lehmann representation so there are no quark production thresholds in any theoretical calculations of observable data.Our prediction for the ratio ms/mu,d is consistent with other model predictions such as Lattice QCD,instanton model,QCD sum rules and the empirical values used widely in the literature.As a by-product of this study,our theoretical results,together with other predictions of physical quantities that used this quark propagator in our previous publications,clearly show that the parameterized form of the fully dressed quark propagator is an applicable and reliable approximation to the solution of the Dyson-Schwinger Equation of quark propagator in the QCD.
Gauge Invariant Cosmological Perturbation Theory
Durrer, R
1993-01-01
After an introduction to the problem of cosmological structure formation, we develop gauge invariant cosmological perturbation theory. We derive the first order perturbation equations of Einstein's equations and energy momentum ``conservation''. Furthermore, the perturbations of Liouville's equation for collisionless particles and Boltzmann's equation for Compton scattering are worked out. We fully discuss the propagation of photons in a perturbed Friedmann universe, calculating the Sachs--Wolfe effect and light deflection. The perturbation equations are extended to accommodate also perturbations induced by seeds. With these general results we discuss some of the main aspects of the texture model for the formation of large scale structure in the Universe (galaxies, clusters, sheets, voids). In this model, perturbations in the dark matter are induced by texture seeds. The gravitational effects of a spherically symmetric collapsing texture on dark matter, baryonic matter and photons are calculated in first orde...
Staggered chiral random matrix theory
Osborn, James C
2010-01-01
We present a random matrix theory (RMT) for the staggered lattice QCD Dirac operator. The staggered RMT is equivalent to the zero-momentum limit of the staggered chiral Lagrangian and includes all taste breaking terms at their leading order. This is an extension of previous work which only included some of the taste breaking terms. We will also present some results for the taste breaking contributions to the partition function and the Dirac eigenvalues.
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.
Quantum Monte Carlo calculations with chiral effective field theory interactions
Energy Technology Data Exchange (ETDEWEB)
Tews, Ingo
2015-10-12
comparing these results with many-body perturbation theory (MBPT), we can study the perturbative convergence of local chiral interactions. We have shown that soft, low-cutoff potentials converge well and can be reliably used in MBPT, while harder potentials are less perturbative and have to be treated within AFDMC. We have also derived consistent local chiral 3N interactions and study these forces in detail. Our results show that local regulators lead to less repulsion from 3N forces compared to nonlocal 3N forces. Finally, we present the neutron-matter equation of state based on local chiral NN and 3N interactions using the AFDMC method as well as results for light nuclei and neutron drops. This work paves the way for systematic QMC calculations with chiral EFT interactions for nuclei and nucleonic matter.
Consistent chiral kinetic theory in Weyl materials: chiral magnetic plasmons
Gorbar, E V; Shovkovy, I A; Sukhachov, P O
2016-01-01
We argue that the correct definition of the electric current in the chiral kinetic theory for Weyl materials should include the Chern--Simons contribution that makes the theory consistent with the local conservation of the electric charge in electromagnetic and strain-induced pseudoelectromagnetic fields. By making use of such a kinetic theory, we study the plasma frequencies of collective modes in Weyl materials in constant magnetic and pseudomagnetic fields taking into account the effects of dynamical electromagnetism. We show that the collective modes are chiral plasmons. While the plasma frequency of the longitudinal collective mode coincides with the Langmuir one, this mode is unusual because it is characterized not only by oscillations of the electric current density, but also oscillations of the chiral current density. The latter are triggered by a dynamical version of the chiral electric separation effect. We also find that the plasma frequencies of the transverse modes split up in a magnetic field. T...
A non-perturbative study of massive gauge theories
DEFF Research Database (Denmark)
Della Morte, Michele; Hernandez, Pilar
2013-01-01
We consider a non-perturbative formulation of an SU(2) massive gauge theory on a space-time lattice, which is also a discretised gauged non-linear chiral model. The lattice model is shown to have an exactly conserved global SU(2) symmetry. If a scaling region for the lattice model exists and the ...
The theory of singular perturbations
De Jager, E M
1996-01-01
The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed. The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathemat
Chiral Effective Theory of Dark Matter Direct Detection
Bishara, Fady; Grinstein, Benjamin; Zupan, Jure
2016-01-01
We present the effective field theory for dark matter interactions with the visible sector that is valid at scales of O(1 GeV). Starting with an effective theory describing the interactions of fermionic and scalar dark matter with quarks, gluons and photons via higher dimension operators that would arise from dimension-five and dimension-six operators above electroweak scale, we perform a nonperturbative matching onto a heavy baryon chiral perturbation theory that describes dark matter interactions with light mesons and nucleons. This is then used to obtain the coefficients of the nuclear response functions using a chiral effective theory description of nuclear forces. Our results consistently keep the leading contributions in chiral counting for each of the initial Wilson coefficients.
Chiral effective theory of dark matter direct detection
Bishara, Fady; Brod, Joachim; Grinstein, Benjamin; Zupan, Jure
2017-02-01
We present the effective field theory for dark matter interactions with the visible sector that is valid at scales of Script O(1 GeV). Starting with an effective theory describing the interactions of fermionic and scalar dark matter with quarks, gluons and photons via higher dimension operators that would arise from dimension-five and dimension-six operators above electroweak scale, we perform a nonperturbative matching onto a heavy baryon chiral perturbation theory that describes dark matter interactions with light mesons and nucleons. This is then used to obtain the coefficients of the nuclear response functions using a chiral effective theory description of nuclear forces. Our results consistently keep the leading contributions in chiral counting for each of the initial Wilson coefficients.
Gauge-fixing approach to lattice chiral gauge theories
Bock, W; Shamir, Y; Bock, Wolfgang; Golterman, Maarten F.L.; Shamir, Yigal
1998-01-01
We review the status of our recent work on the gauge-fixing approach to lattice chiral gauge theories. New numerical results in the reduced version of a model with a U(1) gauge symmetry are presented which strongly indicate that the factorization of the correlation functions of the left-handed neutral and right-handed charged fermion fields, which we established before in perturbation theory, holds also nonperturbatively.
Quantum Monte Carlo calculations with chiral effective field theory interactions.
Gezerlis, A; Tews, I; Epelbaum, E; Gandolfi, S; Hebeler, K; Nogga, A; Schwenk, A
2013-07-19
We present the first quantum Monte Carlo (QMC) calculations with chiral effective field theory (EFT) interactions. To achieve this, we remove all sources of nonlocality, which hamper the inclusion in QMC calculations, in nuclear forces to next-to-next-to-leading order. We perform auxiliary-field diffusion Monte Carlo (AFDMC) calculations for the neutron matter energy up to saturation density based on local leading-order, next-to-leading order, and next-to-next-to-leading order nucleon-nucleon interactions. Our results exhibit a systematic order-by-order convergence in chiral EFT and provide nonperturbative benchmarks with theoretical uncertainties. For the softer interactions, perturbative calculations are in excellent agreement with the AFDMC results. This work paves the way for QMC calculations with systematic chiral EFT interactions for nuclei and nuclear matter, for testing the perturbativeness of different orders, and allows for matching to lattice QCD results by varying the pion mass.
Cosmological perturbation theory and quantum gravity
Brunetti, Romeo; Hack, Thomas-Paul; Pinamonti, Nicola; Rejzner, Katarzyna
2016-01-01
It is shown how cosmological perturbation theory arises from a fully quantized perturbative theory of quantum gravity. Central for the derivation is a non-perturbative concept of gauge-invariant local observables by means of which perturbative invariant expressions of arbitrary order are generated. In particular, in the linearised theory, first order gauge-invariant observables familiar from cosmological perturbation theory are recovered. Explicit expressions of second order quantities are presented as well.
Consistent Chiral Kinetic Theory in Weyl Materials: Chiral Magnetic Plasmons
Gorbar, E. V.; Miransky, V. A.; Shovkovy, I. A.; Sukhachov, P. O.
2017-03-01
We argue that the correct definition of the electric current in the chiral kinetic theory for Weyl materials should include the Chern-Simons contribution that makes the theory consistent with the local conservation of the electric charge in electromagnetic and strain-induced pseudoelectromagnetic fields. By making use of such a kinetic theory, we study the plasma frequencies of collective modes in Weyl materials in constant magnetic and pseudomagnetic fields, taking into account the effects of dynamical electromagnetism. We show that the collective modes are chiral plasmons. While the plasma frequency of the longitudinal collective mode coincides with the Langmuir one, this mode is unusual because it is characterized not only by oscillations of the electric current density, but also by oscillations of the chiral current density. The latter are triggered by a dynamical version of the chiral electric separation effect. We also find that the plasma frequencies of the transverse modes split up in a magnetic field. This finding suggests an efficient means of extracting the chiral shift parameter from the measurement of the plasma frequencies in Weyl materials.
Chiral Disorder and Random Matrix Theory with Magnetism
Nowak, Maciej A; Zahed, Ismail
2013-01-01
We revisit the concept of chiral disorder in QCD in the presence of a QED magnetic field |eH|. Weak magnetism corresponds to |eH| < 1/rho^2 with rho\\approx (1/3) fm the vacuum instanton size, while strong magnetism the reverse. Asymptotics (ultra-strong magnetism) is in the realm of perturbative QCD. We analyze weak magnetism using the concept of the quark return probability in the diffusive regime of chiral disorder. The result is in agreement with expectations from chiral perturbation theory. We analyze strong and ultra-strong magnetism in the ergodic regime using random matrix theory including the effects of finite temperature. The strong magnetism results are in agreement with the currently reported lattice data in the presence of a small shift of the Polyakov line. The ultra-strong magnetism results are consistent with expectations from perturbative QCD. We suggest a chiral random matrix effective action with matter and magnetism to analyze the QCD phase diagram near the critical points under the infl...
Testing gauge-invariant perturbation theory
Törek, Pascal
2016-01-01
Gauge-invariant perturbation theory for theories with a Brout-Englert-Higgs effect, as developed by Fr\\"ohlich, Morchio and Strocchi, starts out from physical, exactly gauge-invariant quantities as initial and final states. These are composite operators, and can thus be considered as bound states. In case of the standard model, this reduces almost entirely to conventional perturbation theory. This explains the success of conventional perturbation theory for the standard model. However, this is due to the special structure of the standard model, and it is not guaranteed to be the case for other theories. Here, we review gauge-invariant perturbation theory. Especially, we show how it can be applied and that it is little more complicated than conventional perturbation theory, and that it is often possible to utilize existing results of conventional perturbation theory. Finally, we present tests of the predictions of gauge-invariant perturbation theory, using lattice gauge theory, in three different settings. In ...
Eikonal perturbation theory in photoionization
Cajiao Vélez, F.; Krajewska, K.; Kamiński, J. Z.
2016-02-01
The eikonal perturbation theory is formulated and applied to photoionization by strong laser pulses. A special emphasis is put on the first order approximation with respect to the binding potential, which is known as the generalized eikonal approximation [2015 Phys. Rev. A 91 053417]. The ordinary eikonal approximation and its domain of applicability is derived from the generalized eikonal approximation. While the former approach is singular for the electron trajectories which return to the potential center, the generalized eikonal avoids this problem. This property makes it a promising tool for further investigations of rescattering and high-order harmonic generation processes.
Chiral symmetry and lattice gauge theory
Creutz, M
1994-01-01
I review the problem of formulating chiral symmetry in lattice gauge theory. I discuss recent approaches involving an infinite tower of additional heavy states to absorb Fermion doublers. For hadronic physics this provides a natural scheme for taking quark masses to zero without requiring a precise tuning of parameters. A mirror Fermion variation provides a possible way of extending the picture to chirally coupled light Fermions. Talk presented at "Quark Confinement and the Hadron Spectrum," Como, Italy, 20-24 June 1994.
Geometric Hamiltonian structures and perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Omohundro, S.
1984-08-01
We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging.
Perturbation theory and renormalisation group equations
Litim, Daniel F; Litim, Daniel F.; Pawlowski, Jan M.
2002-01-01
We discuss the perturbative expansion of several one-loop improved renormalisation group equations. It is shown that in general the integrated renormalisation group flows fail to reproduce perturbation theory beyond one loop.
The Many Uses of Chiral Effective Theories
Pallante, Elisabetta
2008-01-01
I review basic concepts of chiral effective field theories guided by an historical perspective: from the first ideas to the merging with other effective frameworks, and to the interplay with lattice field theory. The impact of recent theoretical developments on phenomenological predictions is review
"Phonon" scattering beyond perturbation theory
Qiu, WuJie; Ke, XueZhi; Xi, LiLi; Wu, LiHua; Yang, Jiong; Zhang, WenQing
2016-02-01
Searching and designing materials with intrinsically low lattice thermal conductivity (LTC) have attracted extensive consideration in thermoelectrics and thermal management community. The concept of part-crystalline part-liquid state, or even part-crystalline part-amorphous state, has recently been proposed to describe the exotic structure of materials with chemical- bond hierarchy, in which a set of atoms is weakly bonded to the rest species while the other sublattices retain relatively strong rigidity. The whole system inherently manifests the coexistence of rigid crystalline sublattices and fluctuating noncrystalline substructures. Representative materials in the unusual state can be classified into two categories, i.e., caged and non-caged ones. LTCs in both systems deviate from the traditional T -1 relationship ( T, the absolute temperature), which can hardly be described by small-parameter-based perturbation approaches. Beyond the classical perturbation theory, an extra rattling-like scattering should be considered to interpret the liquid-like and sublattice-amorphization-induced heat transport. Such a kind of compounds could be promising high-performance thermoelectric materials, due to the extremely low LTCs. Other physical properties for these part-crystalline substances should also exhibit certain novelty and deserve further exploration.
Chiral effective theory with a light scalar and lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Soto, J., E-mail: joan.soto@ub.edu [Departament d' Estructura i Constituents de la Materia, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Catalonia (Spain); Institut de Ciencies del Cosmos, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Catalonia (Spain); Talavera, P., E-mail: pere.talavera@icc.ub.edu [Institut de Ciencies del Cosmos, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Catalonia (Spain); Departament de Fisica i Enginyeria Nuclear, Universitat Politecnica de Catalunya, Comte Urgell 187, E-08036 Barcelona (Spain); Tarrus, J., E-mail: tarrus@ecm.ub.es [Departament d' Estructura i Constituents de la Materia, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Catalonia (Spain); Institut de Ciencies del Cosmos, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Catalonia (Spain)
2013-01-21
We extend the usual chiral perturbation theory framework ({chi}PT) to allow the inclusion of a light dynamical isosinglet scalar. Using lattice QCD results, and a few phenomenological inputs, we explore the parameter space of the effective theory. We discuss the S-wave pion-pion scattering lengths, extract the average value of the two light quark masses and evaluate the impact of the dynamical singlet field in the low-energy constants l{sup Macron }{sub 1}, l{sup Macron }{sub 3} and l{sup Macron }{sub 4} of {chi}PT. We also show how to extract the mass and width of the sigma resonance from chiral extrapolations of lattice QCD data.
Non-Perturbative Theory of Dispersion Interactions
Boström, M; Persson, C; Parsons, D F; Buhmann, S Y; Brevik, I; Sernelius, Bo E
2015-01-01
Some open questions exist with fluctuation-induced forces between extended dipoles. Conventional intuition derives from large-separation perturbative approximations to dispersion force theory. Here we present a full non-perturbative theory. In addition we discuss how one can take into account finite dipole size corrections. It is of fundamental value to investigate the limits of validity of the perturbative dispersion force theory.
Energy Technology Data Exchange (ETDEWEB)
Hilt, Marius
2011-12-13
This thesis is concerned with pion photoproduction (PPP) and pion electroproduction (PEP) in the framework of manifestly Lorentz-invariant baryon chiral perturbation theory. For that purpose two different approaches are used. Firstly, a one-loop-order calculation up to chiral order O(q{sup 4}) including pions and nucleons as degrees of freedom, is performed to describe the energy dependence of the reactions over a large range. To improve the dependence on the virtuality of the photon in PEP, in a second approach vector mesons are included as explicit degrees of freedom. The latter calculation includes one-loop contributions up to chiral order O(q{sup 3}). Only three of the four physical processes of PPP and PEP can be accessed experimentally. These reactions are measured at several different facilities, e.g. Mainz, Bonn, or Saskatoon. The data obtained there are used to explore the limits of chiral perturbation theory. This thesis is the first complete manifestly Lorentz-invariant calculation up to order O(q{sup 4}) for PPP and PEP, and the first calculation ever for these processes including vector mesons explicitly. Beside the calculation of physical observables, a partial wave decomposition is performed and the most important multipoles are analyzed. They may be extracted from the calculated amplitudes and allow one to examine the nucleon and {delta} resonances. The number of diagrams one has to calculate is very large. In order to handle these expressions, several routines were developed for the computer algebra system Mathematica. For the multipole decomposition, two different programs are used. On the one hand, a modified version of the so-called {chi}MAID has been employed. On the other hand, similar routines were developed for Mathematica. In the end, the different calculations are compared with respect to their applicability to PPP and PEP.
Chiral effective field theory and nuclear forces
Machleidt, R
2011-01-01
We review how nuclear forces emerge from low-energy QCD via chiral effective field theory. The presentation is accessible to the non-specialist. At the same time, we also provide considerable detailed information (mostly in appendices) for the benefit of researchers who wish to start working in this field.
The ambiguity in ray perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Snieder, R.; Sambridge, M. [Utrecht Univ., Utrecht (Netherlands)]|[Cambridge Univ., Cambridge (United Kingdom)
1993-12-01
Ray perturbation theory is concerned with the change in ray paths and travel times due to changes in the slowness model or the end-point conditions of rays. Several different formulations of ray perturbation theory have been developed. Even for the same physical problem different perturbation equations have been derived. The reason for this is that ray perturbation theory contains a fundamental ambiguity. One can move a point along a curve without changing the shape of the curve. This means that the mapping from a reference curve to a perturbed curve is not uniquely defined, because on may associated a point on the reference curve with different points on the perturbed curve. The mapping that is used is usually defined implicitly by the choice of the coordinate system or the independent parameter. In this paper, a fomalism is developed where one can specify explicitly the mapping from the reference curve to the perturbed curve by choosing a stretch factor that relates increments in arc length along the reference curve and the perturbed curve. This is incorporated in a theory that is accurate to first order in the ray position and to second order in the travel time. The second order travel time perturbation describes the effect of changes in the position of the ray on the travel time. In the formulation of this paper, paraxial ray perturbations, slowness perturbations, and pure ray bending are treated in a uniform fashion. This may be very useful in nonlinear tomographic inversions which include earthquake relocation.
Harnessing the Power of Chiral Perturbation Theory
Isgur, Nathan
2001-12-01
I have enjoyed noticing the puzzled looks around the conference this week as some participants carefully labelled themselves High Energy Physicists, taking some offense if they are called Nuclear Physicists, and vice versa. This is partly a trivial issue associated with US funding sources, but it also reflects some very deeply-held feelings about Quantum Chromodynamics (QCD): a High Energy Physicist finds the strong interactions a nuisance and is studying QCD to be able to eliminate them, while a Nuclear Physicist believes that the nature and origin of the strong interactions is one of the most important unsolved problems in the Standard Model and studies QCD to be able to explain them...
Invariant Regularization of Supersymmetric Chiral Gauge Theory
Suzuki, H
1999-01-01
We present a regularization scheme which respects the supersymmetry and the maximal background gauge covariance in supersymmetric chiral gauge theories. When the anomaly cancellation condition is satisfied, the effective action in the superfield background field method automatically restores the gauge invariance without counterterms. The scheme also provides a background gauge covariant definition of composite operators that is especially useful in analyzing anomalies. We present several applications: The minimal consistent gauge anomaly; the super-chiral anomaly and the superconformal anomaly; as the corresponding anomalous commutators, the Konishi anomaly and an anomalous supersymmetric transformation law of the supercurrent (the ``central extension'' of N=1 supersymmetry algebra) and of the R-current.
Perturbation theory in light-cone quantization
Energy Technology Data Exchange (ETDEWEB)
Langnau, A.
1992-01-01
A thorough investigation of light-cone properties which are characteristic for higher dimensions is very important. The easiest way of addressing these issues is by analyzing the perturbative structure of light-cone field theories first. Perturbative studies cannot be substituted for an analysis of problems related to a nonperturbative approach. However, in order to lay down groundwork for upcoming nonperturbative studies, it is indispensable to validate the renormalization methods at the perturbative level, i.e., to gain control over the perturbative treatment first. A clear understanding of divergences in perturbation theory, as well as their numerical treatment, is a necessary first step towards formulating such a program. The first objective of this dissertation is to clarify this issue, at least in second and fourth-order in perturbation theory. The work in this dissertation can provide guidance for the choice of counterterms in Discrete Light-Cone Quantization or the Tamm-Dancoff approach. A second objective of this work is the study of light-cone perturbation theory as a competitive tool for conducting perturbative Feynman diagram calculations. Feynman perturbation theory has become the most practical tool for computing cross sections in high energy physics and other physical properties of field theory. Although this standard covariant method has been applied to a great range of problems, computations beyond one-loop corrections are very difficult. Because of the algebraic complexity of the Feynman calculations in higher-order perturbation theory, it is desirable to automatize Feynman diagram calculations so that algebraic manipulation programs can carry out almost the entire calculation. This thesis presents a step in this direction. The technique we are elaborating on here is known as light-cone perturbation theory.
The reaction pi N-> pi pi N in chiral effective field theory with explicit Delta(1232)
Siemens, D; Epelbaum, E; Krebs, H; Meißner, Ulf-G
2014-01-01
The reaction pi N -> pi pi N is studied at tree level up to next-to-leading order in the framework of manifestly covariant baryon chiral perturbation theory with explicit Delta(1232) degrees of freedom. Using total cross section data to determine the relevant low-energy constants, predictions are made for various differential as well as total cross sections at higher energies. A detailed comparison of results based on the heavy-baryon and relativistic formulations of chiral perturbation theory with and without explicit Delta degrees of freedom is given.
The chiral anomaly from M theory
Gursoy, U; Portugues, R; Gursoy, Umut; Hartnoll, Sean A.; Portugues, Ruben
2003-01-01
We argue that the chiral anomaly of $\\Ncal = 1$ super Yang-Mills theory admits a dual description as spontaneous symmetry breaking in M theory on $G_2$ holonomy manifolds. We identify an angle of the $G_2$ background dual to the anomalous $U(1)_R$ current in field theory. This angle is not an isometry of the metric and we therefore develop a theory of ``massive isometry'' to describe fluctuations about such angles. Another example of a massive isometry occurs in the Atiyah-Hitchin metric.
Perturbative spacetimes from Yang-Mills theory
Luna, Andres; Nicholson, Isobel; Ochirov, Alexander; O'Connell, Donal; Westerberg, Niclas; White, Chris D.
2016-01-01
The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.
A Nonperturbative Regulator for Chiral Gauge Theories
Grabowska, Dorota M
2015-01-01
We propose a nonperturbative gauge invariant regulator for $d$-dimensional chiral gauge theories on the lattice. The method involves simulating domain wall fermions in $d+1$ dimensions with quantum gauge fields that reside on one $d$-dimensional surface and are extended into the bulk via gradient flow. The result is a theory of gauged fermions plus mirror fermions, where the mirror fermions couple to the gauge fields via a form factor that becomes exponentially soft with the separation between domain walls. The resultant theory has a local $d$-dimensional interpretation if and only if the chiral fermion representation is anomaly free. A physical realization of this construction leads to mirror fermions in the Standard Model with soft form factors for gauge fields and gravity. These mirror particles could evade detection except by sensitive probes at extremely low energy, and yet still affect vacuum topology, and could gravitate differently than conventional matter.
General degeneracy in density functional perturbation theory
Palenik, Mark C
2016-01-01
Degenerate perturbation theory from quantum mechanics is inadequate in density functional theory (DFT) because of nonlinearity in the Kohn-Sham potential. We develop the fully general degenerate perturbation theory for DFT without assuming that the degeneracy is required by symmetry. The resulting methodology is applied to the iron atom ground state in order to demonstrate the effects of degeneracy that appears both due to symmetry requirements and accidentally, between different representations of the symmetry group.
Axial form factor of the nucleon in the perturbative chiral quark model
Khosonthongkee, K; Faessler, Amand; Gutsche, T; Lyubovitskij, V E; Pumsa-ard, K; Yan, Y
2004-01-01
We apply the perturbative chiral quark model (PCQM) at one loop to analyze the axial form factor of the nucleon. This chiral quark model is based on an effective Lagrangian, where baryons are described by relativistic valence quarks and a perturbative cloud of Goldstone bosons as dictated by chiral symmetry. We apply the formalism to obtain analytical expressions for the axial form factor of the nucleon, which is given in terms of fundamental parameters of low-energy pion-nucleon physics (weak pion decay constant, strong pion-nucleon form factor) and of only one model parameter (radius of the nucleonic three-quark core).
Chiral symmetry and effective field theories for hadronic, nuclear and stellar matter
Energy Technology Data Exchange (ETDEWEB)
Holt, Jeremy W., E-mail: jwholt.phys@gmail.com [Department of Physics, University of Washington, Seattle, 98195 (United States); Rho, Mannque [Department of Physics, Hanyang University, Seoul 133-791 (Korea, Republic of); Institut de Physique Théorique, CEA Saclay, 91191 Gif-sur-Yvette (France); Weise, Wolfram [Physik Department, Technische Universität München, D-85747 Garching (Germany); ECT*, Villa Tambosi, I-38123 Villazzano (Italy)
2016-03-21
Chiral symmetry, first entering in nuclear physics in the 1970s for which Gerry Brown played a seminal role, has led to a stunningly successful framework for describing strongly-correlated nuclear dynamics both in finite and infinite systems. We review how the early, germinal idea conceived with the soft-pion theorems in the pre-QCD era has evolved into a highly predictive theoretical framework for nuclear physics, aptly assessed by Steven Weinberg: “it (chiral effective field theory) allows one to show in a fairly convincing way that what they (nuclear physicists) have been doing all along... is the correct first step in a consistent approximation scheme”. Our review recounts both how the theory presently fares in confronting Nature and how one can understand its extremely intricate workings in terms of the multifaceted aspects of chiral symmetry, namely, chiral perturbation theory, skyrmions, Landau Fermi-liquid theory, the Cheshire cat phenomenon, and hidden local and mended symmetries.
Chiral symmetry and effective field theories for hadronic, nuclear and stellar matter
Holt, Jeremy W; Weise, Wolfram
2014-01-01
Chiral symmetry, first entering in nuclear physics in the 1970's for which Gerry Brown played a seminal role, has led to a stunningly successful framework for describing strongly-correlated nuclear dynamics both in finite and infinite systems. We review how the early germinal idea, conceived with the soft-pion theorems in the pre-QCD era, has evolved into a highly predictive theoretical framework for nuclear physics, aptly assessed by Steven Weinberg: "it (chiral effective field theory) allows one to show in a fairly convincing way that what they (nuclear physicists) have been doing all along... is the correct first step in a consistent approximation scheme." Our review recounts both how the theory presently fares in confronting Nature and how one can understand its extremely intricate workings in terms of the multifaceted aspects of chiral symmetry, namely, chiral perturbation theory, skyrmions, Landau Fermi-liquid theory, the Cheshire cat phenomenon, and hidden local and mended symmetries.
Quantitative methods in classical perturbation theory.
Giorgilli, A.
Poincaré proved that the series commonly used in Celestial mechanics are typically non convergent, although their usefulness is generally evident. Recent work in perturbation theory has enlightened this conjecture of Poincaré, bringing into evidence that the series of perturbation theory, although non convergent in general, furnish nevertheless valuable approximations to the true orbits for a very large time, which in some practical cases could be comparable with the age of the universe. The aim of the author's paper is to introduce the quantitative methods of perturbation theory which allow to obtain such powerful results.
Perturbative Chern-Simons theory revisited
DEFF Research Database (Denmark)
McLellan, Brendan Donald Kenneth
2013-01-01
We reconsider perturbative Chern-Simons theory on a closed and oriented three-manifold with a choice of contact structure following C. Beasley and E. Witten. Closed three manifolds that admit a Sasakian structure are explicitly computed to first order in perturbation in terms of their Seifert dat...
Chiral random matrix theory for staggered fermions
Osborn, James C
2012-01-01
We present a completed random matrix theory for staggered fermions which incorporates all taste symmetry breaking terms at their leading order from the staggered chiral Lagrangian. This is an extension of previous work which only included some of the taste breaking terms. We will also discuss the effects of taste symmetry breaking on the eigenvalues in the weak and strong taste breaking limits, and compare with some results from lattice simulations.
Chiral Orbifold Construction Of Field Theories With Extra Dimensions
Hailu, G
2003-01-01
We build higher dimensional field theories which have chiral fermion zero-modes on orbifolds. We show that orbifold boundary conditions and scalar vacuum expectation values interplay to produce chiral fermions localized on fat three branes. We develop a scheme for computing field propagators in higher dimensional theories obeying chiral orbifold boundary conditions. Using this scheme we compute the loop corrections to an effective field theory in five dimensions. We find that the renormalization group running of the higher dimensional bulk theory leads to a running of the four dimensional brane couplings. We generalize an argument to verify that the chiral anomaly that arises in these chiral orbifold theories is entirely confined on and uniformly distributed over the fixed points of the orbifold, independent of the shape of the chiral zero-modes. We construct a setup in which a scalar field with appropriate profile in the extra dimension is used to address the hierarchy problem and also localize both chiral f...
Testing chiral effective theory with quenched lattice QCD
Giusti, Leonardo; Necco, S; Peña, C; Wennekers, J; Wittig, H
2008-01-01
We investigate two-point correlation functions of left-handed currents computed in quenched lattice QCD with the Neuberger-Dirac operator. We consider two lattice spacings a~0.09,0.12 fm and two different lattice extents L~ 1.5, 2.0 fm; quark masses span both the p- and the epsilon-regimes. We compare the results with the predictions of quenched chiral perturbation theory, with the purpose of testing to what extent the effective theory reproduces quenched QCD at low energy. In the p-regime we test volume and quark mass dependence of the pseudoscalar decay constant and mass; in the epsilon-regime, we investigate volume and topology dependence of the correlators. While the leading order behaviour predicted by the effective theory is very well reproduced by the lattice data in the range of parameters that we explored, our numerical data are not precise enough to test next-to-leading order effects.
Z Extremization in Chiral-Like Chern Simons Theories
Amariti, Antonio
2011-01-01
We study the localized free energy on S^3 of three-dimensional N=2 Chern-Simons matter theories at weak coupling. We compute the two loop R charge in three different ways, namely by the standard perturbative approach, by extremizing the localized partition function at finite N and by applying the standard saddle point approximation for large N. We show that the latter approach does not reproduce the expected result when chiral theories are considered. We circumvent these problems by restoring a reflection symmetry on the eigenvalues in the free energy. Thanks to this symmetrization we find that the three methods employed agree. In particular we match the computation for a model whose four dimensional parent is the quiver gauge theory describing D3 branes probing the Hirzebruch surface. We conclude by commenting on the application of our results and to the strong coupling regime.
Chiral phase transition from string theory.
Parnachev, Andrei; Sahakyan, David A
2006-09-15
The low energy dynamics of a certain D-brane configuration in string theory is described at weak t'Hooft coupling by a nonlocal version of the Nambu-Jona-Lasinio model. We study this system at finite temperature and strong t'Hooft coupling, using the string theory dual. We show that for sufficiently low temperatures chiral symmetry is broken, while for temperatures larger then the critical value, it gets restored. We compute the latent heat and observe that the phase transition is of the first order.
Concise theory of chiral lipid membranes
Tu, Z C
2007-01-01
A theory of chiral lipid membranes is proposed on the basis of a concise free energy density which includes the contributions of the bending and the surface tension of membranes, as well as the chirality and orientational variation of tilting molecules. This theory is consistent with the previous experiments [J.M. Schnur \\textit{et al.}, Science \\textbf{264}, 945 (1994); M.S. Spector \\textit{et al.}, Langmuir \\textbf{14}, 3493 (1998); Y. Zhao, \\textit{et al.}, Proc. Natl. Acad. Sci. USA \\textbf{102}, 7438 (2005)] on self-assembled chiral lipid membranes of DC$_{8,9}$PC. A torus with the ratio between its two generated radii larger than $\\sqrt{2}$ is predicted from the Euler-Lagrange equations. It is found that tubules with helically modulated tilting state are not admitted by the Euler-Lagrange equations, and that they are less energetically favorable than helical ripples in tubules. The pitch angles of helical ripples are theoretically estimated to be about 0$^\\circ$ and 35$^\\circ$, which are close to the mo...
Effective Field Theory of Cosmological Perturbations
Piazza, Federico
2013-01-01
The effective field theory of cosmological perturbations stems from considering a cosmological background solution as a state displaying spontaneous breaking of time translations and (adiabatic) perturbations as the related Nambu-Goldstone modes. With this insight, one can systematically develop a theory for the cosmological perturbations during inflation and, with minor modifications, also describe in full generality the gravitational interactions of dark energy, which are relevant for late-time cosmology. The formalism displays a unique set of Lagrangian operators containing an increasing number of cosmological perturbations and derivatives. We give an introductory description of the unitary gauge formalism for theories with broken gauge symmetry---that allows to write down the most general Lagrangian---and of the Stueckelberg "trick"---that allows to recover gauge invariance and to make the scalar field explicit. We show how to apply this formalism to gravity and cosmology and we reproduce the detailed ana...
Large-Nc Gauge Theory and Chiral Random Matrix Theory
Hanada, Masanori; Lee, Jong-Wan; Yamada, Norikazu
Effective theory approaches and the large-Nc limit are useful for studying the strongly coupled gauge theories. In this talk we consider how the chiral random matrix theory (χRMT) can be used in the study of large-Nc gauge theories. It turns out the parameter regions, in which each of these two approaches are valid, are different. Still, however, we show that the breakdown of chiral symmetry can be detected by combining the large-Nc argument and the χRMT with some cares. As a demonstration, we numerically study the four dimensional SU(Nc) gauge theory with Nf = 2 heavy adjoint fermions on a 24 lattice by using Monte-Carlo simulations, which is related to the infinite volume lattice through the Eguchi-Kawai equivalence.
The Vector Meson Mass in Chiral Effective Field Theory
Hall, Jonathan M M
2014-01-01
A brief overview of Quantum Chromodynamics (QCD) as a non-Abelian gauge field theory, including symmetries and formalism of interest, will precede a focused discussion on the use of an Effective Field Theory (EFT) as a low energy perturbative expansion technique. Regularization schemes involved in Chiral Perturbation Theory (\\c{hi}PT) will be reviewed and compared with EFT. Lattices will be discussed as a useful procedure for studying large mass particles. An Effective Field Theory will be formulated, and the self energy of the \\r{ho} meson for a Finite-Range Regulated (FRR) theory will be calculated. This will be performed in both full QCD and the simpler quenched approximation (QQCD). Finite-volume artefacts, due to the finite box size on the lattice, will be quantified. Currently known lattice results will be used to calculate the \\r{ho} meson mass, and the possibility of unquenching will be explored. The aim of the research was to determine whether a stable unquenching procedure for the \\r{ho} meson could...
Second order perturbation theory for embedded eigenvalues
DEFF Research Database (Denmark)
Faupin, Jeremy; Møller, Jacob Schach; Skibsted, Erik
2011-01-01
We study second order perturbation theory for embedded eigenvalues of an abstract class of self-adjoint operators. Using an extension of the Mourre theory, under assumptions on the regularity of bound states with respect to a conjugate operator, we prove upper semicontinuity of the point spectrum...
Homological Perturbation Theory and Mirror Symmetry
Institute of Scientific and Technical Information of China (English)
Jian ZHOU
2003-01-01
We explain how deformation theories of geometric objects such as complex structures,Poisson structures and holomorphic bundle structures lead to differential Gerstenhaber or Poisson al-gebras. We use homological perturbation theory to construct A∞ algebra structures on the cohomology,and their canonically defined deformations. Such constructions are used to formulate a version of A∞algebraic mirror symmetry.
World-line perturbation theory
van Holten, Jan-Willem
2016-01-01
The motion of a compact body in space and time is commonly described by the world line of a point representing the instantaneous position of the body. In General Relativity such a world-line formalism is not quite straightforward because of the strict impossibility to accommodate point masses and rigid bodies. In many situations of practical interest it can still be made to work using an effective hamiltonian or energy-momentum tensor for a finite number of collective degrees of freedom of the compact object. Even so exact solutions of the equations of motion are often not available. In such cases families of world lines of compact bodies in curved space-times can be constructed by a perturbative procedure based on generalized geodesic deviation equations. Examples for simple test masses and for spinning test bodies are presented.
Adiabatic density-functional perturbation theory
Gonze, Xavier
1995-08-01
The treatment of adiabatic perturbations within density-functional theory is examined, at arbitrary order of the perturbation expansion. Due to the extremal property of the energy functional, standard variation-perturbation theorems can be used. The different methods (Sternheimer equation, extremal principle, Green's function, and sum over state) for obtaining the perturbation expansion of the wave functions are presented. The invariance of the Hilbert space of occupied wave functions with respect to a unitary transformation leads to the definition of a ``parallel-transport-gauge'' and a ``diagonal-gauge'' perturbation expansion. Then, the general expressions are specialized for the second, third, and fourth derivative of the energy, with an example of application of the method up to third order.
On counterterms in cosmological perturbation theory
Goswami, Gaurav
2014-01-01
Cosmological perturbation theory is the theory of fluctuations (scalar as well as tensor) around the inflationary cosmological background solution. It is important to understand the details of the process of renormalization in this theory. In more familiar applications of quantum field theory, the dependence on the external momenta of the dimensionally regulated expression of the one-loop contribution to a correlator determines the number of counter terms (and their forms) required to renormalize it. In this work, it is pointed out that in cosmological perturbation theory, though this still happens, it happens in a completely different way such that in the late time limit, the information about the number and forms of counter terms required gets erased. This is to be compared with what happens in spontaneous symmetry breaking where the use of fluctuation fields around a chosen vacuum seems to suggest that more counter terms shall be needed to renormalize the theory than are actually required. We also comment ...
On Yang--Mills Theories with Chiral Matter at Strong Coupling
Energy Technology Data Exchange (ETDEWEB)
Shifman, M.; /Minnesota U., Theor. Phys. Inst. /Saclay, SPhT; Unsal, Mithat; /SLAC /Stanford U., Phys. Dept.
2008-08-20
Strong coupling dynamics of Yang-Mills theories with chiral fermion content remained largely elusive despite much effort over the years. In this work, we propose a dynamical framework in which we can address non-perturbative properties of chiral, non-supersymmetric gauge theories, in particular, chiral quiver theories on S{sub 1} x R{sub 3}. Double-trace deformations are used to stabilize the center-symmetric vacuum. This allows one to smoothly connect smaller(S{sub 1}) to larger(S{sub 1}) physics (R{sub 4} is the limiting case) where the double-trace deformations are switched off. In particular, occurrence of the mass gap in the gauge sector and linear confinement due to bions are analytically demonstrated. We find the pattern of the chiral symmetry realization which depends on the structure of the ring operators, a novel class of topological excitations. The deformed chiral theory, unlike the undeformed one, satisfies volume independence down to arbitrarily small volumes (a working Eguchi-Kawai reduction) in the large N limit. This equivalence, may open new perspectives on strong coupling chiral gauge theories on R{sub 4}.
Matter Density Perturbations in Modified Teleparallel Theories
Wu, Yi-Peng
2012-01-01
We study the matter density perturbations in modified teleparallel gravity theories, where extra degrees of freedom arise from the local Lorentz violation in the tangent space. We formulate a vierbein perturbation with variables addressing all the 16 components of the vierbein field. By assuming the perfect fluid matter source, we examine the cosmological implication of the 6 unfamiliar new degrees of freedom in modified $f(T)$ gravity theories. We find that despite the new modes in the vierbein scenario provide no explicit significant effect in the small-scale regime, they exhibit some deviation from the standard general relativity results in super-horizon scales.
Four-Dimensional Spin Foam Perturbation Theory
Directory of Open Access Journals (Sweden)
João Faria Martins
2011-10-01
Full Text Available We define a four-dimensional spin-foam perturbation theory for the BF-theory with a B∧B potential term defined for a compact semi-simple Lie group G on a compact orientable 4-manifold M. This is done by using the formal spin foam perturbative series coming from the spin-foam generating functional. We then regularize the terms in the perturbative series by passing to the category of representations of the quantum group U_q(g where g is the Lie algebra of G and q is a root of unity. The Chain-Mail formalism can be used to calculate the perturbative terms when the vector space of intertwiners Λ⊗Λ→A, where A is the adjoint representation of g, is 1-dimensional for each irrep Λ. We calculate the partition function Z in the dilute-gas limit for a special class of triangulations of restricted local complexity, which we conjecture to exist on any 4-manifold M. We prove that the first-order perturbative contribution vanishes for finite triangulations, so that we define a dilute-gas limit by using the second-order contribution. We show that Z is an analytic continuation of the Crane-Yetter partition function. Furthermore, we relate Z to the partition function for the F∧F theory.
Geometric singular perturbation theory in biological practice
Hek, G.
2010-01-01
Geometric singular perturbation theory is a useful tool in the analysis of problems with a clear separation in time scales. It uses invariant manifolds in phase space in order to understand the global structure of the phase space or to construct orbits with desired properties. This paper explains an
A general theory of linear cosmological perturbations: bimetric theories
Lagos, Macarena
2016-01-01
We implement the method developed in [1] to construct the most general parametrised action for linear cosmological perturbations of bimetric theories of gravity. Specifically, we consider perturbations around a homogeneous and isotropic background, and identify the complete form of the action invariant under diffeomorphism transformations, as well as the number of free parameters characterising this cosmological class of theories. We discuss, in detail, the case without derivative interactions, and compare our results with those found in massive bigravity.
Geometric perturbation theory and plasma physics
Energy Technology Data Exchange (ETDEWEB)
Omohundro, S.M.
1985-04-04
Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a question about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem is proved by renormalization group techniques. A natural symplectic structure for thermodynamics is shown to arise asymptotically from the maximum entropy formalism.
SPT 2004: Symmetry and Perturbation Theory
Prinari, Barbara; Rauch-Wojciechowski, Stefan; Terracini, Susanna
2005-01-01
This proceedings volume is a collection of papers presented at the International Conference on SPT2004 focusing on symmetry, perturbation theory, and integrability. The book provides an updated overview of the recent developments in the various different fields of nonlinear dynamics, covering both theory and applications. Special emphasis is given to algebraic and geometric integrability, solutions to the N-body problem of the “choreography” type, geometry and symmetry of dynamical systems, integrable evolution equations, various different perturbation theories, and bifurcation analysis. The contributors to this volume include some of the leading scientists in the field, among them: I Anderson, D Bambusi, S Benenti, S Bolotin, M Fels, W Y Hsiang, V Matveev, A V Mikhailov, P J Olver, G Pucacco, G Sartori, M A Teixeira, S Terracini, F Verhulst and I Yehorchenko.
PERTURBATION THEORY FOR THE FOCK-DIRAC DENSITY MATRIX
ATOMIC ENERGY LEVELS, *ATOMIC ORBITALS, *QUANTUM THEORY , ATOMIC SPECTROSCOPY, ELECTRONS, EXCITATION, FUNCTIONS(MATHEMATICS), MATHEMATICAL ANALYSIS, NUCLEAR SPINS, PERTURBATION THEORY , SOLID STATE PHYSICS, THEORY
Acoustic anisotropic wavefields through perturbation theory
Alkhalifah, Tariq Ali
2013-09-01
Solving the anisotropic acoustic wave equation numerically using finite-difference methods introduces many problems and media restriction requirements, and it rarely contributes to the ability to resolve the anisotropy parameters. Among these restrictions are the inability to handle media with η<0 and the presence of shear-wave artifacts in the solution. Both limitations do not exist in the solution of the elliptical anisotropic acoustic wave equation. Using perturbation theory in developing the solution of the anisotropic acoustic wave equation allows direct access to the desired limitation-free solutions, that is, solutions perturbed from the elliptical anisotropic background medium. It also provides a platform for parameter estimation because of the ability to isolate the wavefield dependency on the perturbed anisotropy parameters. As a result, I derive partial differential equations that relate changes in the wavefield to perturbations in the anisotropy parameters. The solutions of the perturbation equations represented the coefficients of a Taylor-series-type expansion of the wavefield as a function of the perturbed parameter, which is in this case η or the tilt of the symmetry axis. The expansion with respect to the symmetry axis allows use of an acoustic transversely isotropic media with a vertical symmetry axis (VTI) kernel to estimate the background wavefield and the corresponding perturbation coefficients. The VTI extrapolation kernel is about one-fourth the cost of the transversely isotropic model with a tilt in the symmetry axis kernel. Thus, for a small symmetry axis tilt, the cost of migration using a first-order expansion can be reduced. The effectiveness of the approach was demonstrated on the Marmousi model.
Chiral effective theory with a light scalar and lattice QCD
Soto, J; Tarrús, J
2011-01-01
We extend the usual chiral perturbation theory framework ($\\chi$PT) to allow the inclusion of a light dynamical isosinglet scalar. Using lattice QCD results, and a few phenomenological inputs, we explore the parameter space of the effective theory. The extended theory collects already at LO the ball park contribution to the pion mass and decay constant, thus achieving an accuracy that is comparable to the one of the standard $\\chi$PT at NLO results. We check explicitly that radiative corrections do not spoil this behavior and keep the theory stable under mild variations of the parameters. The parameter sets that are compatible with the current mass and width of the sigma resonance turn out to reproduce the experimental values of the S-wave pion-pion scattering lengths very accurately. We also extract the average value of the two light quark--masses and evaluate the impact of the dynamical singlet field in the low--energy constants $\\bar{l}_3$ and $\\bar{l}_4$ of $\\chi$PT. We emphasize that more accurate lattic...
Chiral Boson Theory on the Light-Front
Srivastava, P P
1999-01-01
The {\\it front form} framework for describing the quantized theory of chiral boson is discussed. It avoids the conflict with the requirement of the principle of microcausality as is found in the conventional equal- time treatment. The discussion of the Floreanini-Jackiw model and its modified version for describing the chiral boson becomes very transparent on the light-front.
Stochastic multireference Epstein-Nesbet perturbation theory
Sharma, Sandeep; Jeanmairet, Guillaume; Alavi, Ali; Umrigar, C J
2016-01-01
We extend the recently proposed heat-bath configuration interaction (HCI) method [Holmes, Tubman, Umrigar, J. Chem. Theory Comput. 12, 3674 (2016)], by introducing a stochastic algorithm for performing multireference Epstein-Nesbet perturbation theory, in order to completely eliminate the severe memory bottleneck of the original method. The proposed stochastic algorithm has several attractive features. First, there is no sign problem that plagues several quantum Monte Carlo methods. Second, instead of using Metropolis-Hastings sampling, we use the Alias method to directly sample determinants from the reference wavefunction, thus avoiding correlations between consecutive samples. Third, in addition to removing the memory bottleneck, stochastic-HCI (s-HCI) is faster than the deterministic variant for most systems if a stochastic error of 0.1 mHa is acceptable. Fourth, within the s-HCI algorithm one can trade memory for a modest increase in computer time. Fifth, the perturbative calculation is embarrassingly par...
Molecular Cluster Perturbation Theory. I. Formalism
Byrd, Jason N; Molt,, Robert W; Bartlett, Rodney J; Sanders, Beverly A; Lotrich, Victor F
2014-01-01
We present second-order molecular cluster perturbation theory (MCPT(2)), a methodology to calculate arbitrarily large systems with explicit calculation of individual wavefunctions in a coupled cluster framework. This new MCPT(2) framework uses coupled cluster perturbation theory and an expansion in terms of molecular dimer interactions to obtain molecular wavefunctions that are infinite order in both the electronic fluctuation operator and all possible dimer (and products of dimers) interactions. The MCPT(2) framework has been implemented in the new SIA/ACES parallel architecture, making use of the advanced dynamic memory control and fine grained parallelism to perform very large explicit molecular cluster calculations. To illustrate the power of this method, we have computed energy shifts and lattice site dipole moments for the polar and non-polar configurations of solid hydrogen fluoride by scaling an explicit lattice to the bulk limit. The explicit lattice size without periodic boundary conditions was scal...
Improving perturbation theory with cactus diagrams
Constantinou, M; Skouroupathis, A; Constantinou, Martha; Panagopoulos, Haralambos; Skouroupathis, Apostolos
2006-01-01
We study a systematic improvement of perturbation theory for gauge fields on the lattice [hep-lat/0606001]; the improvement entails resumming, to all orders in the coupling constant, a dominant subclass of tadpole diagrams. This method, originally proposed for the Wilson gluon action, is extended here to encompass all possible gluon actions made of closed Wilson loops; any fermion action can be employed as well. The effect of resummation is to replace various parameters in the action (coupling constant, Symanzik and clover coefficient) by ``dressed'' values; the latter are solutions to certain coupled integral equations, which are easy to solve numerically. Some positive features of this method are: a) It is gauge invariant, b) it can be systematically applied to improve (to all orders) results obtained at any given order in perturbation theory, c) it does indeed absorb in the dressed parameters the bulk of tadpole contributions. Two different applications are presented: The additive renormalization of fermio...
The neutron electric dipole form factor in the perturbative chiral quark model
Dib, C; Gutsche, T; Kovalenko, S; Kuckei, J; Lyubovitskij, V E; Pumsa-ard, K; Dib, Claudio; Faessler, Amand; Gutsche, Thomas; Kovalenko, Sergey; Kuckei, Jan; Lyubovitskij, Valery E.; Pumsa-ard, Kem
2006-01-01
We calculate the electric dipole form factor of the neutron in a perturbative chiral quark model, parameterizing CP-violation of generic origin by means of effective electric dipole moments of the constituent quarks and their CP-violating couplings to the chiral fields. We discuss the relation of these effective parameters to more fundamental ones such as the intrinsic electric and chromoelectric dipole moments of quarks and the Weinberg parameter. From the existing experimental upper limits on the neutron EDM we derive constraints on these CP-violating parameters.
Perturbation theory for solitons in optical fibers
Kaup, D. J.
1990-11-01
Using a singular perturbation expansion, we study the evolution of a Raman loss compensated soliton in an optical fiber. Our analytical results agree quite well with the numerical results of Mollenauer, Gordon, and Islam [IEEE J. Quantum Electron. QE-22, 157 (1986)]. However, there are some differences in that our theory predicts an additional structure that was only partially seen in the numerical calculations. Our analytical results do give a quite good qualitative and quantitative check of the numerical results.
BIFURCATION-THEORY APPLIED TO CHIRAL SYMMETRY-BREAKING
ATKINSON, D
1990-01-01
Chiral symmetry breaking in quantum electrodynamics and quantum chromodynamics is considered as a problem in bifurcation theory. Inequalities and positivity play key roles, as they do in much of the work of Andre Martin.
Higgs-Yukawa model in chirally-invariant lattice field theory
Energy Technology Data Exchange (ETDEWEB)
Bulava, John [CERN, Geneva (Switzerland). Physics Department; Gerhold, Philipp; Kallarackal, Jim; Nagy, Attila [Humboldt Univ. Berlin (Germany). Inst. fuer Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Knippschild, Bastian [National Taiwan Univ., Taipei (China). Dept. of Physics; Lin, C.J. David [National Chiao-Tung Univ., Hsinchu (China). Inst. of Physics; National Centre for Theoretical Sciences, Hsinchu (China). Div. of Physics; Nagai, Kei-Ichi [Nagoya Univ., Nagoya, Aichi (Japan). Kobayashi-Maskawa Institute; Ogawa, Kenji [Chung-Yuan Christian Univ., Chung-Li (China). Dept. of Physics
2012-10-15
Non-perturbative numerical lattice studies of the Higgs-Yukawa sector of the standard model with exact chiral symmetry are reviewed. In particular, we discuss bounds on the Higgs boson mass at the standard model top quark mass, and in the presence of heavy fermions. We present a comprehensive study of the phase structure of the theory at weak and very strong values of the Yukawa coupling as well as at non-zero temperature.
Perturbative quantum gravity in double field theory
Boels, Rutger H.; Horst, Christoph
2016-04-01
We study perturbative general relativity with a two-form and a dilaton using the double field theory formulation which features explicit index factorisation at the Lagrangian level. Explicit checks to known tree level results are performed. In a natural covariant gauge a ghost-like scalar which contributes even at tree level is shown to decouple consistently as required by perturbative unitarity. In addition, a lightcone gauge is explored which bypasses the problem altogether. Using this gauge to study BCFW on-shell recursion, we can show that most of the D-dimensional tree level S-matrix of the theory, including all pure graviton scattering amplitudes, is reproduced by the double field theory. More generally, we argue that the integrand may be reconstructed from its single cuts and provide limited evidence for off-shell cancellations in the Feynman graphs. As a straightforward application of the developed technology double field theory-like expressions for four field string corrections are derived.
Perturbative quantum gravity in double field theory
Boels, Rutger H
2015-01-01
We study perturbative general relativity with a two-form and a dilaton using the double field theory formulation which features explicit index factorisation at the Lagrangian level. Explicit checks to known tree level results are performed. In a natural covariant gauge a ghost-like scalar which contributes even at tree level is shown to decouple consistently as required by perturbative unitarity. In addition, a lightcone gauge is explored which bypasses the problem altogether. Using this gauge to study BCFW on-shell recursion, we can show that most of the D-dimensional tree level S-matrix of the theory, including all pure graviton scattering amplitudes, is reproduced by the double field theory. More generally, we argue that the integrand may be reconstructed from its single cuts and provide limited evidence for off-shell cancellations in the Feynman graphs. As a straightforward application of the developed technology double field theory-like expressions for four field string corrections are derived.
Perturbation theory for plasmonic modulation and sensing
Raman, Aaswath
2011-05-25
We develop a general perturbation theory to treat small parameter changes in dispersive plasmonic nanostructures and metamaterials. We specifically apply it to dielectric refractive index and metallic plasma frequency modulation in metal-dielectric nanostructures. As a numerical demonstration, we verify the theory\\'s accuracy against direct calculations for a system of plasmonic rods in air where the metal is defined by a three-pole fit of silver\\'s dielectric function. We also discuss new optical behavior related to plasma frequency modulation in such systems. Our approach provides new physical insight for the design of plasmonic devices for biochemical sensing and optical modulation and future active metamaterial applications. © 2011 American Physical Society.
Electromagnetic form factors of the baryon octet in the perturbative chiral quark model
Cheedket, S; Gutsche, T; Faessler, A; Pumsa-ard, K; Yan, Y; Gutsche, Th.; Faessler, Amand
2002-01-01
We apply the perturbative chiral quark model at one loop to analyze the electromagnetic form factors of the baryon octet. The analytic expressions for baryon form factors, which are given in terms of fundamental parameters of low-energy pion-nucleon physics(weak pion decay constant, axial nucleon coupling, strong pion-nucleon form factor), and the numerical results for baryon magnetic moments, charge and magnetic radii are presented. Our results are in good agreement with experimental data.
Electromagnetic nucleon-delta transition in the perturbative chiral quark model
Pumsa-ard, K; Gutsche, T; Faessler, A; Cheedket, S; Gutsche, Th.; Faessler, Amand
2003-01-01
We apply the perturbative chiral quark model to the gamma N -> Delta transition. The four momentum dependence of the respective transverse helicity amplitudes A(1/2) and A(3/2) is determined at one loop in the pseudoscalar Goldstone boson fluctuations. Inclusion of excited states in the quark propagator is shown to result in a reasonable description of the experimental values for the helicity amplitudes at the real photon point.
Resurgence in quantum field theory: nonperturbative effects in the principal chiral model.
Cherman, Aleksey; Dorigoni, Daniele; Dunne, Gerald V; Ünsal, Mithat
2014-01-17
We explain the physical role of nonperturbative saddle points of path integrals in theories without instantons, using the example of the asymptotically free two-dimensional principal chiral model (PCM). Standard topological arguments based on homotopy considerations suggest no role for nonperturbative saddles in such theories. However, the resurgence theory, which unifies perturbative and nonperturbative physics, predicts the existence of several types of nonperturbative saddles associated with features of the large-order structure of the perturbation theory. These points are illustrated in the PCM, where we find new nonperturbative "fracton" saddle point field configurations, and suggest a quantum interpretation of previously discovered "uniton" unstable classical solutions. The fractons lead to a semiclassical realization of IR renormalons in the circle-compactified theory and yield the microscopic mechanism of the mass gap of the PCM.
Molecular cluster perturbation theory. I. Formalism
Byrd, Jason N.; Jindal, Nakul; Molt, Robert W., Jr.; Bartlett, Rodney J.; Sanders, Beverly A.; Lotrich, Victor F.
2015-11-01
We present second-order molecular cluster perturbation theory (MCPT(2)), a linear scaling methodology to calculate arbitrarily large systems with explicit calculation of individual wave functions in a coupled-cluster framework. This new MCPT(2) framework uses coupled-cluster perturbation theory and an expansion in terms of molecular dimer interactions to obtain molecular wave functions that are infinite order in both the electronic fluctuation operator and all possible dimer (and products of dimers) interactions. The MCPT(2) framework has been implemented in the new SIA/Aces4 parallel architecture, making use of the advanced dynamic memory control and fine-grained parallelism to perform very large explicit molecular cluster calculations. To illustrate the power of this method, we have computed energy shifts, lattice site dipole moments, and harmonic vibrational frequencies via explicit calculation of the bulk system for the polar and non-polar polymorphs of solid hydrogen fluoride. The explicit lattice size (without using any periodic boundary conditions) was expanded up to 1000 HF molecules, with 32,000 basis functions and 10,000 electrons. Our obtained HF lattice site dipole moments and harmonic vibrational frequencies agree well with the existing literature.
Testing gravity theories using tensor perturbations
Lin, Weikang; Ishak-Boushaki, Mustapha B.
2017-01-01
Primordial gravitational waves constitute a promising probe of the very early universe physics and the laws of gravity. We study the changes to tensor-mode perturbations that can arise in various modified gravity theories. These include a modified friction and a nonstandard dispersion relation. We introduce a physically motivated parametrization of these effects and use current data to obtain excluded parameter spaces. Taking into account the foreground subtraction, we then perform a forecast analysis focusing on the tensor-mode modified-gravity parameters as constrained by future experiments COrE, Stage-IV and PIXIE. For the tensor-to-scalar ratio r=0.01, we find the minimum detectible modified-gravity effects. In particular, the minimum detectable graviton mass is about 7.8˜9.7×10-33 eV, which is of the same order of magnitude as the graviton mass that allows massive gravity to produce late-time cosmic acceleration. Finally, we study the tensor-mode perturbations in modified gravity during inflation. We find that, the tensor spectral index would be additionally related to the friction parameter ν0 by nT=-3ν0-r/8. In some cases, the future experiments will be able to distinguish this relation from the standard one. In sum, primordial gravitational waves provide a complementary avenue to test gravity theories.
Spectral Density Functions and Their Sum Rules in an Effective Chiral Field Theory
Klevansky, S P
1997-01-01
The validity of Weinberg's two sum rules for massless QCD, as well as the six additional sum rules introduced into chiral perturbation theory by Gasser and Leutwyler, are investigated for the extended Nambu-Jona-Lasinio chiral model that includes vector and axial vector degrees of freedom. A detailed analysis of the vector, axial vector and coupled pion plus longitudinal axial vector modes is given. We show that, under Pauli-Villars regularization of the meson polarization amplitudes that determine the spectral density functions, all of the sum rules involving inverse moments higher than zero are automatically obeyed by the model spectral densities. By contrast, the zero moment sum rules acquire a non-vanishing right hand side that is proportional to the quark condensate density of the non-perturbative groundstate. We use selected sum rules in conjunction with other calculations to obtain explicit expressions for the scale-independent coupling constants $\\bar l_i$ of chiral perturbation theory in the combinat...
Theory of ion-chirality relation in ferroelectric liquid crystals
Lahiri, T.; Pal Majumder, T.
2012-04-01
The presence of impurity ions in ferroelectric liquid crystals (FLC) could produce a significant impact on the chirality of the medium with a possible modification in the polarization profile of the system. We theoretically observed these possibilities by considering an in-plane and bulk free energy density for the sample. Based on a suitable chirality transfer formalism, we explained the role of impurity ions in altering the chiral nature of a FLC medium. A continuous transition from modulated phases to uniform phases is also predicted within the framework of this theory. Then, we investigated the possible modification in the polarization profile driven by ionic impurities.
Perturbation Theory of the Cosmological Log-Density Field
DEFF Research Database (Denmark)
Wang, Xin; Neyrinck, Mark; Szapudi, István
2011-01-01
, motivating an analytic study of it. In this paper, we develop cosmological perturbation theory for the power spectrum of this field. Our formalism is developed in the context of renormalized perturbation theory, which helps to regulate the convergence behavior of the perturbation series, and of the Taylor...
Comparison of Some Exact and Perturbative Results for a Supersymmetric SU($N_c$) Gauge Theory
DEFF Research Database (Denmark)
Ryttov, Thomas; Shrock, Robert
2012-01-01
We consider vectorial, asymptotically free ${\\cal N}=1$ supersymmetric SU($N_c$) gauge theories with $N_f$ copies of massless chiral super fields in various representations and study how perturbative predictions for the lower boundary of the infrared conformal phase, as a function of $N_f$, compare...... S_2$, and (iv) $A_2 + \\bar A_2$, where $F$, $Adj$, $S_2$, and $A_2$ denote, respectively, the fundamental, adjoint, and symmetric and antisymmetric rank-2 tensor representations. We find that perturbative results slightly overestimate the value of $N_{f,cr}$ relative to the respective exact results...... for these representations, i.e., slightly underestimate the interval in $N_f$ for which the theory has infrared conformal behavior. Our results provide a measure of how closely perturbative calculations reproduce exact results for these theories....
Chiral-scale effective theory including a dilatonic meson
Li, Yan-Ling; Rho, Mannque
2016-01-01
A scale-invariant chiral effective Lagrangian is constructed for octet pions and a dilaton figuring as Nambu-Goldstone bosons with vector mesons incorporated as hidden gauge fields. The Lagrangian is built to the next-to-leading order in chiral-scale counting without baryon fields and then to leading order including baryons. The resulting theory is hidden scale-symmetric and local symmetric. We also discuss some possible applications of the present Lagrangian.
Manifestly Covariant Gauge-invariant Cosmological Perturbation Theory
Miedema, P G
2010-01-01
It is shown that a first-order cosmological perturbation theory for the open, flat and closed Friedmann-Lemaitre-Robertson-Walker universes admits one, and only one, gauge-invariant variable which describes the perturbation to the energy density and which becomes equal to the usual Newtonian energy density in the non-relativistic limit. The same holds true for the perturbation to the particle number density. Using these two new variables, a new manifestly gauge-invariant cosmological perturbation theory has been developed. Density perturbations evolve diabatically. Perturbations in the total energy density are gravitationally coupled to perturbations in the particle number density, irrespective of the nature of the particles. There is, in first-order, no back-reaction of perturbations to the global expansion of the universe. Small-scale perturbations in the radiation-dominated era oscillate with an increasing amplitude, whereas in older, less precise treatments, oscillating perturbations are found with a decr...
Testing gravity theories using tensor perturbations
Lin, Weikang; Ishak, Mustapha
2016-12-01
Primordial gravitational waves constitute a promising probe of the very early Universe and the laws of gravity. We study in this work changes to tensor-mode perturbations that can arise in various proposed modified gravity theories. These include additional friction effects, nonstandard dispersion relations involving a massive graviton, a modified speed, and a small-scale modification. We introduce a physically motivated parametrization of these effects and use current available data to obtain exclusion regions in the parameter spaces. Taking into account the foreground subtraction, we then perform a forecast analysis focusing on the tensor-mode modified-gravity parameters as constrained by the future experiments COrE, Stage-IV and PIXIE. For a fiducial value of the tensor-to-scalar ratio r =0.01 , we find that an additional friction of 3.5-4.5% compared to GR will be detected at 3 -σ by these experiments, while a decrease in friction will be more difficult to detect. The speed of gravitational waves needs to be by 5-15% different from the speed of light for detection. We find that the minimum detectable graviton mass is about 7.8 - 9.7 ×10-33 eV , which is of the same order of magnitude as the graviton mass that allows massive gravity theories to produce late-time cosmic acceleration. Finally, we study the tensor-mode perturbations in modified gravity during inflation using our parametrization. We find that, in addition to being related to r , the tensor spectral index would be related to the friction parameter ν0 by nT=-3 ν0-r /8 . Assuming that the friction parameter is unchanged throughout the history of the Universe, and that ν0 is much larger than r , the future experiments considered here will be able to distinguish this modified-gravity consistency relation from the standard inflation consistency relation, and thus can be used as a further test of modified gravity. In summary, tensor-mode perturbations and cosmic-microwave-background B
Chiral Symmetry in Light-Cone Field Theory
Lenz, F; Thies, M; Yazaki, K
2004-01-01
An analysis of spontaneously broken chiral symmetry in light-cone field theory is presented. The non-locality inherent to light-cone field theory requires revision of the standard procedure in the derivation of Ward-Takahashi identities. We derive the general structure of chiral Ward-Takahashi identities and construct them explicitly for various model field theories. Gell-Mann-Oakes-Renner relations and relations between fermion propagators and the structure functions of Nambu-Goldstone bosons are discussed and the necessary modifications of the Ward-Takahashi identities due to the axial anomaly are indicated.
Lie transform Hamiltonian perturbation theory for limit cycle systems
Shah, Tirth; Chakraborty, Sagar
2016-01-01
Usage of a Hamiltonian perturbation theory for nonconservative system is counterintuitive and in general, a technical impossibility by definition. However, the dual (time independent) Hamiltonian formalism for nonconservative systems have opened the door for using various Hamiltonian (and hence, Lagrangian) perturbation theories for investigating the dynamics of such systems. Following the recent extension of the canonical perturbation theory that brings Li\\'enard systems possessing limit cycles under its scope, here we show that the Lie transform Hamiltonian perturbation theory can also be generalized to find perturbative solutions for similar systems. The Lie transform perturbation theories are comparatively easier while seeking higher order corrections in the perturbative series for the solutions and they are also numerically implementable using any symbolic algebra package. For the sake of concreteness, we have illustrated the methodology using the important example of the van der Pol oscillator. While th...
Modified perturbation theory for the Yukawa model
Poluektov, Yu M
2016-01-01
A new formulation of perturbation theory for a description of the Dirac and scalar fields (the Yukawa model) is suggested. As the main approximation the self-consistent field model is chosen, which allows in a certain degree to account for the effects caused by the interaction of fields. Such choice of the main approximation leads to a normally ordered form of the interaction Hamiltonian. Generation of the fermion mass due to the interaction with exchange of the scalar boson is investigated. It is demonstrated that, for zero bare mass, the fermion can acquire mass only if the coupling constant exceeds the critical value determined by the boson mass. In this connection, the problem of the neutrino mass is discussed.
Perturbative analysis in higher-spin theories
Didenko, V. E.; Misuna, N. G.; Vasiliev, M. A.
2016-07-01
A new scheme of the perturbative analysis of the nonlinear HS equations is developed giving directly the final result for the successive application of the homotopy integrations which appear in the standard approach. It drastically simplifies the analysis and results from the application of the standard spectral sequence approach to the higherspin covariant derivatives, allowing us in particular to reduce multiple homotopy integrals resulting from the successive application of the homotopy trick to a single integral. Efficiency of the proposed method is illustrated by various examples. In particular, it is shown how the Central on-shell theorem of the free theory immediately results from the nonlinear HS field equations with no intermediate computations.
Spectral clustering based on matrix perturbation theory
Institute of Scientific and Technical Information of China (English)
TIAN Zheng; LI XiaoBin; JU YanWei
2007-01-01
This paper exposes some intrinsic characteristics of the spectral clustering method by using the tools from the matrix perturbation theory. We construct a weight matrix of a graph and study its eigenvalues and eigenvectors. It shows that the number of clusters is equal to the number of eigenvalues that are larger than 1, and the number of points in each of the clusters can be approximated by the associated eigenvalue. It also shows that the eigenvector of the weight matrix can be used directly to perform clustering; that is, the directional angle between the two-row vectors of the matrix derived from the eigenvectors is a suitable distance measure for clustering. As a result, an unsupervised spectral clustering algorithm based on weight matrix (USCAWM) is developed. The experimental results on a number of artificial and real-world data sets show the correctness of the theoretical analysis.
Heavy-tailed chiral random matrix theory
Kanazawa, Takuya
2016-05-01
We study an unconventional chiral random matrix model with a heavy-tailed probabilistic weight. The model is shown to exhibit chiral symmetry breaking with no bilinear condensate, in analogy to the Stern phase of QCD. We solve the model analytically and obtain the microscopic spectral density and the smallest eigenvalue distribution for an arbitrary number of flavors and arbitrary quark masses. Exotic behaviors such as non-decoupling of heavy flavors and a power-law tail of the smallest eigenvalue distribution are illustrated.
Heavy-tailed chiral random matrix theory
Kanazawa, Takuya
2016-01-01
We study an unconventional chiral random matrix model with a heavy-tailed probabilistic weight. The model is shown to exhibit chiral symmetry breaking with no bilinear condensate, in analogy to the Stern phase of QCD. We solve the model analytically and obtain the microscopic spectral density and the smallest eigenvalue distribution for an arbitrary number of flavors and arbitrary quark masses. Exotic behaviors such as non-decoupling of heavy flavors and a power-law tail of the smallest eigenvalue distribution are illustrated.
Collective Modes of Chiral Kinetic Theory in Magnetic Field
Stephanov, Mikhail; Yin, Yi
2015-01-01
We study collective excitations in systems described by chiral kinetic theory in external magnetic field. We consider high-temperature weak-coupling plasma, as well as high-density Landau Fermi liquid with interaction not restricted to be weak. We show that chiral magnetic wave (CMW) emerges in hydrodynamic regime (at frequencies smaller than collision relaxation rate) and the CMW velocity is determined by thermodynamic properties only. We find that in a plasma of opposite chiralities, at frequencies smaller than the chirality-flipping rate, the CMW excitation turns into a vector-like diffusion mode. In the interacting Fermi liquid, the CMW turns into the Landau zero sound mode in the high-frequency collisionless regime.
Redeveloping gyrokietic theory for multi-scale perturbation
Zhang, Shuangxi; Li, Jiquan
2016-01-01
It's pointed out in this paper that the existing and extensively used pullback transformation of charged particle's Lagrangian 1-form involves an illegal application of the pullback transformation for 1-form not including any perturbed scale to 1-form including perturbed scale. Therefore, modern gyrokinetic theory can not correctly deal with multi-scale perturbation. The coordinate transformation adopted by modern gyrokinetic theory can't avoid the violation of near identity transformation as well, which in fact is the main character that gyrokinetic theory should obey. In this paper, we develop a new Lie perturbed transformation theory for charged particle's Lagrangian 1-form based on the covariant transformation formula for 1-form. Compared with the ordering of modern gyrokinetic theory, this theory widens the amplitude range of perturbation, includes scales of spatial gradient and oscillating frequency of perturbation, and avoids the violation of near identity transformation as well. When combining the new...
Field-enlarging transformations and chiral theories
Sladkowski, J
1995-01-01
A field-enlarging transformation in the chiral electrodynamics is performed. This introduces an additional gauge symmetry to the model that is unitary and anomaly-free and allows for comparison of different models discussed in the literature. The problem of superfluous degrees of freedom and their influence on quantization is discussed. Several "mysteries" are explained from this point of view.
Brida, Mattia Dalla; Vilaseca, Pol
2016-01-01
The chirally rotated Schr\\"odinger functional ($\\chi$SF) renders the mechanism of automatic $O(a)$ improvement compatible with Schr\\"odinger functional (SF) renormalization schemes. Here we define a family of renormalization schemes based on the $\\chi$SF for a complete basis of $\\Delta F = 2$ parity-odd four-fermion operators. We compute the corresponding scale-dependent renormalization constants to one-loop order in perturbation theory and obtain their NLO anomalous dimensions by matching to the $\\overline{\\textrm{MS}}$ scheme. Due to automatic $O(a)$ improvement, once the $\\chi$SF is renormalized and improved at the boundaries, the step scaling functions (SSF) of these operators approach their continuum limit with $O(a^{2})$ corrections without the need of operator improvement.
Ren, Xiu-Lei; Meng, Jie
2013-01-01
We construct the chiral Lagrangians relevant in studies of the ground-state octet baryon masses up to $\\mathcal{O}(a^2)$ by taking into account discretization effects and calculate the masses up to $\\mathcal{O}(p^4)$ in the extended-on-mass-shell scheme. As an application, we study the latest $n_f=2+1$ LQCD data on the ground-state octet baryon masses form the PACS-CS, QCDSF-UKQCD, HSC, and NPLQCD Collaborations. It is shown that the discretization effects for the studied LQCD simulations are at the order of one to two percent for lattice spacings up to $0.15$ fm and the pion mass up to 500 MeV.
Non-perturbative String Theory from Water Waves
Energy Technology Data Exchange (ETDEWEB)
Iyer, Ramakrishnan; Johnson, Clifford V.; /Southern California U.; Pennington, Jeffrey S.; /SLAC
2012-06-14
We use a combination of a 't Hooft limit and numerical methods to find non-perturbative solutions of exactly solvable string theories, showing that perturbative solutions in different asymptotic regimes are connected by smooth interpolating functions. Our earlier perturbative work showed that a large class of minimal string theories arise as special limits of a Painleve IV hierarchy of string equations that can be derived by a similarity reduction of the dispersive water wave hierarchy of differential equations. The hierarchy of string equations contains new perturbative solutions, some of which were conjectured to be the type IIA and IIB string theories coupled to (4, 4k ? 2) superconformal minimal models of type (A, D). Our present paper shows that these new theories have smooth non-perturbative extensions. We also find evidence for putative new string theories that were not apparent in the perturbative analysis.
Power Counting Regime of Chiral Effective Field Theory and Beyond
Hall, J M M; Leinweber, D B
2010-01-01
Chiral effective field theory complements numerical simulations of quantum chromodynamics (QCD) on a space-time lattice. It provides a model-independent formalism for connecting lattice simulation results at finite volume and a variety of quark masses to the physical world. The asymptotic nature of the chiral expansion places the focus on the first few terms of the expansion. Thus, knowledge of the power-counting regime (PCR) of chiral effective field theory, where higher-order terms of the expansion may be regarded as negligible, is as important as knowledge of the expansion itself. Through the consideration of a variety of renormalization schemes and associated parameters, techniques to identify the PCR where results are independent of the renormalization scheme are established. The nucleon mass is considered as a benchmark for illustrating this general approach. Because the PCR is small, the numerical simulation results are also examined to search for the possible presence of an intrinsic scale which may b...
Testing gravity theories using tensor perturbations
Lin, Weikang
2016-01-01
Primordial gravitational waves constitute a promising probe of the very-early universe and the laws of gravity. We study changes to tensor mode perturbations that can arise in various proposed modified gravity (MG) theories. These include additional friction effects, non-standard dispersion relations involving a massive graviton, a modified speed, and a small-scale modification. We introduce a physically-motivated parameterization of these effects and use current available data to obtain exclusion regions in the parameter spaces. Taking into account the foreground subtraction, we then perform a forecast analysis focusing on the tensor mode MG parameters as constrained by the future experiments COrE, Stage-IV and PIXIE. For a fiducial value of the tensor-to-scalar ratio r=0.01, we find that an additional friction of 3.5-4.5% compared to GR will be detected at $3\\sigma$ by these experiments while a decrease in friction will be more difficult to detect. The speed of gravitational waves needs to be 5-15% differen...
Gluon Propagator in Fractional Analytic Perturbation Theory
Allendes, Pedro; Cvetič, Gorazd
2014-01-01
We consider the gluon propagator in the Landau gauge at low spacelike momenta and with the dressing function $Z(Q^2)$ at the two-loop order. We incorporate the nonperturbative effects by making the (noninteger) powers of the QCD coupling in the dressing function $Z(Q^2)$ analytic (holomorphic) via the Fractional Analytic Perturbation Theory (FAPT) model, and simultaneously introducing the gluon dynamical mass in the propagator as motivated by the previous analyses of the Dyson-Schwinger equations. The obtained propagator has behavior compatible with the unquenched lattice data ($N_f=2+1$) at low spacelike momenta $0.4 \\ {\\rm GeV} < Q \\lesssim 10$ GeV. We conclude that the removal of the unphysical Landau singularities of the powers of the coupling via the (F)APT prescription, in conjunction with the introduction of the dynamical mass $M \\approx 0.62$ GeV of the gluon, leads to an acceptable behavior of the propagator in the infrared regime.
Kato expansion in quantum canonical perturbation theory
Nikolaev, Andrey
2016-06-01
This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson's ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.
Kato expansion in quantum canonical perturbation theory
Nikolaev, A S
2015-01-01
This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. The corresponding computational algorithm is more efficient for high perturbative orders than the algorithms of Van Vleck and Magnus methods.
Chiral anomalies in N=1 supersymmetric Yang-Mills theories
Energy Technology Data Exchange (ETDEWEB)
Girardi, G.; Grimm, R.; Stora, R. (Grenoble-1 Univ., 74 - Annecy (France). Lab. de Physique des Particules)
1985-06-20
We establish a manifestly supersymmetric, compact, formula for the chiral anomalies of supersymmetric gauge theories. This result is obtained by combining superspace geometry with the usual algebra of anomalies. Except for a Wess-Zumino type term, we obtain an expression which is polynomial in the coefficients of the superconnection form.
Perturbative expansion of Chern-Simons theory
SAWON, Justin
2005-01-01
An overview of the perturbative expansion of the Chern--Simons path integral is given. The main goal is to describe how trivalent graphs appear: as they already occur in the perturbative expansion of an analogous finite-dimensional integral, we discuss this case in detail.
Perturbation Theory for Parent Hamiltonians of Matrix Product States
Szehr, Oleg; Wolf, Michael M.
2015-05-01
This article investigates the stability of the ground state subspace of a canonical parent Hamiltonian of a Matrix product state against local perturbations. We prove that the spectral gap of such a Hamiltonian remains stable under weak local perturbations even in the thermodynamic limit, where the entire perturbation might not be bounded. Our discussion is based on preceding work by Yarotsky that develops a perturbation theory for relatively bounded quantum perturbations of classical Hamiltonians. We exploit a renormalization procedure, which on large scale transforms the parent Hamiltonian of a Matrix product state into a classical Hamiltonian plus some perturbation. We can thus extend Yarotsky's results to provide a perturbation theory for parent Hamiltonians of Matrix product states and recover some of the findings of the independent contributions (Cirac et al in Phys Rev B 8(11):115108, 2013) and (Michalakis and Pytel in Comm Math Phys 322(2):277-302, 2013).
Large Nc volume reduction and chiral random matrix theory
Lee, Jong-Wan; Yamada, Norikazu
2013-01-01
Motivated by recent progress on the understanding of the Eguchi-Kawai (EK) volume equivalence and growing interest in conformal window, we simultaneously use the large-Nc volume reduction and Chiral Random Matrix Theory (chRMT) to study the chiral symmetry breaking of four dimensional SU(Nc) gauge theory with adjoint fermions in the large Nc limit. Although some cares are required because the chRMT limit and 't Hooft limit are not compatible in general, we show that the breakdown of the chiral symmetry can be detected in large-Nc gauge theories. As a first step, we mainly focus on the quenched approximation to establish the methodology. We first confirm that heavy adjoint fermions, introduced as the center symmetry preserver, work as expected and thanks to them the volume reduction holds. Using massless overlap fermion as a probe, we then calculate the low-lying Dirac spectrum for fermion in the adjoint representation to compare to that of chRMT, and find that chiral symmetry is indeed broken in the quenched ...
Gauge Invariant Effective Action in Abelian Chiral Gauge Theory on the Lattice
Suzuki, H
1999-01-01
Lüscher's recent formulation of Abelian chiral gauge theories on the lattice, in the vacuum (or perturbative) sector in infinite lattice volume, is re-interpreted in terms of the lattice covariant regularization. The gauge invariance of the effective action and the integrability of the gauge current in anomaly-free cases become transparent then. The real part of the effective action is simply one-half of that of the Dirac fermion and, when the Dirac operator has proper properties in the continuum limit, the imaginary part in the continuum limit reproduces the $\\eta$-invariant.}
Perturbative Gravity and Gauge Theory Relations: A Review
Directory of Open Access Journals (Sweden)
Thomas Søndergaard
2012-01-01
Full Text Available This paper is dedicated to the amazing Kawai-Lewellen-Tye relations, connecting perturbative gravity and gauge theories at tree level. The main focus is on n-point derivations and general properties both from a string theory and pure field theory point of view. In particular, the field theory part is based on some very recent developments.
Gauge and motion in perturbation theory
Pound, Adam
2015-01-01
Through second order in perturbative general relativity, a small compact object in an external vacuum spacetime obeys a generalized equivalence principle: although it is accelerated with respect to the external background geometry, it is in free fall with respect to a certain \\emph{effective} vacuum geometry. However, this single principle takes very different mathematical forms, with very different behaviors, depending on how one treats perturbed motion. Furthermore, any description of perturbed motion can be altered by a gauge transformation. In this paper, I clarify the relationship between two treatments of perturbed motion and the gauge freedom in each. I first show explicitly how one common treatment, called the Gralla-Wald approximation, can be derived from a second, called the self-consistent approximation. I next present a general treatment of smooth gauge transformations in both approximations, in which I emphasise that the approximations' governing equations can be formulated in an invariant manner...
Anomalies of the entanglement entropy in chiral theories
Iqbal, Nabil; Wall, Aron C.
2016-10-01
We study entanglement entropy in theories with gravitational or mixed U(1) gauge-gravitational anomalies in two, four and six dimensions. In such theories there is an anomaly in the entanglement entropy: it depends on the choice of reference frame in which the theory is regulated. We discuss subtleties regarding regulators and entanglement entropies in anomalous theories. We then study the entanglement entropy of free chiral fermions and self-dual bosons and show that in sufficiently symmetric situations this entanglement anomaly comes from an imbalance in the flux of modes flowing through the boundary, controlled by familiar index theorems.
Massive renormalization scheme and perturbation theory at finite temperature
Energy Technology Data Exchange (ETDEWEB)
Blaizot, Jean-Paul, E-mail: jean-paul.blaizot@cea.fr [Institut de Physique Théorique, CNRS/URA2306, CEA-Saclay, 91191 Gif-sur-Yvette (France); Wschebor, Nicolás [Instituto de Fìsica, Faculdad de Ingeniería, Universidade de la República, 11000 Montevideo (Uruguay)
2015-02-04
We argue that the choice of an appropriate, massive, renormalization scheme can greatly improve the apparent convergence of perturbation theory at finite temperature. This is illustrated by the calculation of the pressure of a scalar field theory with quartic interactions, at 2-loop order. The result, almost identical to that obtained with more sophisticated resummation techniques, shows a remarkable stability as the coupling constant grows, in sharp contrast with standard perturbation theory.
Numerical stochastic perturbation theory in the Schroedinger functional
Energy Technology Data Exchange (ETDEWEB)
Brambilla, Michele; Di Renzo, Francesco; Hesse, Dirk [Parma Univ. (Italy); INFN, Parma (Italy); Dalla Brida, Mattia [Trinity College Dublin (Ireland). School of Mathematics; Sint, Stefan [Trinity College Dublin (Ireland). School of Mathematics; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2013-11-15
The Schroedinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the fact that perturbative calculations quickly become cumbersome with the inclusion of higher orders in the gauge coupling and hence the use of an automated perturbation theory framework is desirable. We present the implementation of the SF in numerical stochastic perturbation theory (NSPT) and compare first results for the running coupling at two loops in pure SU(3) Yang-Mills theory with the literature.
Chirality of tensor perturbations for complex values of the Immirzi parameter
Bethke, Laura
2011-01-01
In this paper we generalise previous work on tensor perturbations in a de Sitter background in terms of Ashtekar variables to cover all complex values of the Immirzi parameter gamma (previous work was restricted to imaginary gamma). Particular attention is paid to the case of real gamma. Following the same approach as in the imaginary case, we can obtain physical graviton states by invoking reality and torsion free conditions. The Hamiltonian in terms of graviton states has the same form whether gamma has a real part or not; however changes occur for the vacuum energy and fluctuations. Specifically, we observe a gamma dependent chiral asymmetry in the vacuum fluctuations only if gamma has an imaginary part. Ordering prescriptions also change this asymmetry. We thus present a measurable result for CMB polarisation experiments that could shed light on the workings of quantum gravity.
Puhr, M
2016-01-01
We use exactly chiral overlap lattice fermions to investigate the Chiral Separation Effect in quenched QCD at finite density. We employ a recently developed numerical method which allows, for the first time, to address the transport properties of exactly chiral lattice fermions with non-zero chemical potential. Studying the axial current along the external magnetic field, we find a linear dependence consistent with the free fermion result for topologically trivial gauge field configurations. However, for configurations with nontrivial topology in the confinement regime the axial current is strongly suppressed due to contributions of topological modes of the Dirac operator, which suggests that non-perturbative corrections to the Chiral Separation Effect have topological origin.
Lemler, Paul M.; Vaccaro, Patrick
2016-06-01
The non-resonant interaction of electromagnetic radiation with an isotropic ensemble of chiral molecules, which causes the incident state of linear polarization to undergo a signed rotation, long has served as a metric for gauging the enantiomeric purity of asymmetric syntheses. While the underlying phenomenon of circular birefringence (CB) typically is probed in the condensed phase, recent advances in ultrasensitive circular-differential detection schemes, as exemplified by the techniques of Cavity Ring-Down Polarimetry (CRDP), have permitted the first quantitative analyses of such processes to be performed in rarefied media. Efforts to extend vapor-phase investigations of CB to new families of chiral substrates will be discussed, with particular emphasis directed towards the elucidation of intrinsic (e.g., solvent-free) properties and their mediation by environmental perturbations (e.g., solvation). Specific species targeted by this work will include the stereoselective building blocks phenylpropylene oxide and α-methylbenzyl amine, both of which exhibit pronounced solvent-dependent changes in measured optical activity. The nature of chiroptical response in different environments will be highlighted, with quantum-chemical calculations serving to unravel the structural and electronic provenance of observed behavior.
Siegert pseudostate perturbation theory: one- and two-threshold cases
Toyota, K; Watanabe, S; Toyota, Koudai; Morishita, Toru; Watanabe, Shinichi
2005-01-01
Perturbation theory for the Siegert pseudostates (SPS) [Phys.Rev.A 58, 2077 (1998) and Phys.Rev.A 67, 032714 (2003)] is studied for the case of two energetically separated thresholds. The perturbation formulas for the one-threshold case are derived as a limiting case whereby we reconstruct More's theory for the decaying states [Phys.Rev.A 3,1217(1971)] and amend an error. The perturbation formulas for the two-threshold case have additional terms due to the non-standard orthogonality relationship of the Siegert Pseudostates. We apply the theory to a 2-channel model problem, and find the rate of convergence of the perturbation expansion should be examined with the aide of the variance $D= ||E-\\sum_{n}\\lambda^n E^{(n)}||$ instead of the real and imaginary parts of the perturbation energy individually.
Classical and Quantum Theory of Perturbations in Inflationary Universe Models
Brandenberger, R H; Mukhanov, V
1993-01-01
A brief introduction to the gauge invariant classical and quantum theory of cosmological perturbations is given. The formalism is applied to inflationary Universe models and yields a consistent and unified description of the generation and evolution of fluctuations. A general formula for the amplitude of cosmological perturbations in inflationary cosmology is derived.
Perturbation theory for intermolecular forces including exchange
Lekkerkerker, H.N.W.; Laidlaw, W.G.
1970-01-01
Generalized solutions to the Kisenschitz and London perturbation equations are derived. It is pointed out that the results obtained in the formalisms proposed by Hirschfelder (HAV), by Hirschfelder and Silbey, by Murrell and Shaw, and by Musher and Amos are special cases of the generalized treatment
Non-perturbative Heavy Quark Effective Theory
DEFF Research Database (Denmark)
Della Morte, Michele; Heitger, Jochen; Simma, Hubert;
2015-01-01
We review a lattice strategy how to non-perturbatively determine the coefficients in the HQET expansion of all components of the heavy-light axial and vector currents, including 1/m_h-corrections. We also discuss recent preliminary results on the form factors parameterizing semi-leptonic B-decays...
Survey of mathematical foundations of QFT and perturbative string theory
Sati, H.; Schreiber, U.
2011-01-01
Recent years have seen noteworthy progress in the mathematical formulation of quantum field theory and perturbative string theory. We give a brief survey of these developments. It serves as an introduction to the more detailed collection "Mathematical Foundations of Quantum Field Theory and Perturba
Non perturbative methods in two dimensional quantum field theory
Abdalla, Elcio; Rothe, Klaus D
1991-01-01
This book is a survey of methods used in the study of two-dimensional models in quantum field theory as well as applications of these theories in physics. It covers the subject since the first model, studied in the fifties, up to modern developments in string theories, and includes exact solutions, non-perturbative methods of study, and nonlinear sigma models.
BRST analysis of QCD$_{2}$ as a perturbed WZW theory
Cabra, D C; Schaposnik, F A
1995-01-01
Integrability of Quantum Chromodynamics in 1+1 dimensions has recently been suggested by formulating it as a perturbed conformal Wess-Zumino-Witten Theory. The present paper further elucidates this formulation, by presenting a detailed BRST analysis.
A Simple First-Principles Homogenization Theory for Chiral Metamaterials
Directory of Open Access Journals (Sweden)
Carlo Rizza
2015-04-01
Full Text Available We discuss a simple first-principles homogenization theory for describing, in the long-wavelength limit, the effective bianisotropic response of a periodic metamaterial composite without intrinsic chiral and magnetic inclusions. In the case where the dielectric contrast is low, we obtain a full analytical description which can be considered the extension of Landau-Lifshitz-Looyenga effective-medium formulation in the context of periodic metamaterials.
de Sitter limit of inflation and nonlinear perturbation theory
Jarnhus, Philip R
2007-01-01
We study the fourth order action of comoving curvature perturbations in an inflationary universe in order to understand more systematically the de Sitter limit in nonlinear cosmological perturbation theory. We derive the action of the curvature perturbations to fourth order in the comoving gauge, and show that it vanishes sufficiently fast in the de Sitter limit. By studying the de Sitter limit, we then extrapolate to the n'th order action of comoving curvature perturbations and discuss the slow-roll order of the n-point correlation function.
Nonlinear Acoustics -- Perturbation Theory and Webster's Equation
Jorge, Rogério
2013-01-01
Webster's horn equation (1919) offers a one-dimensional approximation for low-frequency sound waves along a rigid tube with a variable cross-sectional area. It can be thought as a wave equation with a source term that takes into account the nonlinear geometry of the tube. In this document we derive this equation using a simplified fluid model of an ideal gas. By a simple change of variables, we convert it to a Schr\\"odinger equation and use the well-known variational and perturbative methods to seek perturbative solutions. As an example, we apply these methods to the Gabriel's Horn geometry, deriving the first order corrections to the linear frequency. An algorithm to the harmonic modes in any order for a general horn geometry is derived.
Effective gravitational couplings for cosmological perturbations in generalized Proca theories
De Felice, Antonio; Kase, Ryotaro; Mukohyama, Shinji; Tsujikawa, Shinji; Zhang, Ying-li
2016-01-01
We consider the finite interactions of the generalized Proca theory including the sixth-order Lagrangian and derive the full linear perturbation equations of motion on the flat Friedmann-Lema\\^{i}tre-Robertson-Walker background in the presence of a matter perfect fluid. By construction, the propagating degrees of freedom (besides the matter perfect fluid) are two transverse vector perturbations, one longitudinal scalar, and two tensor polarizations. The Lagrangians associated with intrinsic vector modes neither affect the background equations of motion nor the second-order action of tensor perturbations, but they do give rise to non-trivial modifications to the no-ghost condition of vector perturbations and to the propagation speeds of vector and scalar perturbations. We derive the effective gravitational coupling $G_{\\rm eff}$ with matter density perturbations under a quasi-static approximation on scales deep inside the sound horizon. We find that the existence of intrinsic vector modes allows a possibility ...
Siegert pseudostate perturbation theory: one- and two-threshold cases
Toyota, Koudai; Morishita, Toru; Watanabe, Shinichi
2005-01-01
Perturbation theory for the Siegert pseudostates (SPS) [Phys.Rev.A 58, 2077 (1998) and Phys.Rev.A 67, 032714 (2003)] is studied for the case of two energetically separated thresholds. The perturbation formulas for the one-threshold case are derived as a limiting case whereby we reconstruct More's theory for the decaying states [Phys.Rev.A 3,1217(1971)] and amend an error. The perturbation formulas for the two-threshold case have additional terms due to the non-standard orthogonality relations...
Non-perturbative Nekrasov partition function from string theory
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, I., E-mail: ignatios.antoniadis@cern.ch [Department of Physics, CERN – Theory Division, CH-1211 Geneva 23 (Switzerland); Florakis, I., E-mail: florakis@mppmu.mpg.de [Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, 80805 München (Germany); Hohenegger, S., E-mail: stefan.hohenegger@cern.ch [Department of Physics, CERN – Theory Division, CH-1211 Geneva 23 (Switzerland); Narain, K.S., E-mail: narain@ictp.trieste.it [High Energy Section, The Abdus Salam International Center for Theoretical Physics, Strada Costiera, 11-34014 Trieste (Italy); Zein Assi, A., E-mail: zeinassi@cern.ch [Department of Physics, CERN – Theory Division, CH-1211 Geneva 23 (Switzerland); Centre de Physique Théorique (UMR CNRS 7644), Ecole Polytechnique, 91128 Palaiseau (France)
2014-03-15
We calculate gauge instanton corrections to a class of higher derivative string effective couplings introduced in [1]. We work in Type I string theory compactified on K3×T{sup 2} and realise gauge instantons in terms of D5-branes wrapping the internal space. In the field theory limit we reproduce the deformed ADHM action on a general Ω-background from which one can compute the non-perturbative gauge theory partition function using localisation. This is a non-perturbative extension of [1] and provides further evidence for our proposal of a string theory realisation of the Ω-background.
Perturbation theories for the thermodynamic properties of fluids and solids
Solana, J R
2013-01-01
This book, Perturbation Theories for the Thermodynamic Properties of Fluids and Solids, provides a comprehensive review of current perturbation theories-as well as integral equation theories and density functional theories-for the equilibrium thermodynamic and structural properties of classical systems. Emphasizing practical applications, the text avoids complex theoretical derivations as much as possible. It begins with discussions of the nature of intermolecular forces and simple potential models. The book also presents a summary of statistical mechanics concepts and formulae. In addition, i
Nucleon propagation through nuclear matter in chiral effective field theory
Mallik, S; Mishra, Hiranmaya
2007-01-01
We treat the propagation of nucleon in nuclear matter by evaluating the ensemble average of the two-point function of nucleon currents in the framework of the chiral effective field theory. We first derive the effective parameters of nucleon to one loop. The resulting formula for the effective mass was known previously and gives an absurd value at normal nuclear density. We then modify it following Weinberg's method for the two-nucleon system in the effective theory. Our results for the effective mass and the width of nucleon are compared with those in the literature.
Nucleon propagation through nuclear matter in chiral effective field theory
Energy Technology Data Exchange (ETDEWEB)
Mallik, S. [Saha Institute of Nuclear Physics, Kolkata (India); Mishra, H. [Physical Research Laboratory, Theory Divison, Ahmedabad (India)
2007-05-15
We treat the propagation of a nucleon in nuclear matter by evaluating the ensemble average of the two-point function of the nucleon currents in the framework of chiral effective field theory. We first derive the effective parameters of the nucleon to one loop. The resulting formula for the effective mass has been known since before and gives an absurd value at normal nuclear density. We then modify it following Weinberg's method for the two-nucleon system in the effective theory. Our results for the effective mass and the width of the nucleon are compared with those in the literature. (orig.)
Nucleon propagation through nuclear matter in chiral effective field theory
Mallik, S.; Mishra, H.
2007-05-01
We treat the propagation of a nucleon in nuclear matter by evaluating the ensemble average of the two-point function of the nucleon currents in the framework of chiral effective field theory. We first derive the effective parameters of the nucleon to one loop. The resulting formula for the effective mass has been known since before and gives an absurd value at normal nuclear density. We then modify it following Weinberg’s method for the two-nucleon system in the effective theory. Our results for the effective mass and the width of the nucleon are compared with those in the literature.
Anomalies of the Entanglement Entropy in Chiral Theories
Iqbal, Nabil
2015-01-01
We study entanglement entropy in theories with gravitational or mixed U(1) gauge-gravitational anomalies in two, four and six dimensions. In such theories there is an anomaly in the entanglement entropy: it depends on the choice of reference frame in which the theory is regulated. We discuss subtleties regarding regulators and entanglement entropies in anomalous theories. We then study the entanglement entropy of free chiral fermions and self-dual bosons and show that in sufficiently symmetric situations this entanglement anomaly comes from an imbalance in the flux of modes flowing through the boundary, controlled by familiar index theorems. In two and four dimensions we use anomalous Ward identities to find general expressions for the transformation of the entanglement entropy under a diffeomorphism. (In the case of a mixed anomaly there is an alternative presentation of the theory in which the entanglement entropy is not invariant under a U(1) gauge transformation. The free-field manifestation of this pheno...
$K \\to \\pi \\pi \\pi \\gamma$ in chiral perturbation theory
D'Ambrosio, G; Isidori, Gino; Neufeld, H
1996-01-01
We present a complete analysis of K -> 3 pi gamma decays to O(p^4) in the low-energy expansion of the Standard Model. We employ the notion of "generalized bremsstrahlung" to take full advantage of experimental information on the corresponding non-radiative K -> 3 pi decays.
The perturbative ghost propagator in Landau gauge from numerical stochastic perturbation theory
Di Renzo, F; Perlt, H; Schiller, A; Torrero, C
2008-01-01
We present one- and two-loop results for the ghost propagator in Landau gauge calculated in Numerical Stochastic Perturbation Theory (NSPT). The one-loop results are compared with available standard Lattice Perturbation Theory in the infinite-volume limit. We discuss in detail how to perform the different necessary limits in the NSPT approach and discuss a recipe to treat logarithmic terms by introducing ``finite-lattice logs''. We find agreement with the one-loop result from standard Lattice Perturbation Theory and estimate, from the non-logarithmic part of the ghost propagator in two-loop order, the unknown constant contribution to the ghost self-energy in the RI'-MOM scheme in Landau gauge. That constant vanishes within our numerical accuracy.
Chaos in Chiral Condensates in Gauge Theories
Hashimoto, Koji; Murata, Keiju; Yoshida, Kentaroh
2016-12-01
Assigning a chaos index for dynamics of generic quantum field theories is a challenging problem because the notion of a Lyapunov exponent, which is useful for singling out chaotic behavior, works only in classical systems. We address the issue by using the AdS /CFT correspondence, as the large Nc limit provides a classicalization (other than the standard ℏ→0 ) while keeping nontrivial quantum condensation. We demonstrate the chaos in the dynamics of quantum gauge theories: The time evolution of homogeneous quark condensates ⟨q ¯q ⟩ and ⟨q ¯γ5q ⟩ in an N =2 supersymmetric QCD with the S U (Nc) gauge group at large Nc and at a large 't Hooft coupling λ ≡NcgYM2 exhibits a positive Lyapunov exponent. The chaos dominates the phase space for energy density E ≳(6 ×1 02)×mq4(Nc/λ2), where mq is the quark mass. We evaluate the largest Lyapunov exponent as a function of (Nc,λ ,E ) and find that the N =2 supersymmetric QCD is more chaotic for smaller Nc.
Ambitwistor Strings: Worldsheet Approaches to perturbative Quantum Field Theories
Geyer, Yvonne
2016-01-01
Tree-level scattering amplitudes in massless theories not only exhibit a simplicity entirely unexpected from Feynman diagrams, but also an underlying structure remarkably reminiscent of worldsheet theory correlators. These features can be explained by ambitwistor strings - two-dimensional chiral conformal field theories in an auxiliary target space, the complexified phase space of null geodesics. The aim of this thesis is to explore the ambitwistor string approach to understand these structures in amplitudes, and thereby provide a new angle on quantum field theories. The first part of the thesis provides a user-friendly introduction to ambitwistor strings, as well as a condensed overview over the literature and some novel results. Emphasising the study of tree-level amplitudes, we then explore the wide-ranging impact of ambitwistor strings for an extensive family of massless theories, and discuss the duality between asymptotic symmetries and the low energy behaviour of a theory from the point of view of the w...
Perturbative algebraic quantum field theory at finite temperature
Energy Technology Data Exchange (ETDEWEB)
Lindner, Falk
2013-08-15
We present the algebraic approach to perturbative quantum field theory for the real scalar field in Minkowski spacetime. In this work we put a special emphasis on the inherent state-independence of the framework and provide a detailed analysis of the state space. The dynamics of the interacting system is constructed in a novel way by virtue of the time-slice axiom in causal perturbation theory. This method sheds new light in the connection between quantum statistical dynamics and perturbative quantum field theory. In particular it allows the explicit construction of the KMS and vacuum state for the interacting, massive Klein-Gordon field which implies the absence of infrared divergences of the interacting theory at finite temperature, in particular for the interacting Wightman and time-ordered functions.
Renormalization Group Optimized Perturbation Theory at Finite Temperatures
Kneur, J -L
2015-01-01
A recently developed variant of the so-called optimized perturbation theory (OPT), making it perturbatively consistent with renormalization group (RG) properties, RGOPT, was shown to drastically improve its convergence for zero temperature theories. Here the RGOPT adapted to finite temperature is illustrated with a detailed evaluation of the two-loop pressure for the thermal scalar $ \\lambda\\phi^4$ field theory. We show that already at the simple one-loop level this quantity is exactly scale-invariant by construction and turns out to qualitatively reproduce, with a rather simple procedure, results from more sophisticated resummation methods at two-loop order, such as the two-particle irreducible approach typically. This lowest order also reproduces the exact large-$N$ results of the $O(N)$ model. Although very close in spirit, our RGOPT method and corresponding results differ drastically from similar variational approaches, such as the screened perturbation theory or its QCD-version, the (resummed) hard therm...
Convergence of coupled cluster perturbation theory
Eriksen, Janus Juul; Matthews, Devin A; Jørgensen, Poul; Olsen, Jeppe
2016-01-01
The convergence of a recently proposed coupled cluster (CC) family of perturbation series [Eriksen et al., J. Chem. Phys. 140, 064108 (2014)], in which the energetic difference between a parent and a target CC model is expanded in orders of the M{\\o}ller-Plesset (MP) fluctuation potential, is investigated for four prototypical closed-shell systems (Ne, singlet methylene, distorted HF, and the fluoride anion) in standard and augmented basis sets. In these investigations, energy corrections of the various series have been calculated to high orders and their convergence radii determined by probing for possible front- and back-door intruder states. In summary, we conclude how it is primarily the choice of target state, and not the choice of parent state, which ultimately governs the convergence behavior of a given series. For example, restricting the target state to, say, triple or quadruple excitations might remove intruders present in series that target the full configuration interaction (FCI) limit, such as th...
Primordial Perturbations in Einstein-Aether and BPSH Theories
Armendariz-Picon, Cristian; Garriga, Jaume
2010-01-01
We study the primordial perturbations generated during a stage of single-field inflation in Einstein-aether theories. Quantum fluctuations of the inflaton and aether fields seed long wavelength adiabatic and isocurvature scalar perturbations, as well as transverse vector perturbations. Geometrically, the isocurvature mode is the potential for the velocity field of the aether with respect to matter. For a certain range of parameters, this mode may lead to a sizable random velocity of the aether within the observable universe. The adiabatic mode corresponds to curvature perturbations of co-moving slices (where matter is at rest). In contrast with the standard case, it has a non-vanishing anisotropic stress on large scales. Scalar and vector perturbations may leave significant imprints on the cosmic microwave background. We calculate their primordial spectra, analyze their contributions to the temperature anisotropies, and formulate some of the phenomenological constraints that follow from observations. These ma...
On a Geometric Theory of Generalized Chiral Elasticity with Discontinuities
Directory of Open Access Journals (Sweden)
Suhendro I.
2008-01-01
Full Text Available In this work we develop, in a somewhat extensive manner, a geometric theory of chiral elasticity which in general is endowed with geometric discontinuities (sometimes referred to as defects. By itself, the present theory generalizes both Cosserat and void elasticity theories to a certain extent via geometrization as well as by taking intoaccount the action of the electromagnetic field, i.e., the incorporation of the electromagnetic field into the description of the so-called microspin (chirality also forms the underlying structure of this work. As we know, the description of the electromagnetic field as a unified phenomenon requires four-dimensional space-time rather than three-dimensional space as its background. For this reason we embed the three-dimensional material space in four-dimensional space-time. This way, the electromagnetic spin is coupled to the non-electromagnetic microspin, both being parts of the completemicrospin to be added to the macrospin in the full description of vorticity. In short, our objective is to generalize the existing continuum theories by especially describing microspin phenomena in a fully geometric way.
On a Geometric Theory of Generalized Chiral Elasticity with Discontinuities
Directory of Open Access Journals (Sweden)
Suhendro I.
2008-01-01
Full Text Available In this work we develop, in a somewhat extensive manner, a geometric theory of chiral elasticity which in general is endowed with geometric discontinuities (sometimes re- ferred to as defects . By itself, the present theory generalizes both Cosserat and void elasticity theories to a certain extent via geometrization as well as by taking into ac- count the action of the electromagnetic field, i.e., the incorporation of the electromag- netic field into the description of the so-called microspin ( chirality also forms the un- derlying structure of this work. As we know, the description of the electromagnetic field as a unified phenomenon requires four-dimensional space-time rather than three- dimensional space as its background. For this reason we embed the three-dimensional material space in four-dimensional space-time. This way, the electromagnetic spin is coupled to the non-electromagnetic microspin, both being parts of the complete mi- crospin to be added to the macrospin in the full description of vorticity. In short, our objective is to generalize the existing continuum theories by especially describing mi- crospin phenomena in a fully geometric way.
Perturbation Theory of the Cosmological Log-Density Field
Wang, Xin; Szapudi, István; Szalay, Alex; Chen, Xuelei; Lesgourgues, Julien; Riotto, Antonio; Sloth, Martin; 10.1088/0004-637X/735/1/32
2011-01-01
The matter density field exhibits a nearly lognormal probability density distribution (PDF) after entering into the nonlinear regime. Recently, it has been shown that the shape of the power spectrum of a logarithmically transformed density field is very close to the linear density power spectrum, motivating an analytic study of it. In this paper, we develop cosmological perturbation theory for the power spectrum of this field. Our formalism is developed in the context of renormalized perturbation theory, which helps to regulate the convergence behavior of the perturbation series, and of the Taylor- series expansion we use of the logarithmic mapping. This approach allows us to handle the critical issue of density smoothing in a straightforward way. We also compare our perturbative results with simulation measurements.
Brillouin-Wigner perturbation theory in open electromagnetic systems
Muljarov, E A; Zimmermann, R; 10.1209/0295-5075/92/50010
2012-01-01
A Brillouin-Wigner perturbation theory is developed for open electromagnetic systems which are characterised by discrete resonant states with complex eigenenergies. Since these states are exponentially growing at large distances, a modified normalisation is introduced that allows a simple spectral representation of the Green's function. The perturbed modes are found by solving a linear eigenvalue problem in matrix form. The method is illustrated on exactly solvable one- and three-dimensional examples being, respectively, a dielectric slab and a microsphere.
A Theory of the Perturbed Consumer with General Budgets
DEFF Research Database (Denmark)
McFadden, Daniel L; Fosgerau, Mogens
We consider demand systems for utility-maximizing consumers facing general budget constraints whose utilities are perturbed by additive linear shifts in marginal utilities. Budgets are required to be compact but are not required to be convex. We define demand generating functions (DGF) whose......-valued and smooth in their arguments. We also give sufficient conditions for integrability of perturbed demand. Our analysis provides a foundation for applications of consumer theory to problems with nonlinear budget constraints....
Perturbation theory for string sigma models
Bianchi, Lorenzo
2016-01-01
In this thesis we investigate quantum aspects of the Green-Schwarz superstring in various AdS backgrounds relevant for the AdS/CFT correspondence, providing several examples of perturbative computations in the corresponding integrable sigma-models. We start by reviewing in details the supercoset construction of the superstring action in $AdS_5 \\times S^5$, pointing out the limits of this procedure for $AdS_4$ and $AdS_3$ backgrounds. For the $AdS_4 \\times CP^3$ case we give a thorough derivation of an alternative action, based on the double-dimensional reduction of eleven-dimensional super-membranes. We then consider the expansion about the BMN vacuum and the S-matrix for the scattering of worldsheet excitations in the decompactification limit. To evaluate its elements efficiently we describe a unitarity-based method resulting in a very compact formula yielding the cut-constructible part of any one-loop two-dimensional S-matrix. In the second part of this review we analyze the superstring action on $AdS_4 \\ti...
Quantum fields in the non-perturbative regime. Yang-Mills theory and gravity
Energy Technology Data Exchange (ETDEWEB)
Eichhorn, Astrid
2011-09-06
In this thesis we study candidates for fundamental quantum field theories, namely non-Abelian gauge theories and asymptotically safe quantum gravity. Whereas the first ones have a stronglyinteracting low-energy limit, the second one enters a non-perturbative regime at high energies. Thus, we apply a tool suited to the study of quantum field theories beyond the perturbative regime, namely the Functional Renormalisation Group. In a first part, we concentrate on the physical properties of non-Abelian gauge theories at low energies. Focussing on the vacuum properties of the theory, we present an evaluation of the full effective potential for the field strength invariant F{sub {mu}}{sub {nu}}F{sup {mu}}{sup {nu}} from non-perturbative gauge correlation functions and find a non-trivial minimum corresponding to the existence of a dimension four gluon condensate in the vacuum. We also relate the infrared asymptotic form of the {beta} function of the running background-gauge coupling to the asymptotic behavior of Landau-gauge gluon and ghost propagators and derive an upper bound on their scaling exponents. We then consider the theory at finite temperature and study the nature of the confinement phase transition in d = 3+1 dimensions in various non-Abelian gauge theories. For SU(N) with N= 3,..,12 and Sp(2) we find a first-order phase transition in agreement with general expectations. Moreover our study suggests that the phase transition in E(7) Yang-Mills theory also is of first order. Our studies shed light on the question which property of a gauge group determines the order of the phase transition. In a second part we consider asymptotically safe quantum gravity. Here, we focus on the Faddeev-Popov ghost sector of the theory, to study its properties in the context of an interacting UV regime. We investigate several truncations, which all lend support to the conjecture that gravity may be asymptotically safe. In a first truncation, we study the ghost anomalous dimension
Perturbed period-doubling bifurcation. I. Theory
DEFF Research Database (Denmark)
Svensmark, Henrik; Samuelsen, Mogens Rugholm
1990-01-01
-defined way that is a function of the amplitude and the frequency of the signal. New scaling laws between the amplitude of the signal and the detuning δ are found; these scaling laws apply to a variety of quantities, e.g., to the shift of the bifurcation point. It is also found that the stability...... of a microwave-driven Josephson junction confirm the theory. Results should be of interest in parametric-amplification studies....
A Brief Overview of Hard-Thermal-Loop Perturbation Theory
Institute of Scientific and Technical Information of China (English)
SU Nan
2012-01-01
The poor convergence of quantum field theory at finite temperature has been one of the main obstacles in the practical applications of thermal QCD for decades. Here we briefly review the progress of hard-thermal-loop perturbation theory （HTLpt） in reorganizing the perturbative expansion in order to improve the convergence. The quantum mechanical anharmonic oscillator is used as a simple example to show the breakdown of weak-coupling expansion, and variational perturbation theory is introduced as an effective resummation scheme for divergent weak-coupling expansions. We discuss HTLpt thermodynamic calculations for QED, pure-glue QCD, and QCD with Nf = 3 up to three-loop order. The results suggest that HTLpt provides a systematic framework that can be used to calculate both static and dynamic quantities for temperatures relevant at LHC.
Perturbative study of Yang-Mills theory in the infrared
Siringo, Fabio
2015-01-01
Pure Yang-Mills SU(N) theory is studied in four dimensional space and Landau gauge by a double perturbative expansion based on a massive free-particle propagator. By dimensional regularization, all diverging mass terms cancel exactly in the double expansion, without the need to include mass counterterms that would spoil the symmetry of the original Lagrangian. The emerging perturbation theory is safe in the infrared and shares the same behaviour of the standard perturbation theory in the UV. At one-loop, Gluon and ghost propagators are found in excellent agreement with the data of lattice simulations and an infrared-safe running coupling is derived. A natural scale m=0.5-0.6 GeV is extracted from the data for N=3.
A brief overview of hard-thermal-loop perturbation theory
Su, Nan
2012-01-01
The poor convergence of quantum field theory at finite temperature has been one of the main obstacles in the practical applications of thermal QCD for decades. Here we briefly review the progress of hard-thermal-loop perturbation theory (HTLpt) in reorganizing the perturbative expansion in order to improve the convergence. The quantum mechanical anharmonic oscillator is used as a simple example to show the breakdown of weak-coupling expansion, and variational perturbation theory is introduced as an effective resummation scheme for divergent weak-coupling expansions. We discuss HTLpt thermodynamic calculations for QED, pure-glue QCD, and QCD with N_f=3 up to three-loop order. The results suggest that HTLpt provides a systematic framework that can be used to calculate both static and dynamic quantities for temperatures relevant at LHC.
Bayesian analysis of truncation errors in chiral effective field theory
Melendez, J.; Furnstahl, R. J.; Klco, N.; Phillips, D. R.; Wesolowski, S.
2016-09-01
In the Bayesian approach to effective field theory (EFT) expansions, truncation errors are derived from degree-of-belief (DOB) intervals for EFT predictions. By encoding expectations about the naturalness of EFT expansion coefficients for observables, this framework provides a statistical interpretation of the standard EFT procedure where truncation errors are estimated using the order-by-order convergence of the expansion. We extend and test previous calculations of DOB intervals for chiral EFT observables, examine correlations between contributions at different orders and energies, and explore methods to validate the statistical consistency of the EFT expansion parameter. Supported in part by the NSF and the DOE.
Complex Langevin dynamics for chiral random matrix theory
Mollgaard, A.; Splittorff, K.
2013-12-01
We apply complex Langevin dynamics to chiral random matrix theory at nonzero chemical potential. At large quark mass, the simulations agree with the analytical results while incorrect convergence is found for small quark masses. The region of quark masses for which the complex Langevin dynamics converges incorrectly is identified as the region where the fermion determinant frequently traces out a path surrounding the origin of the complex plane during the Langevin flow. This links the incorrect convergence to an ambiguity in the Langevin force due to the presence of the logarithm of the fermion determinant in the action.
Complex Langevin Dynamics for chiral Random Matrix Theory
Mollgaard, A
2013-01-01
We apply complex Langevin dynamics to chiral random matrix theory at nonzero chemical potential. At large quark mass the simulations agree with the analytical results while incorrect convergence is found for small quark masses. The region of quark masses for which the complex Langevin dynamics converges incorrectly is identified as the region where the fermion determinant frequently traces out a path surrounding the origin of the complex plane during the Langevin flow. This links the incorrect convergence to an ambiguity in the Langevin force due to the presence of the logarithm of the fermion determinant in the action.
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.
Lie transforms and their use in Hamiltonian perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Cary, J.R.
1978-06-01
A review is presented of the theory of Lie transforms as applied to Hamiltonian systems. We begin by presenting some general background on the Hamiltonian formalism and by introducing the operator notation for canonical transformations. We then derive the general theory of Lie transforms. We derive the formula for the new Hamiltonian when one uses a Lie transform to effect a canonical transformation, and we use Lie transforms to prove a very general version of Noether's theorem, or the symmetry-equals-invariant theorem. Next we use the general Lie transform theory to derive Deprit's perturbation theory. We illustrate this perturbation theory by application to two well-known problems in classical mechanics. Finally we present a chapter on conventions. There are many ways to develop Lie transforms. The last chapter explains the reasons for the choices made here.
Dynamic aspect of the chiral phase transition in the mode coupling theory
Ohnishi, K; Ohta, K
2005-01-01
We analyze the dynamic aspect of the chiral phase transition. We apply the mode coupling theory to the linear sigma model and derive the kinetic equation for the chiral phase transition. We challenge Hohenberg and Halperin's classification scheme of dynamic critical phenomena in which the dynamic universality class of the chiral phase transition has been identified with that of the antiferromagnet. We point out a crucial difference between the chiral dynamics and the antiferromagnet system. We also calculate the dynamic critical exponent for the chiral phase transition. Our result is $z=1-\\eta/2\\cong 0.98$ which is contrasted with $z=d/2=1.5$ of the antiferromagnet.
Algebraic geometry informs perturbative quantum field theory
Broadhurst, David
2014-01-01
Single-scale Feynman diagrams yield integrals that are periods, namely projective integrals of rational functions of Schwinger parameters. Algebraic geometry may therefore inform us of the types of number to which these integrals evaluate. We give examples at 3, 4 and 6 loops of massive Feynman diagrams that evaluate to Dirichlet $L$-series of modular forms and examples at 6, 7 and 8 loops of counterterms that evaluate to multiple zeta values or polylogarithms of the sixth root of unity. At 8 loops and beyond, algebraic geometry informs us that polylogs are insufficient for the evaluation of terms in the beta-function of $\\phi^4$ theory. Here, modular forms appear as obstructions to polylogarithmic evaluation.
Epelbaum, Evgeny; Lee, Dean; Meißner, Ulf-G
2008-01-01
We present lattice calculations for the ground state energy of dilute neutron matter at next-to-leading order in chiral effective field theory. This study follows a series of recent papers on low-energy nuclear physics using chiral effective field theory on the lattice. In this work we introduce an improved spin- and isospin-projected leading-order action which allows for a perturbative treatment of corrections at next-to-leading order and smaller estimated errors. Using auxiliary fields and Euclidean-time projection Monte Carlo, we compute the ground state of 8, 12, and 16 neutrons in a periodic cube, covering a density range from 2% to 10% of normal nuclear density.
Chiral Fermions on the Lattice
Bietenholz, Wolfgang
2010-01-01
In the last century the non-perturbative regularization of chiral fermions was a long-standing problem. We review how this problem was finally overcome by the formulation of a modified but exact form of chiral symmetry on the lattice. This also provides a sound definition of the topological charge of lattice gauge configurations. We illustrate a variety of applications to QCD in the p-, the epsilon- and the delta-regime, where simulation results can now be related to Random Matrix Theory and Chiral Perturbation Theory. The latter contains Low Energy Constants as free parameters, and we comment on their evaluation from first principles of QCD.
Chiral effective field theory predictions for muon capture on deuteron and $^3$He
Energy Technology Data Exchange (ETDEWEB)
Laura E. Marcucci, A. Kievsky, S. Rosati, R. Schiavilla, M. Viviani
2012-01-01
The muon-capture reactions {sup 2}H({mu}{sup -}, {nu}{sub {mu}})nn and {sup 3}He({mu}{sup -},{nu}{sub {mu}}){sup 3}H are studied with nuclear strong-interaction potentials and charge-changing weak currents, derived in chiral effective field theory. The low-energy constants (LEC's) c{sub D} and c{sub E}, present in the three-nucleon potential and (c{sub D}) axial-vector current, are constrained to reproduce the A=3 binding energies and the triton Gamow-Teller matrix element. The vector weak current is related to the isovector component of the electromagnetic current via the conserved-vector-current constraint, and the two LEC's entering the contact terms in the latter are constrained to reproduce the A=3 magnetic moments. The muon capture rates on deuteron and {sup 3}He are predicted to be 399 {+-} 3 sec{sup -1} and 1494 {+-} 21 sec{sup -1}, respectively, where the spread accounts for the cutoff sensitivity as well as uncertainties in the LEC's and electroweak radiative corrections. By comparing the calculated and precisely measured rates on {sup 3}He, a value for the induced pseudoscalar form factor is obtained in good agreement with the chiral perturbation theory prediction.
Tensor perturbations in a general class of Palatini theories
Jiménez, Jose Beltrán; Olmo, Gonzalo J
2015-01-01
We study a general class of gravitational theories formulated in the Palatini approach and derive the equations governing the evolution of tensor perturbations. In the absence of torsion, the connection can be solved as the Christoffel symbols of an auxiliary metric which is non-trivially related to the space-time metric. We then consider background solutions corresponding to a perfect fluid and show that the tensor perturbations equations (including anisotropic stresses) for the auxiliary metric around such a background take an Einstein-like form. This facilitates the study in a homogeneous and isotropic cosmological scenario where we explicitly establish the relation between the auxiliary metric and the space-time metric tensor perturbations. As a general result, we show that both tensor perturbations coincide in the absence of anisotropic stresses.
Tensor perturbations in a general class of Palatini theories
Beltrán Jiménez, Jose; Heisenberg, Lavinia; Olmo, Gonzalo J.
2015-06-01
We study a general class of gravitational theories formulated in the Palatini approach and derive the equations governing the evolution of tensor perturbations. In the absence of torsion, the connection can be solved as the Christoffel symbols of an auxiliary metric which is non-trivially related to the space-time metric. We then consider background solutions corresponding to a perfect fluid and show that the tensor perturbations equations (including anisotropic stresses) for the auxiliary metric around such a background take an Einstein-like form. This facilitates the study in a homogeneous and isotropic cosmological scenario where we explicitly establish the relation between the auxiliary metric and the space-time metric tensor perturbations. As a general result, we show that both tensor perturbations coincide in the absence of anisotropic stresses.
Simple perturbative renormalization scheme for supersymmetric gauge theories
Energy Technology Data Exchange (ETDEWEB)
Foda, O.E. (Purdue Univ., Lafayette, IN (USA). Dept. of Physics)
1983-06-30
We show that the manifestly supersymmetric and gauge-invariant results of Supersymmetric Dimensional renormalization (SDR) are reproduceable through a simple, and mathematically consistent perturbative renormalization technique, where regularization is attained via a map that deforms the momentum space Feynman integrands in a specific way. In particular, it introduces a multiplicative factor of ((p+q)/..delta..)/sup -/delta in each momentum-space loop integral, where p is the magnitude of the loop momentum, q is an arbitrary constant to be chosen as will be explained, thus compensating for loss of translation invariance in p, ..lambda.. is a renormalization mass, and delta is a suitable non-integer: the analog of epsilon in dimensional schemes. All Dirac algebra and integration are four-dimensional, and renormalization is achieved by subtracting poles in delta, followed by setting delta->O. The mathematical inconsistencies of SDR are evaded by construction, since the numbers of fermion and boson degrees of freedom remain unchanged but analytic continuation in the number of dimensions is bypassed. Thus, the technique is equally viable in component and in superfield formalisms, and all anomalies are realized. The origin of the chiral anomaly is that no choice of q satisfies both gauge and chiral Ward identities simultaneously.
Effective gravitational couplings for cosmological perturbations in generalized Proca theories
De Felice, Antonio; Heisenberg, Lavinia; Kase, Ryotaro; Mukohyama, Shinji; Tsujikawa, Shinji; Zhang, Ying-li
2016-08-01
We consider the finite interactions of the generalized Proca theory including the sixth-order Lagrangian and derive the full linear perturbation equations of motion on the flat Friedmann-Lemaître-Robertson-Walker background in the presence of a matter perfect fluid. By construction, the propagating degrees of freedom (besides the matter perfect fluid) are two transverse vector perturbations, one longitudinal scalar, and two tensor polarizations. The Lagrangians associated with intrinsic vector modes neither affect the background equations of motion nor the second-order action of tensor perturbations, but they do give rise to nontrivial modifications to the no-ghost condition of vector perturbations and to the propagation speeds of vector and scalar perturbations. We derive the effective gravitational coupling Geff with matter density perturbations under a quasistatic approximation on scales deep inside the sound horizon. We find that the existence of intrinsic vector modes allows a possibility for reducing Geff. In fact, within the parameter space, Geff can be even smaller than the Newton gravitational constant G at the late cosmological epoch, with a peculiar phantom dark energy equation of state (without ghosts). The modifications to the slip parameter η and the evolution of the growth rate f σ8 are discussed as well. Thus, dark energy models in the framework of generalized Proca theories can be observationally distinguished from the Λ CDM model according to both cosmic growth and expansion history. Furthermore, we study the evolution of vector perturbations and show that outside the vector sound horizon the perturbations are nearly frozen and start to decay with oscillations after the horizon entry.
Perturbative Quantum Gravity and its Relation to Gauge Theory
Directory of Open Access Journals (Sweden)
Bern Zvi
2002-01-01
Full Text Available In this review we describe a non-trivial relationship between perturbative gauge theory and gravity scattering amplitudes. At the semi-classical or tree-level, the scattering amplitudes of gravity theories in flat space can be expressed as a sum of products of well defined pieces of gauge theory amplitudes. These relationships were first discovered by Kawai, Lewellen, and Tye in the context of string theory, but hold more generally. In particular, they hold for standard Einstein gravity. A method based on $D$-dimensional unitarity can then be used to systematically construct all quantum loop corrections order-by-order in perturbation theory using as input thegravity tree amplitudes expressed in terms of gauge theory ones. More generally, the unitarity method provides a means for perturbatively quantizing massless gravity theories without the usual formal apparatus associated with the quantization of constrained systems. As one application, this method was used to demonstrate that maximally supersymmetric gravity is less divergent in the ultraviolet than previously thought.
Taming Landau singularities in QCD perturbation theory: The analytic approach
Stefanis, N G
2013-01-01
The aim of this topical article is to outline the fundamental ideas underlying the recently developed Fractional Analytic Perturbation Theory (FAPT) of QCD and present its main calculational tools. For this, it is first necessary to review previous methods to apply QCD perturbation theory at low spacelike momentum scales, where the influence of the Landau singularities becomes inevitable. Several concepts are considered and their limitations are pointed out. The usefulness of FAPT is discussed in terms of two characteristic hadronic quantities: the perturbatively calculable part of the pion's electromagnetic form factor in the spacelike region and the Higgs-boson decay into a b\\bar b pair in the timelike region. In the first case, the focus is on the optimization of the prediction with respect to the choice of the renormalization scheme and the dependence on the renormalization and the factorization scales. The second case serves to show that the application of FAPT to this reaction reaches already at the fou...
Adjoint operators and perturbation theory of black holes
Cartas-Fuentevilla, R
2000-01-01
We present a new approach for finding conservation laws in the perturbation theory of black holes which applies for the more general cases of non-Hermitian equations governing the perturbations. The approach is based on a general result which establishes that a covariantly conserved current can be obtained from a solution of any system of homogeneous linear differential equations and a solution of the adjoint system. It is shown that the results obtained from the present approach become essentially the same (with some diferences) to those obtained by means of the traditional methods in the simplest black hole geometry corresponding to the Schwarzschild space-time. The future applications of our approach for studying the perturbations of black hole space-time in string theory is discussed.
Scherrer, Arne; Vuilleumier, Rodolphe; Sebastiani, Daniel
2016-08-01
We report the first fully ab initio calculation of dynamical vibrational circular dichroism spectra in the liquid phase using nuclear velocity perturbation theory (NVPT) derived electronic currents. Our approach is rigorous and general and thus capable of treating weak interactions of chiral molecules as, e.g., chirality transfer from a chiral molecule to an achiral solvent. We use an implementation of the NVPT that is projected along the dynamics to obtain the current and magnetic dipole moments required for accurate intensities. The gauge problem in the liquid phase is resolved in a twofold approach. The electronic expectation values are evaluated in a distributed origin gauge, employing maximally localized Wannier orbitals. In a second step, the gauge invariant spectrum is obtained in terms of a scaled molecular moments, which allows to systematically include solvent effects while keeping a significant signal-to-noise ratio. We give a thorough analysis and discussion of this choice of gauge for the liquid phase. At low temperatures, we recover the established double harmonic approximation. The methodology is applied to chiral molecules ((S)-d2-oxirane and (R)-propylene-oxide) in the gas phase and in solution. We find an excellent agreement with the theoretical and experimental references, including the emergence of signals due to chirality transfer from the solute to the (achiral) solvent.
Scherrer, Arne; Vuilleumier, Rodolphe; Sebastiani, Daniel
2016-08-28
We report the first fully ab initio calculation of dynamical vibrational circular dichroism spectra in the liquid phase using nuclear velocity perturbation theory (NVPT) derived electronic currents. Our approach is rigorous and general and thus capable of treating weak interactions of chiral molecules as, e.g., chirality transfer from a chiral molecule to an achiral solvent. We use an implementation of the NVPT that is projected along the dynamics to obtain the current and magnetic dipole moments required for accurate intensities. The gauge problem in the liquid phase is resolved in a twofold approach. The electronic expectation values are evaluated in a distributed origin gauge, employing maximally localized Wannier orbitals. In a second step, the gauge invariant spectrum is obtained in terms of a scaled molecular moments, which allows to systematically include solvent effects while keeping a significant signal-to-noise ratio. We give a thorough analysis and discussion of this choice of gauge for the liquid phase. At low temperatures, we recover the established double harmonic approximation. The methodology is applied to chiral molecules ((S)-d2-oxirane and (R)-propylene-oxide) in the gas phase and in solution. We find an excellent agreement with the theoretical and experimental references, including the emergence of signals due to chirality transfer from the solute to the (achiral) solvent.
Lattice regularization of gauge theories without loss of chiral symmetry
't Hooft, Gerardus
1994-01-01
Abstract: A lattice regularization procedure for gauge theories is proposed in which fermions are given a special treatment such that all chiral flavor symmetries that are free of Adler-Bell-Jackiw anomalies are kept intact. There is no doubling of fermionic degrees of freedom. A price paid for this feature is that the number of fermionic degrees of freedom per unit cell is still infinite, although finiteness of the complete functional integrals can be proven (details are outlined in an Appendix). Therefore, although perhaps of limited usefulness for numerical simulations, our scheme can be applied for studying aspects such as analytic convergence questions, spontaneous symmetry breakdown and baryon number violation in non-Abelian gauge theories.
Chishtie, F A
2002-01-01
Pade approximants (PA) have been widely applied in practically all areas of physics. This thesis focuses on developing PA as tools for both perturbative and non- perturbative quantum field theory (QFT). In perturbative QFT, we systematically estimate higher (unknown) loop terms via the asymptotic formula devised by Samuel et al. This algorithm, generally denoted as the asymptotic Pade approximation procedure (APAP), has greatly enhanced scope when it is applied to renormalization-group-(RG-) invariant quantities. A presently-unknown higher-loop quantity can then be matched with the approximant over the entire momentum region of phenomenological interest. Furthermore, the predicted value of the RG coefficients can be compared with the RG-accessible coefficients (at the higher-loop order), allowing a clearer indication of the accuracy of the predicted RG-inaccessible term. This methodology is applied to hadronic Higgs decay rates (H → bb¯ and H → gg, both within the Standard Model and...
Basics of thermal field theory - a tutorial on perturbative computations
Laine, Mikko; Vuorinen, Aleksi
2017-01-01
These lecture notes, suitable for a two-semester introductory course or self-study, offer an elementary and self-contained exposition of the basic tools and concepts that are encountered in practical computations in perturbative thermal field theory. Selected applications to heavy ion collision physics and cosmology are outlined in the last chapter.
The Breakdown of String Perturbation Theory for Many External Particles
Ghosh, Sudip
2016-01-01
We consider massless string scattering amplitudes in a limit where the number of external particles becomes very large, while the energy of each particle remains small. Using the growth of the volume of the relevant moduli space, and by means of independent numerical evidence, we argue that string perturbation theory breaks down in this limit. We discuss some remarkable implications for the information paradox.
Numerical study of chiral plasma instability within the classical statistical field theory approach
Buividovich, P V
2015-01-01
We report on a numerical study of the real-time dynamics of chirally imbalanced lattice Dirac fermions coupled to dynamical electromagnetic field. To this end we use the classical statistical field theory approach, in which the quantum evolution of fermions is simulated exactly, and electromagnetic fields are treated as classical. Motivated by recent experiments on chirally imbalanced Dirac semimetals, we use the Wilson-Dirac lattice Hamiltonian for fermions in order to model the emergent nature of chiral symmetry at low energies. In general, we observe that the backreaction of fermions on the electromagnetic field prevents the system from acquiring large chirality imbalance. In the case of chirality pumping in parallel electric and magnetic fields, electric field is screened by the produced on-shell fermions and the accumulation of chirality is hence stopped. In the case of evolution with initially present chirality imbalance, axial charge tends to decay at the expense of nonzero helicity of electromagnetic ...
Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin-Barnes Representation
Directory of Open Access Journals (Sweden)
Samuel Friot
2010-10-01
Full Text Available Using a method mixing Mellin-Barnes representation and Borel resummation we show how to obtain hyperasymptotic expansions from the (divergent formal power series which follow from the perturbative evaluation of arbitrary ''N-point'' functions for the simple case of zero-dimensional φ4 field theory. This hyperasymptotic improvement appears from an iterative procedure, based on inverse factorial expansions, and gives birth to interwoven non-perturbative partial sums whose coefficients are related to the perturbative ones by an interesting resurgence phenomenon. It is a non-perturbative improvement in the sense that, for some optimal truncations of the partial sums, the remainder at a given hyperasymptotic level is exponentially suppressed compared to the remainder at the preceding hyperasymptotic level. The Mellin-Barnes representation allows our results to be automatically valid for a wide range of the phase of the complex coupling constant, including Stokes lines. A numerical analysis is performed to emphasize the improved accuracy that this method allows to reach compared to the usual perturbative approach, and the importance of hyperasymptotic optimal truncation schemes.
Ward identities and gauge independence in general chiral gauge theories
Anselmi, Damiano
2015-01-01
Using the Batalin-Vilkovisky formalism, we study the Ward identities and the equations of gauge dependence in potentially anomalous general gauge theories, renormalizable or not. A crucial new term, absent in manifestly nonanomalous theories, is responsible for interesting effects. We prove that gauge invariance always implies gauge independence, which in turn ensures perturbative unitarity. Precisely, we consider potentially anomalous theories that are actually free of gauge anomalies thanks to the Adler-Bardeen theorem. We show that when we make a canonical transformation on the tree-level action, it is always possible to re-renormalize the divergences and re-fine-tune the finite local counterterms, so that the renormalized $\\Gamma $ functional of the transformed theory is also free of gauge anomalies, and is related to the renormalized $\\Gamma $ functional of the starting theory by a canonical transformation. An unexpected consequence of our results is that the beta functions of the couplings may depend on...
Nonperturbative Quantum Physics from Low-Order Perturbation Theory.
Mera, Héctor; Pedersen, Thomas G; Nikolić, Branislav K
2015-10-02
The Stark effect in hydrogen and the cubic anharmonic oscillator furnish examples of quantum systems where the perturbation results in a certain ionization probability by tunneling processes. Accordingly, the perturbed ground-state energy is shifted and broadened, thus acquiring an imaginary part which is considered to be a paradigm of nonperturbative behavior. Here we demonstrate how the low order coefficients of a divergent perturbation series can be used to obtain excellent approximations to both real and imaginary parts of the perturbed ground state eigenenergy. The key is to use analytic continuation functions with a built-in singularity structure within the complex plane of the coupling constant, which is tailored by means of Bender-Wu dispersion relations. In the examples discussed the analytic continuation functions are Gauss hypergeometric functions, which take as input fourth order perturbation theory and return excellent approximations to the complex perturbed eigenvalue. These functions are Borel consistent and dramatically outperform widely used Padé and Borel-Padé approaches, even for rather large values of the coupling constant.
Invariant exchange perturbation theory for multicenter systems: Time-dependent perturbations
Energy Technology Data Exchange (ETDEWEB)
Orlenko, E. V., E-mail: eorlenko@mail.ru; Evstafev, A. V.; Orlenko, F. E. [St. Petersburg State Technical University (Russian Federation)
2015-02-15
A formalism of exchange perturbation theory (EPT) is developed for the case of interactions that explicitly depend on time. Corrections to the wave function obtained in any order of perturbation theory and represented in an invariant form include exchange contributions due to intercenter electron permutations in complex multicenter systems. For collisions of atomic systems with an arbitrary type of interaction, general expressions are obtained for the transfer (T) and scattering (S) matrices in which intercenter electron permutations between overlapping nonorthogonal states belonging to different centers (atoms) are consistently taken into account. The problem of collision of alpha particles with lithium atoms accompanied by the redistribution of electrons between centers is considered. The differential and total charge-exchange cross sections of lithium are calculated.
Cosmological perturbation theory at three-loop order
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-09-15
We analyze the dark matter power spectrum at three-loop order in standard perturbation theory of large scale structure. We observe that at late times the loop expansion does not converge even for large scales (small momenta) well within the linear regime, but exhibits properties compatible with an asymptotic series. We propose a technique to restore the convergence in the limit of small momentum, and use it to obtain a perturbative expansion with improved convergence for momenta in the range where baryonic acoustic oscillations are present. Our results are compared with data from N-body simulations at different redshifts, and we find good agreement within this range.
Alien calculus and non perturbative effects in Quantum Field Theory
Bellon, Marc P.
2016-12-01
In many domains of physics, methods for dealing with non-perturbative aspects are required. Here, I want to argue that a good approach for this is to work on the Borel transforms of the quantities of interest, the singularities of which give non-perturbative contributions. These singularities in many cases can be largely determined by using the alien calculus developed by Jean Écalle. My main example will be the two point function of a massless theory given as a solution of a renormalization group equation.
Advanced Methods in Black-Hole Perturbation Theory
Pani, Paolo
2013-01-01
Black-hole perturbation theory is a useful tool to investigate issues in astrophysics, high-energy physics, and fundamental problems in gravity. It is often complementary to fully-fledged nonlinear evolutions and instrumental to interpret some results of numerical simulations. Several modern applications require advanced tools to investigate the linear dynamics of generic small perturbations around stationary black holes. Here, we present an overview of these applications and introduce extensions of the standard semianalytical methods to construct and solve the linearized field equations in curved spacetime. Current state-of-the-art techniques are pedagogically explained and exciting open problems are presented.
Strange quark asymmetry in the proton in chiral effective theory
Wang, X G; Melnitchouk, W; Salamu, Y; Thomas, A W; Wang, P
2016-01-01
We perform a comprehensive analysis of the strange-antistrange parton distribution function (PDF) asymmetry in the proton in the framework of chiral effective theory, including the full set of lowest order kaon loop diagrams with off-shell and contact interactions, in addition to the usual on-shell contributions previously discussed in the literature. We identify the presence of $\\delta$-function contributions to the $\\bar s$ PDF at $x=0$, with a corresponding valence-like component of the $s$-quark PDF at larger $x$, which allows greater flexibility for the shape of $s-\\bar s$. Expanding the moments of the PDFs in terms of the pseudoscalar kaon mass, we compute the leading nonanalytic behavior of the number and momentum integrals of the $s$ and $\\bar s$ distributions, consistent with the chiral symmetry of QCD. We discuss the implications of our results for the understanding of the NuTeV anomaly and for the phenomenology of strange quark PDFs in global QCD analysis.
Equivalence of Two Contour Prescriptions in Superstring Perturbation Theory
Sen, Ashoke
2016-01-01
Conventional superstring perturbation theory based on the world-sheet approach gives divergent results for the S-matrix whenever the total center of mass energy of the incoming particles exceeds the threshold of production of any final state consistent with conservation laws. Two systematic approaches have been suggested for dealing with this difficulty. The first one involves deforming the integration cycles over the moduli space of punctured Riemann surfaces into complexified moduli space. The second one treats the amplitude as a sum of superstring field theory Feynman diagrams and deforms the integration contours over loop energies of the Feynman diagram into the complex plane. In this paper we establish the equivalence of the two prescriptions to all orders in perturbation theory. Since the second approach is known to lead to unitary amplitudes, this establishes the consistency of the first prescription with unitarity.
Optimized Perturbation Theory at Finite Temperature Two-Loop Analysis
Chiku, S
2000-01-01
We study the optimized perturbation theory (OPT) at finite temperature, which is a self-consistent resummation method. Firstly, we generalize the idea of the OPT to optimize the coupling constant in lambda phi^4 theory, and give a proof of the renormalizability of this generalized OPT. Secondly, the principle of minimal sensitivity and the criterion of the fastest apparent convergence, which are conditions to determine the optimal parameter values, are examined in lambda phi^4 theory. Both conditions exhibit a second-order transition at finite temperature with critical exponent beta = 0.5 in the two-loop approximation.
Generalized Møller-Plesset Partitioning in Multiconfiguration Perturbation Theory.
Kobayashi, Masato; Szabados, Ágnes; Nakai, Hiromi; Surján, Péter R
2010-07-13
Two perturbation (PT) theories are developed starting from a multiconfiguration (MC) zero-order function. To span the configuration space, the theories employ biorthogonal vector sets introduced in the MCPT framework. At odds with previous formulations, the present construction operates with the full Fockian corresponding to a principal determinant, giving rise to a nondiagonal matrix of the zero-order resolvent. The theories provide a simple, generalized Møller-Plesset (MP) second-order correction to improve any reference function, corresponding either to a complete or incomplete model space. Computational demand of the procedure is determined by the iterative inversion of the Fockian, similarly to the single reference MP theory calculated in a localized basis. Relation of the theory to existing multireference (MR) PT formalisms is discussed. The performance of the present theories is assessed by adopting the antisymmetric product of strongly orthogonal geminal (APSG) wave functions as the reference function.
Chiral nucleon-nucleon forces in nuclear structure calculations
Directory of Open Access Journals (Sweden)
Coraggio L.
2016-01-01
Full Text Available Realistic nuclear potentials, derived within chiral perturbation theory, are a major breakthrough in modern nuclear structure theory, since they provide a direct link between nuclear physics and its underlying theory, namely the QCD. As a matter of fact, chiral potentials are tailored on the low-energy regime of nuclear structure physics, and chiral perturbation theory provides on the same footing two-nucleon forces as well as many-body ones. This feature fits well with modern advances in ab-initio methods and realistic shell-model. Here, we will review recent nuclear structure calculations, based on realistic chiral potentials, for both finite nuclei and infinite nuclear matter.
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
Adam, J.; Tater, M.; Truhlík, E.; Epelbaum, E.; Machleidt, R.; Ricci, P.
2012-03-01
The doublet capture rate Λ1 / 2 of the negative muon capture in deuterium is calculated employing the nuclear wave functions generated from accurate nucleon-nucleon (NN) potentials constructed at next-to-next-to-next-to-leading order of heavy-baryon chiral perturbation theory and the weak meson exchange current operator derived within the same formalism. All but one of the low-energy constants that enter the calculation were fixed from pion-nucleon and nucleon-nucleon scattering data. The low-energy constant dˆR (cD), which cannot be determined from the purely two-nucleon data, was extracted recently from the triton β-decay and the binding energies of the three-nucleon systems. The calculated values of Λ1 / 2 show a rather large spread for the used values of the dˆR. Precise measurement of Λ1 / 2 in the future will not only help to constrain the value of dˆR, but also provide a highly nontrivial test of the nuclear chiral EFT framework. Besides, the precise knowledge of the constant dˆR will allow for consistent calculations of other two-nucleon weak processes, such as proton-proton fusion and solar neutrino scattering on deuterons, which are important for astrophysics.
Adam, J; Tater, M; Truhlik, E; Epelbaum, E; Machleidt, R; Ricci, P
2011-01-01
The doublet capture rate of the negative muon capture in deuterium is calculated employing the nuclear wave functions generated from accurate nucleon-nucleon potentials constructed at next-to-next-to-next-to-leading order of heavy-baryon chiral perturbation theory and the weak meson exchange current operator derived within the same formalism. All but one of the low-energy constants that enter the calculation were fixed from pion-nucleon and nucleon-nucleon scattering data. The low-energy constant d^R (c_D), which cannot be determined from the purely two-nucleon data, was extracted recently from the triton beta-decay and the binding energies of the three-nucleon systems. The calculated values of the doublet capture rates show a rather large spread for the used values of the d^R. Precise measurement of the doublet capture rate in the future will not only help to constrain the value of d^R, but also provide a highly nontrivial test of the nuclear chiral EFT framework. Besides, the precise knowledge of the consta...
Real Representation in Chiral Gauge Theories on the Lattice
Suzuki, H
2000-01-01
The Weyl fermion belonging to the real representation of the gauge group provides a simple illustrative example for L\\"uscher's gauge-invariant lattice formulation of chiral gauge theories. We can explicitly construct the fermion integration measure globally over the gauge-field configuration space in the arbitrary topological sector; there is no global obstruction corresponding to the Witten anomaly. It is shown that this Weyl formulation is equivalent to a lattice formulation based on the Majorana (left--right-symmetric) fermion, in which the fermion partition function is given by the Pfaffian with a definite sign, up to physically irrelevant contact terms. This observation suggests a natural relative normalization of the fermion measure in different topological sectors for the Weyl fermion belonging to the complex representation.
Bayesian parameter estimation for chiral effective field theory
Wesolowski, Sarah; Furnstahl, Richard; Phillips, Daniel; Klco, Natalie
2016-09-01
The low-energy constants (LECs) of a chiral effective field theory (EFT) interaction in the two-body sector are fit to observable data using a Bayesian parameter estimation framework. By using Bayesian prior probability distributions (pdfs), we quantify relevant physical expectations such as LEC naturalness and include them in the parameter estimation procedure. The final result is a posterior pdf for the LECs, which can be used to propagate uncertainty resulting from the fit to data to the final observable predictions. The posterior pdf also allows an empirical test of operator redundancy and other features of the potential. We compare results of our framework with other fitting procedures, interpreting the underlying assumptions in Bayesian probabilistic language. We also compare results from fitting all partial waves of the interaction simultaneously to cross section data compared to fitting to extracted phase shifts, appropriately accounting for correlations in the data. Supported in part by the NSF and DOE.
Perturbations of single-field inflation in modified gravity theory
Directory of Open Access Journals (Sweden)
Taotao Qiu
2015-05-01
Full Text Available In this paper, we study the case of single field inflation within the framework of modified gravity theory where the gravity part has an arbitrary form f(R. Via a conformal transformation, this case can be transformed into its Einstein frame where it looks like a two-field inflation model. However, due to the existence of the isocurvature modes in such a multi-degree-of-freedom (m.d.o.f. system, the (curvature perturbations are not equivalent in two frames, so despite of its convenience, it is illegal to treat the perturbations in its Einstein frame as the “real” ones as we always do for pure f(R theory or single field with nonminimal coupling. Here by pulling the results of curvature perturbations back into its original Jordan frame, we show explicitly the power spectrum and spectral index of the perturbations in the Jordan frame, as well as how it differs from the Einstein frame. We also fit our results with the newest Planck data. Since there is large parameter space in these models, we show that it is easy to fit the data very well.
Perturbative algebraic quantum field theory an introduction for mathematicians
Rejzner, Kasia
2016-01-01
Perturbative Algebraic Quantum Field Theory (pAQFT), the subject of this book, is a complete and mathematically rigorous treatment of perturbative quantum field theory (pQFT) that doesn’t require the use of divergent quantities. We discuss in detail the examples of scalar fields and gauge theories and generalize them to QFT on curved spacetimes. pQFT models describe a wide range of physical phenomena and have remarkable agreement with experimental results. Despite this success, the theory suffers from many conceptual problems. pAQFT is a good candidate to solve many, if not all of these conceptual problems. Chapters 1-3 provide some background in mathematics and physics. Chapter 4 concerns classical theory of the scalar field, which is subsequently quantized in chapters 5 and 6. Chapter 7 covers gauge theory and chapter 8 discusses QFT on curved spacetimes and effective quantum gravity. The book aims to be accessible researchers and graduate students interested in the mathematical foundations of pQFT are th...
Perturbation theory and nonperturbative effects: A happy marriage ?
Chýla, J.
1992-03-01
Perturbation expansions in renormalized quantum field theories are reformulated in a way that permits a straightforward handling of situations when in the conventional approach, i.e. in fixed renormalization scheme, these expansions are factorially divergent and even of asymptotically constant sign. The result takes the form of convergent (under certain circumstances) expansions in a set of functions Z k(a, χ) of the couplant and the free parameter χ which specifies the procedure involved. The value of χ is shown to be correlated to the basic properties of nonperturbative effects as embodied in power corrections. Close connection of this procedure to Borel summation technique is demonstrated and its relation to conventional perturbation theory in fixed renormalization schemes elucidated.
On the non-linear scale of cosmological perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [Theory Division, CERN, 1211 Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas, E-mail: diego.blas@cern.ch, E-mail: mathias.garny@desy.de, E-mail: Thomas.Konstandin@desy.de [DESY, Notkestr. 85, 22607 Hamburg (Germany)
2013-09-01
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections at any order in perturbation theory. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
A gravitational memory effect in "boosted" black hole perturbation theory
Gleiser, R J; Dominguez, Alfredo E.; Gleiser, Reinaldo J.
2003-01-01
Black hole perturbation theory, or more generally, perturbation theory on a Schwarzschild bockground, has been applied in several contexts, but usually under the simplifying assumption that the ADM momentum vanishes, namely, that the evolution is carried out and observed in the ``center of momentum frame''. In this paper we consider some consequences of the inclusion of a non vanishing ADM momentum in the initial data. We first provide a justification for the validity of the transformation of the initial data to the ``center of momentum frame'', and then analyze the effect of this transformation on the gravitational wave amplitude. The most significant result is the possibility of a type of gravitational memory effect that appears to have no simple relation with the well known Christodoulou effect.
Perturbation Theory in Supersymmetric QED: Infrared Divergences and Gauge Invariance
Dine, Michael; Haber, Howard E; Haskins, Laurel Stephenson
2016-01-01
We study some aspects of perturbation theory in $N=1$ supersymmetric abelian gauge theories with massive charged matter. In general gauges, infrared (IR) divergences and nonlocal behavior arise in 1PI diagrams, associated with a $1/k^4$ term in the propagator for the vector superfield. We examine this structure in supersymmetric QED. The IR divergences are gauge-dependent and must cancel in physical quantities like the electron pole mass. We demonstrate that cancellation takes place in a nontrivial way, amounting to a reorganization of the perturbative series from powers of $e^2$ to powers of $e$. We also show how these complications are avoided in cases where a Wilsonian effective action can be defined.
Inflationary perturbation theory is geometrical optics in phase space
Seery, David; Frazer, Jonathan; Ribeiro, Raquel H
2012-01-01
A pressing problem in comparing inflationary models with observation is the accurate calculation of correlation functions. One approach is to evolve them using ordinary differential equations ("transport equations"), analogous to the Schwinger-Dyson hierarchy of in-out quantum field theory. We extend this approach to the complete set of momentum space correlation functions. A formal solution can be obtained using raytracing techniques adapted from geometrical optics. We reformulate inflationary perturbation theory in this language, and show that raytracing reproduces the familiar "delta N" Taylor expansion. Our method produces ordinary differential equations which allow the Taylor coefficients to be computed efficiently. We use raytracing methods to express the gauge transformation between field fluctuations and the curvature perturbation, zeta, in geometrical terms. Using these results we give a compact expression for the nonlinear gauge-transform part of fNL in terms of the principal curvatures of uniform e...
Microscopic Dirac Spectrum in a 2d Gauge Theory with Zero Chiral Condensate
2013-01-01
Fermionic theories with a vanishing chiral condensate (in the chiral limit) have recently attracted considerable interest; in particular variants of multi-flavour QCD are candidates for this behaviour. Here we consider the 2-flavour Schwinger model as a simple theory with this property. Based on simulations with light dynamical overlap fermions, we test the hypothesis that in such models the low lying Dirac eigenvalues could be decorrelated. That has been observed in 4d Yang-Mills theories at...
SUSY sine-Gordon theory as a perturbed conformal field theory and finite size effects
Bajnok, Z; Palla, L; Takács, G; Wagner, F
2004-01-01
We consider SUSY sine-Gordon theory in the framework of perturbed conformal field theory. Using an argument from Zamolodchikov, we obtain the vacuum structure and the kink adjacency diagram of the theory, which is cross-checked against the exact S matrix prediction, first-order perturbed conformal field theory (PCFT), the NLIE method and truncated conformal space approach. We provide evidence for consistency between the usual Lagrangian description and PCFT on the one hand, and between PCFT, NLIE and a massgap formula conjectured by Baseilhac and Fateev, on the other. In addition, we extend the NLIE description to all the vacua of the theory.
Feynman integral and perturbation theory in quantum tomography
Fedorov, Aleksey
2013-11-01
We present a definition for tomographic Feynman path integral as representation for quantum tomograms via Feynman path integral in the phase space. The proposed representation is the potential basis for investigation of Path Integral Monte Carlo numerical methods with quantum tomograms. Tomographic Feynman path integral is a representation of solution of initial problem for evolution equation for tomograms. The perturbation theory for quantum tomograms is constructed.
A modified multi-reference second order perturbation theory
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
A new scheme with extended model space is proposed to improve the calculation of multi-reference second order perturbation theory (MRPT2). The new scheme preserves the concise code structure of the original program, and avoids intruder states in constructions of the potential energy surface, which is confirmed by a series of comparable calculations. The new MRPT2 program is an available tool for the research of molecular excited states and electronic spectrum.
Mathematical Derivation of Chiral Anomaly in Lattice Gauge Theory with Wilson's Action
Hattori, T G; Hattori, Tetsuya; Watanabe, Hiroshi
1998-01-01
Chiral U(1) anomaly is derived with mathematical rigor for a Euclidean fermion coupled to a smooth external U(1) gauge field on an even dimensional torus as a continuum limit of lattice regularized fermion field theory with the Wilson term in the action. The present work rigorously proves for the first time that the Wilson term correctly reproduces the chiral anomaly.
Density-functional perturbation theory goes time-dependent
Gebauer, Ralph; Rocca, Dario; Baroni, Stefano
2009-01-01
The scope of time-dependent density-functional theory (TDDFT) is limited to the lowest portion of the spectrum of rather small systems (a few tens of atoms at most). In the static regime, density-functional perturbation theory (DFPT) allows one to calculate response functions of systems as large as currently dealt with in ground-state simulations. In this paper we present an effective way of combining DFPT with TDDFT. The dynamical polarizability is first expressed as an off-diagonal matrix e...
Efficient perturbation theory to improve the density matrix renormalization group
Tirrito, Emanuele; Ran, Shi-Ju; Ferris, Andrew J.; McCulloch, Ian P.; Lewenstein, Maciej
2017-02-01
The density matrix renormalization group (DMRG) is one of the most powerful numerical methods available for many-body systems. It has been applied to solve many physical problems, including the calculation of ground states and dynamical properties. In this work, we develop a perturbation theory of the DMRG (PT-DMRG) to greatly increase its accuracy in an extremely simple and efficient way. Using the canonical matrix product state (MPS) representation for the ground state of the considered system, a set of orthogonal basis functions {| ψi> } is introduced to describe the perturbations to the ground state obtained by the conventional DMRG. The Schmidt numbers of the MPS that are beyond the bond dimension cutoff are used to define these perturbation terms. The perturbed Hamiltonian is then defined as H˜i j= ; its ground state permits us to calculate physical observables with a considerably improved accuracy compared to the original DMRG results. We benchmark the second-order perturbation theory with the help of a one-dimensional Ising chain in a transverse field and the Heisenberg chain, where the precision of the DMRG is shown to be improved O (10 ) times. Furthermore, for moderate L the errors of the DMRG and PT-DMRG both scale linearly with L-1 (with L being the length of the chain). The linear relation between the dimension cutoff of the DMRG and that of the PT-DMRG at the same precision shows a considerable improvement in efficiency, especially for large dimension cutoffs. In the thermodynamic limit we show that the errors of the PT-DMRG scale with √{L-1}. Our work suggests an effective way to define the tangent space of the ground-state MPS, which may shed light on the properties beyond the ground state. This second-order PT-DMRG can be readily generalized to higher orders, as well as applied to models in higher dimensions.
Quark-gluon vertex: A perturbation theory primer and beyond
Bermudez, R.; Albino, L.; Gutiérrez-Guerrero, L. X.; Tejeda-Yeomans, M. E.; Bashir, A.
2017-02-01
There has been growing evidence that the infrared enhancement of the form factors defining the full quark-gluon vertex plays an important role in realizing a dynamical breakdown of chiral symmetry in quantum chromodynamics, leading to the observed spectrum and properties of hadrons. Both the lattice and the Schwinger-Dyson communities have begun to calculate these form factors in various kinematical regimes of momenta involved. A natural consistency check for these studies is that they should match onto the perturbative predictions in the ultraviolet, where nonperturbative effects mellow down. In this article, we carry out a numerical analysis of the one-loop result for all the form factors of the quark-gluon vertex. Interestingly, even the one-loop results qualitatively encode most of the infrared enhancement features expected of their nonperturbative counter parts. We analyze various kinematical configurations of momenta: symmetric, on shell, and asymptotic. The on-shell limit enables us to compute anomalous chromomagnetic moment of quarks. The asymptotic results have implications for the multiplicative renormalizability of the quark propagator and its connection with the Landau-Khalatnikov-Fradkin transformations, allowing us to analyze and compare various Ansätze proposed so far.
Institute of Scientific and Technical Information of China (English)
WANG Zhi-Min; WANG Qing
2001-01-01
Bosonic part of SU(2)L U(1)Y effective chiral Lagrangian for electroweak symmetry breaking is derived from an underlying technicolor theory with no approximation. The underlying theory is assumed to be the most general gauge theory without fundamental scalars. A condensate is required to exist in the theory which breaks SU(2)L U(1)Y dynamically to U(1)em and the anomaly of the theory caused by gauge interaction must be cancelled. The formulation offers general definitions in terms of underlying theory for the low energy constants in effective chiral Lagrangian.``
Chiral Dynamics With Wilson Fermions
Splittorff, K
2012-01-01
Close to the continuum the lattice spacing affects the smallest eigenvalues of the Wilson Dirac operator in a very specific manner determined by the way in which the discretization breaks chiral symmetry. These effects can be computed analytically by means of Wilson chiral perturbation theory and Wilson random matrix theory. A number of insights on chiral Dynamics with Wilson fermions can be obtained from the computation of the microscopic spectrum of the Wilson Dirac operator. For example, the unusual volume scaling of the smallest eigenvalues observed in lattice simulations has a natural explanation. The dynamics of the eigenvalues of the Wilson Dirac operator also allow us to determine the additional low energy constants of Wilson chiral perturbation theory and to understand why the Sharpe-Singleton scenario is only realized in unquenched simulations.
Superstring Perturbation Theory and Ramond-Ramond Backgrounds
Berenstein, D E; Berenstein, David; Leigh, Robert G.
1999-01-01
We consider perturbative Type II superstring theory in the covariant NSR formalism in the presence of NSNS and RR backgrounds. A concrete example that we have in mind is the geometry of D3-branes which in the near-horizon region is AdS_5 x S_5, although our methods may be applied to other backgrounds as well. We show how conformal invariance of the string path integral is maintained order by order in the number of holes. This procedure makes uses of the Fischler-Susskind mechanism to build up the background geometry. A simple formal expression is given for a \\sigma-model Lagrangian. This suggests a perturbative expansion in 1/g^2N and 1/N. As applications, we consider at leading order the mixing of RR and NSNS states, and the realization of the spacetime supersymmetry algebra.
Renewal theory for perturbed random walks and similar processes
Iksanov, Alexander
2016-01-01
This book offers a detailed review of perturbed random walks, perpetuities, and random processes with immigration. Being of major importance in modern probability theory, both theoretical and applied, these objects have been used to model various phenomena in the natural sciences as well as in insurance and finance. The book also presents the many significant results and efficient techniques and methods that have been worked out in the last decade. The first chapter is devoted to perturbed random walks and discusses their asymptotic behavior and various functionals pertaining to them, including supremum and first-passage time. The second chapter examines perpetuities, presenting results on continuity of their distributions and the existence of moments, as well as weak convergence of divergent perpetuities. Focusing on random processes with immigration, the third chapter investigates the existence of moments, describes long-time behavior and discusses limit theorems, both with and without scaling. Chapters fou...
Cosmological perturbation theory in the synchronous and conformal newtonian gauges
Ma Chung Pei; Ma, Chung Pei; Bertschinger, Edmund
1995-01-01
This paper presents a systematic treatment of the linear theory of scalar gravitational perturbations in the synchronous gauge and the conformal Newtonian (or longitudinal) gauge. It differs from others in the literature in that we give, in both gauges, a complete discussion of all particle species that are relevant to any flat cold dark matter (CDM), hot dark matter (HDM), or CDM+HDM models (including a possible cosmological constant). The particles considered include CDM, baryons, photons, massless neutrinos, and massive neutrinos (an HDM candidate), where the CDM and baryons are treated as fluids while a detailed phase-space description is given to the photons and neutrinos. Particular care is applied to the massive neutrino component, which has been either ignored or approximated crudely in previous works. Isentropic initial conditions on super-horizon scales are derived. The coupled, linearized Boltzmann, Einstein and fluid equations that govern the evolution of the metric and density perturbations are t...
Adiabaticity and gravity theory independent conservation laws for cosmological perturbations
Romano, Antonio Enea; Sasaki, Misao
2015-01-01
We carefully study the implications of adiabaticity for the behavior of cosmological perturbations. There are essentially three similar but different definitions of non-adiabaticity: one is appropriate for a thermodynamic fluid $\\delta P_{nad}$, another is for a general matter field $\\delta P_{c,nad}$, and the last one is valid only on superhorizon scales. The first two definitions coincide if $c_s^2=c_w^2$ where $c_s$ is the propagation speed of the perturbation, while $c_w^2=\\dot P/\\dot\\rho$. Assuming the adiabaticity in the general sense, $\\delta P_{c,nad}=0$, we derive a relation between the lapse function in the comoving slicing $A_c$ and $\\delta P_{nad}$ valid for arbitrary matter field in any theory of gravity, by using only momentum conservation. The relation implies that as long as $c_s\
Power counting for nuclear forces in chiral effective field theory
Long, Bingwei
2016-01-01
The present note summarizes the discourse on power counting issues of chiral nuclear forces, with an emphasis on renormalization-group invariance. Given its introductory nature, I will lean toward narrating a coherent point of view on the concepts, rather than covering comprehensively the development of chiral nuclear forces in different approaches.
Power counting for nuclear forces in chiral effective field theory
Long, Bingwei
2016-02-01
The present note summarizes the discourse on power counting issues of chiral nuclear forces, with an emphasis on renormalization-group invariance. Given its introductory nature, I will lean toward narrating a coherent point of view on the concepts, rather than covering comprehensively the development of chiral nuclear forces in different approaches.
Wavefunction of the Universe and Chern-Simons perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Soo Chopin [Department of Physics, National Cheng Kung University Tainan 70101, Taiwan (China)
2002-03-21
The Chern-Simons exact solution of four-dimensional quantum gravity with nonvanishing cosmological constant is presented in metric variables as the partition function of Chern-Simons theory with nontrivial source. The perturbative expansion is given, and the wavefunction is computed to the lowest order of approximation for the Cauchy surface which is topologically a 3-sphere. The state is well-defined even at degenerate and vanishing values of the dreibein. Reality conditions for the Ashtekar variables are also taken into account, and remarkable features of the Chern-Simons state and their relevance to cosmology are pointed out.
Perturbative Vacuum Wavefunctional for Gauge Theories in the Milne Space
Jeon, Sangyong
2015-01-01
The spectrum of vacuum fluctuations in the Milne space (i.e. the tau-eta coordinate system) is an important ingredient in the thermalization studies in relativistic heavy ion collisions. In this paper, the Schrodinger functional for the gauge theory perturbative vacuum is derived for the Milne space. The Wigner-transform of the corresponding vacuum density functional is also found together with the propagators. We finally identify the fluctuation spectrum in vacuum, and show the equivalence between the present approach and the symplectic product based method.
Perfect Lattice Perturbation Theory A Study of the Anharmonic Oscillator
Bietenholz, W
1999-01-01
As an application of perfect lattice perturbation theory, we construct an O(\\lambda) perfect lattice action for the anharmonic oscillator analytically in momentum space. In coordinate space we obtain a set of 2-spin and 4-spin couplings \\propto \\lambda, which we evaluate for various masses. These couplings never involve variables separated by more than two lattice spacings. The O(\\lambda) perfect action is simulated and compared to the standard action. We discuss the improvement for the first two energy gaps \\Delta E_1, \\Delta E_2 and for the scaling quantity \\Delta E_2 / \\Delta E1 in different regimes of the interaction parameter, and of the correlation length.
Tritium $\\beta$-decay in chiral effective field theory
Baroni, A; Kievsky, A; Marcucci, L E; Schiavilla, R; Viviani, M
2016-01-01
We evaluate the Fermi and Gamow-Teller (GT) matrix elements in tritium \\beta-decay by including in the charge-changing weak current the corrections up to one loop recently derived in nuclear chiral effective field theory (\\chi EFT). The trinucleon wave functions are obtained from hyperspherical-harmonics solutions of the Schrodinger equation with two- and three-nucleon potentials corresponding to either \\chi EFT (the N3LO/N2LO combination) or meson-exchange phenomenology (the AV18/UIX combination). We find that contributions due to loop corrections in the axial current are, in relative terms, as large as (and in some cases, dominate) those from one-pion exchange, which nominally occur at lower order in the power counting. We also provide values for the low-energy constants multiplying the contact axial current and three-nucleon potential, required to reproduce the experimental GT matrix element and trinucleon binding energies in the N3LO/N2LO and AV18/UIX calculations.
Higgs boson mass limits in perturbative unification theories
Tobe, K; Tobe, Kazuhiro; Wells, James D.
2002-01-01
Motivated in part by recent demonstrations that electroweak unification into a simple group may occur at a low scale, we detail the requirements on the Higgs mass if the unification is to be perturbative. We do this for the Standard Model effective theory, minimal supersymmetry, and next-to-minimal supersymmetry with an additional singlet field. Within the Standard Model framework, we find that perturbative unification with sin2(thetaW)=1/4 occurs at Lambda=3.8 TeV and requires m_h<460 GeV, whereas perturbative unification with sin2(thetaW)=3/8 requires mh<200 GeV. In supersymmetry, the presentation of the Higgs mass predictions can be significantly simplified, yet remain meaningful, by using a single supersymmetry breaking parameter Delta_S. We present Higgs mass limits in terms of Delta_S for the minimal supersymmetric model and the next-to-minimal supersymmetric model. We show that in next-to-minimal supersymmetry, the Higgs mass upper limit can be as large as 500 GeV even for moderate supersymmetry ...
Parity violation in few-nucleon systems within a chiral effective field theory framework
Viviani, Michele
2016-09-01
We study the effect the nucleon-nucleon parity violation (PV) interaction, induced by the weak interaction between quarks, in few-nucleon systems. First, we discuss the derivation of the nucleon-nucleon PV interaction within a chiral effective field theory framework, in particular its extension to next-to-next-to-leading order (N2LO), recently reported in. We report on an alternative derivation of this N2LO PV interaction using our technique based on the time-ordered perturbation theory, accounting also for cancellations between the contributions of irreducible diagrams and the contributions due to non-static corrections from energy denominators of reducible diagrams. Ultraviolet divergences associated with the loop corrections are isolated in dimensional regularization. A detailed analysis of the number of independent low-energy constants (LEC's) entering the potential is carried out. Then, we investigate PV effects induced by this updated potential on several few-nucleon observables, including the p-> - p longitudinal asymmetry, the neutron spin rotation in n-> - p and n-> - d scattering, and the longitudinal asymmetry in the 3He (n-> , p)3 H charge-exchange reaction.
Takahashi, Kazufumi
2016-01-01
We analyze the mode stability of odd-parity perturbations of black holes with linearly time-dependent scalar hair in shift-symmetric Horndeski theories. We show that a large class of black-hole solutions in these theories suffer from ghost or gradient instability, while there are some classes of solutions that are stable under linear odd-parity perturbations in the context of mode analysis.
SMD-based numerical stochastic perturbation theory arXiv
Dalla Brida, Mattia
The viability of a variant of numerical stochastic perturbation theory, where the Langevin equation is replaced by the SMD algorithm, is examined. In particular, the convergence of the process to a unique stationary state is rigorously established and the use of higher-order symplectic integration schemes is shown to be highly profitable in this context. For illustration, the gradient-flow coupling in finite volume with Schr\\"odinger functional boundary conditions is computed to two-loop (i.e. NNL) order in the SU(3) gauge theory. The scaling behaviour of the algorithm turns out to be rather favourable in this case, which allows the computations to be driven close to the continuum limit.
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...
Exponential time-dependent perturbation theory in rotationally inelastic scattering
Cross, R. J.
1983-08-01
An exponential form of time-dependent perturbation theory (the Magnus approximation) is developed for rotationally inelastic scattering. A phase-shift matrix is calculated as an integral in time over the anisotropic part of the potential. The trajectory used for this integral is specified by the diagonal part of the potential matrix and the arithmetic average of the initial and final velocities and the average orbital angular momentum. The exponential of the phase-shift matrix gives the scattering matrix and the various cross sections. A special representation is used where the orbital angular momentum is either treated classically or may be frozen out to yield the orbital sudden approximation. Calculations on Ar+N2 and Ar+TIF show that the theory generally gives very good agreement with accurate calculations, even where the orbital sudden approximation (coupled-states) results are seriously in error.
The perturbative structure of spin glass field theory
Temesvári, T.
2014-03-01
Cubic replicated field theory is used to study the glassy phase of the short-range Ising spin glass just below the transition temperature, and for systems above, at, and slightly below the upper critical dimension six. The order parameter function is computed up to two-loop order. There are two, well-separated bands in the mass spectrum, just as in mean field theory. The small mass band acts as an infrared cutoff, whereas contributions from the large mass region can be computed perturbatively (d>6), or interpreted by the ɛ-expansion around the critical fixed point (d=6-ɛ). The one-loop calculation of the (momentum-dependent) longitudinal mass, and the whole replicon sector is also presented. The innocuous behavior of the replicon masses while crossing the upper critical dimension shows that the ultrametric replica symmetry broken phase remains stable below six dimensions.
The perturbative structure of spin glass field theory
Energy Technology Data Exchange (ETDEWEB)
Temesvári, T., E-mail: temtam@helios.elte.hu
2014-03-15
Cubic replicated field theory is used to study the glassy phase of the short-range Ising spin glass just below the transition temperature, and for systems above, at, and slightly below the upper critical dimension six. The order parameter function is computed up to two-loop order. There are two, well-separated bands in the mass spectrum, just as in mean field theory. The small mass band acts as an infrared cutoff, whereas contributions from the large mass region can be computed perturbatively (d>6), or interpreted by the ϵ-expansion around the critical fixed point (d=6−ϵ). The one-loop calculation of the (momentum-dependent) longitudinal mass, and the whole replicon sector is also presented. The innocuous behavior of the replicon masses while crossing the upper critical dimension shows that the ultrametric replica symmetry broken phase remains stable below six dimensions.
Large-$N_c$ gauge theory and chiral random matrix theory
Hanada, Masanori; Yamada, Norikazu
2013-01-01
We discuss how the $1/N_c$ expansion and the chiral random matrix theory ($\\chi$RMT) can be used in the study of large-$N_c$ gauge theories. We first clarify the parameter region in which each of these two approaches is valid: while the fermion mass $m$ is fixed in the standard large-$N_c$ arguments ('t Hooft large-$N_c$ limit), $m$ must be scaled appropriately with a certain negative power of $N_c$ in order for the gauge theories to be described by the $\\chi$RMT. Then, although these two limits are not compatible in general, we show that the breakdown of chiral symmetry can be detected by combining the large-$N_c$ argument and the $\\chi$RMT with some cares. As a concrete example, we numerically study the four dimensional $SU(N_c)$ gauge theory with $N_f=2$ heavy adjoint fermions, introduced as the center symmetry preserver keeping the infrared physics intact, on a $2^4$ lattice. By looking at the low-lying eigenvalues of the Dirac operator for a massless probe fermion in the adjoint representation, we find t...
Stringy horizons and generalized FZZ duality in perturbation theory
Giribet, Gaston
2017-02-01
We study scattering amplitudes in two-dimensional string theory on a black hole bakground. We start with a simple derivation of the Fateev-Zamolodchikov-Zamolodchikov (FZZ) duality, which associates correlation functions of the sine-Liouville integrable model on the Riemann sphere to tree-level string amplitudes on the Euclidean two-dimensional black hole. This derivation of FZZ duality is based on perturbation theory, and it relies on a trick originally due to Fateev, which involves duality relations between different Selberg type integrals. This enables us to rewrite the correlation functions of sine-Liouville theory in terms of a special set of correlators in the gauged Wess-Zumino-Witten (WZW) theory, and use this to perform further consistency checks of the recently conjectured Generalized FZZ (GFZZ) duality. In particular, we prove that n-point correlation functions in sine-Liouville theory involving n - 2 winding modes actually coincide with the correlation functions in the SL(2,R)/U(1) gauged WZW model that include n - 2 oscillator operators of the type described by Giveon, Itzhaki and Kutasov in reference [1]. This proves the GFZZ duality for the case of tree level maximally winding violating n-point amplitudes with arbitrary n. We also comment on the connection between GFZZ and other marginal deformations previously considered in the literature.
Stringy horizons and generalized FZZ duality in perturbation theory
Giribet, Gaston
2016-01-01
We study scattering amplitudes in two-dimensional string theory on a black hole bakground. We start with a simple derivation of the Fateev-Zamolodchikov-Zamolodchikov (FZZ) duality, which associates correlation functions of the sine-Liouville integrable model on the Riemann sphere to tree-level string amplitudes on the Euclidean two-dimensional black hole. This derivation of FZZ duality is based on perturbation theory, and it relies on a trick originally due to Fateev, which involves duality relations between different Selberg type integrals. This enables us to rewrite the correlation functions of sine-Liouville theory in terms of a special set of correlators in the gauged Wess-Zumino-Witten (WZW) theory, and use this to perform further consistency checks of the recently conjectured Generalized FZZ (GFZZ) duality. In particular, we prove that n-point correlation functions in sine-Liouville theory involving n-2 winding modes actually coincide with the correlation functions in the SL(2,R)/U(1) gauged WZW model ...
The chirally rotated Schr\\"odinger functional: theoretical expectations and perturbative tests
Brida, Mattia Dalla; Vilaseca, Pol
2016-01-01
The chirally rotated Schr\\"odinger functional ($\\chi$SF) with massless Wilson-type fermions provides an alternative lattice regularization of the Schr\\"odinger functional (SF), with different lattice symmetries and a common continuum limit expected from universality. The explicit breaking of flavour and parity symmetries needs to be repaired by tuning the bare fermion mass and the coefficient of a dimension 3 boundary counterterm. Once this is achieved one expects the mechanism of automatic O($a$) improvement to be operational in the $\\chi$SF, in contrast to the standard formulation of the SF. This is expected to significantly improve the attainable precision for step-scaling functions of some composite operators. Furthermore, the $\\chi$SF offers new strategies to determine finite renormalization constants which are traditionally obtained from chiral Ward identities. In this paper we consider a complete set of fermion bilinear operators, define corresponding correlation functions and explain the relation to t...
Technical fine-tuning problem in renormalized perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Foda, O.E.
1983-01-01
The technical - as opposed to physical - fine tuning problem, i.e. the stability of tree-level gauge hierarchies at higher orders in renormalized perturbation theory, in a number of different models is studied. These include softly-broken supersymmetric models, and non-supersymmetric ones with a hierarchy of spontaneously-broken gauge symmetries. The models are renormalized using the BPHZ prescription, with momentum subtractions. Explicit calculations indicate that the tree-level hierarchy is not upset by the radiative corrections, and consequently no further fine-tuning is required to maintain it. Furthermore, this result is shown to run counter to that obtained via Dimensional Renormalization, (the only scheme used in previous literature on the subject). The discrepancy originates in the inherent local ambiguity in the finite parts of subtracted Feynman integrals. Within fully-renormalized perturbation theory the answer to the technical fine-tuning question (in the sense of whether the radiative corrections will ''readily'' respect the tree level gauge hierarchy or not) is contingent on the renormalization scheme used to define the model at the quantum level, rather than on the model itself. In other words, the need for fine-tuning, when it arises, is an artifact of the application of a certain class of renormalization schemes.
Recent Developments in String Theory From Perturbative Dualities to M-Theory
Haack, M; Lüst, Dieter; Haack, Michael; Kors, Boris; Lust, Dieter
1999-01-01
These lectures intend to give a pedagogical introduction into some of the developments in string theory during the last years. They include perturbative T-duality and non perturbative S- and U-dualities, their unavoidable demand for D-branes, an example of enhanced gauge symmetry at fixed points of the T-duality group, a review of classical solitonic solutions in general relativity, gauge theories and tendimensional supergravity, a discussion of their BPS nature, Polchinski's observations that allow to view D-branes as RR charged states in the non perturbative string spectrum, the application of all this to the computation of the black hole entropy and Hawking radiation and finally a brief survey of how everything fits together in M-theory.
On invariants and scalar chiral correlation functions in N=1 superconformal field theories
Knuth, Holger
2010-01-01
A general expression for the four-point function with vanishing total R-charge of anti-chiral and chiral superfields in N=1 superconformal theories is given. It is obtained by applying the exponential of a simple universal nilpotent differential operator to an arbitrary function of two cross ratios. To achieve this the nilpotent superconformal invariants according to Park are focused. Several dependencies between these invariants are presented, so that eight nilpotent invariants and 27 monomials of these invariants of degree d>2 are left being linearly independent. It is analyzed, how terms within the four-point function of general scalar superfields cancel in order to fulfill the chiral restrictions.
Cosmological Perturbation Theory and the Evolution of Small-Scale Inhomogeneities
Miedema, P G
2011-01-01
It is shown that a first-order cosmological perturbation theory for the open, flat and closed Friedmann-Lemaitre-Robertson-Walker universes admits one, and only one, gauge-invariant variable which describes the perturbation to the energy density and which becomes equal to the usual Newtonian energy density in the non-relativistic limit. The same holds true for the perturbation to the particle number density. Using these two new variables, a new manifestly gauge-invariant cosmological perturbation theory based on the Lifshitz-Khalatnikov theory has been developed. Perturbations in the total energy density are gravitationally coupled to perturbations in the particle number density, irrespective of the nature of the particles. There is, in first-order, no back-reaction of perturbations to the global expansion of the universe. Small-scale perturbations in the radiation-dominated era oscillate with an increasing amplitude. Density perturbations do not evolve adiabatically, as is usually assumed, but diabatically, ...
Chiral thermodynamics of nuclear matter
Energy Technology Data Exchange (ETDEWEB)
Fiorilla, Salvatore
2012-10-23
The equation of state of nuclear matter is calculated at finite temperature in the framework of in-medium chiral perturbation theory up to three-loop order. The dependence of its thermodynamic properties on the isospin-asymmetry is investigated. The chiral quark condensate is evaluated for symmetric nuclear matter. Its behaviour as a function of density and temperature sets important nuclear physics constraints for the QCD phase diagram.
Topological string theory, modularity and non-perturbative physics
Energy Technology Data Exchange (ETDEWEB)
Rauch, Marco
2011-09-15
In this thesis the holomorphic anomaly of correlators in topological string theory, matrix models and supersymmetric gauge theories is investigated. In the first part it is shown how the techniques of direct integration known from topological string theory can be used to solve the closed amplitudes of Hermitian multi-cut matrix models with polynomial potentials. In the case of the cubic matrix model, explicit expressions for the ring of non-holomorphic modular forms that are needed to express all closed matrix model amplitudes are given. This allows to integrate the holomorphic anomaly equation up to holomorphic modular terms that are fixed by the gap condition up to genus four. There is an one-dimensional submanifold of the moduli space in which the spectral curve becomes the Seiberg-Witten curve and the ring reduces to the non-holomorphic modular ring of the group {gamma}(2). On that submanifold, the gap conditions completely fix the holomorphic ambiguity and the model can be solved explicitly to very high genus. Using these results it is possible to make precision tests of the connection between the large order behavior of the 1/N expansion and non-perturbative effects due to instantons. Finally, it is argued that a full understanding of the large genus asymptotics in the multi-cut case requires a new class of non-perturbative sectors in the matrix model. In the second part a holomorphic anomaly equation for the modified elliptic genus of two M5-branes wrapping a rigid divisor inside a Calabi-Yau manifold is derived using wall-crossing formulae and the theory of mock modular forms. The anomaly originates from restoring modularity of an indefinite theta-function capturing the wall-crossing of BPS invariants associated to D4- D2-D0 brane systems. The compatibility of this equation with anomaly equations previously observed in the context of N=4 topological Yang-Mills theory on P{sup 2} and E-strings obtained from wrapping M5-branes on a del Pezzo surface which in
On invariants and scalar chiral correlation functions in N=1 superconformal field theories
Knuth, Holger
2010-01-01
A general expression for the four-point function with vanishing total R-charge of anti-chiral and chiral superfields in N=1 superconformal theories is given. It is obtained by applying the exponential of a simple universal nilpotent differential operator to an arbitrary function of two cross ratios. To achieve this the nilpotent superconformal invariants according to Park are focused. Several dependencies between these invariants are presented, so that eight nilpotent invariants and 27 monomi...
Complex curves and non-perturbative effects in c=1 string theory
Alexandrov, S
2004-01-01
We investigate a complex curve in the $c=1$ string theory which provides a geometric interpretation for different kinds of D-branes. The curve is constructed for a theory perturbed by a tachyon potential using its matrix model formulation. The perturbation removes the degeneracy of the non-perturbed curve and allows to identify its singularities with ZZ branes. Also, using the constructed curve, we find non-perturbative corrections to the free energy and elucidate their CFT origin.
Second-order perturbation theory: problems on large scales
Pound, Adam
2015-01-01
In general-relativistic perturbation theory, a point mass accelerates away from geodesic motion due to its gravitational self-force. Because the self-force is small, one can often approximate the motion as geodesic. However, it is well known that self-force effects accumulate over time, making the geodesic approximation fail on long timescales. It is less well known that this failure at large times translates to a failure at large distances as well. At second perturbative order, two large-distance pathologies arise: spurious secular growth and infrared-divergent retarded integrals. Both stand in the way of practical computations of second-order self-force effects. Utilizing a simple flat-space scalar toy model, I develop methods to overcome these obstacles. The secular growth is tamed with a multiscale expansion that captures the system's slow evolution. The divergent integrals are eliminated by matching to the correct retarded solution at large distances. I also show how to extract conservative self-force ef...
One-Group Perturbation Theory Applied to Measurements with Void
Energy Technology Data Exchange (ETDEWEB)
Persson, Rolf
1966-09-15
Formulas suitable for evaluating progressive as well as single rod substitution measurements are derived by means of one-group perturbation theory. The diffusion coefficient may depend on direction and position. By using the buckling concept one can derive expressions which are quite simple and the perturbed flux can be taken into account in a comparatively simple way. By using an unconventional definition of cells a transition region is introduced quite logically. Experiments with voids around metal rods, diam. 3.05 cm, have been analysed. The agreement between extrapolated and directly measured buckling values is excellent, the buckling difference between lattices with water-filled and voided shrouds being 0. 263 {+-} 0.015/m{sup 2} and 0.267 {+-} 0.005/m{sup 2} resp. From single-rod experiments differences between diffusion coefficients are determined to {delta}D{sub r}/D = 0.083 {+-} 0.004 and {delta}D{sub z}/D = 0.120 {+-} 0.018. With air-filled shrouds there is consequently anisotropy in the neutron diffusion and we have (D{sub z}/D{sub r}){sub air} = 1.034 {+-} 0.020.
Instanton calculus and chiral one-point functions in supersymmetric gauge theories
Fujii, S; Moriyama, S; Okada, S; Fujii, Shigeyuki; Kanno, Hiroaki; Moriyama, Sanefumi; Okada, Soichi
2007-01-01
We compute topological one-point functions of the chiral operator Tr (\\phi^k) in the maximally confining phase of N=1 U(N) supersymmetric gauge theory, which is obtained from N=2 theory by turning on a tree level superpotential W(\\Phi). Localization theorem for toric action allows us to express these one-point functions as polynomials in the equivariant parameter \\hbar and the parameter of instanton expansion q=\\Lambda^{2N}. The chiral one-point functions are of particular interest from gauge/string theory correspondence, since they are related to the Gromov-Witten theory of P^1. Based on a combinatorial identity that gives summation formula over Young diagram of relevant functions, we find a relation among chiral one-point functions, which recursively determines the \\hbar expansion of the generating function of one-point functions.
Perturbative anti-brane potentials in heterotic M-theory
Energy Technology Data Exchange (ETDEWEB)
Gray, James [Institut d' Astrophysique de Paris and APC, Universite de Paris 7, 98 bis, Bd. Arago 75014, Paris (France); Lukas, Andre [Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP (United Kingdom); Ovrut, Burt [Department of Physics, University of Pennsylvania, Philadelphia, PA 19104-6395 (United States)
2007-01-15
We derive the perturbative four-dimensional effective theory describing heterotic M theory with branes and anti-branes in the bulk space. The back-reaction of both the branes and anti-branes is explicitly included. To first order in the heterotic {epsilon}{sub S} expansion, we find that the forces on branes and anti-branes vanish and that the KKLT procedure of simply adding to the supersymmetric theory the probe approximation to the energy density of the anti-brane reproduces the correct potential. However, there are additional non-supersymmetric corrections to the gauge-kinetic functions and matter terms. The new correction to the gauge kinetic functions is important in a discussion of moduli stabilization. At second order in the {epsilon}{sub S} expansion, we find that the forces on the branes and anti-branes become non-vanishing. These forces are not precisely in the naive form that one may have anticipated and, being second order in the small parameter {epsilon}{sub S}, they are relatively weak. This suggests that moduli stabilization in heterotic models with anti-branes is achievable. (authors)
Statistics of cosmic density profiles from perturbation theory
Bernardeau, Francis; Codis, Sandrine
2013-01-01
The joint probability distribution function (PDF) of the density within multiple concentric spherical cells is considered. It is shown how its cumulant generating function can be obtained at tree order in perturbation theory as the Legendre transform of a function directly built in terms of the initial moments. In the context of the upcoming generation of large-scale structure surveys, it is conjectured that this result correctly models such a function for finite values of the variance. Detailed consequences of this assumption are explored. In particular the corresponding one-cell density probability distribution at finite variance is computed for realistic power spectra, taking into account its scale variation. It is found to be in agreement with $\\Lambda$-CDM simulations at the few percent level for a wide range of density values and parameters. Related explicit analytic expansions at the low and high density tails are given. The conditional (at fixed density) and marginal probability of the slope -- the de...
Determination of the sediment carrying capacity based on perturbed theory.
Ni, Zhi-hui; Zeng, Qiang; Li-chun, Wu
2014-01-01
According to the previous studies of sediment carrying capacity, a new method of sediment carrying capacity on perturbed theory was proposed. By taking into account the average water depth, average flow velocity, settling velocity, and other influencing factors and introducing the median grain size as one main influencing factor in deriving the new formula, we established a new sediment carrying capacity formula. The coefficients were determined by the principle of dimensional analysis, multiple linear regression method, and the least square method. After that, the new formula was verified through measuring data of natural rivers and flume tests and comparing the verified results calculated by Cao Formula, Zhang Formula, Li Formula, Engelung-Hansen Formula, Ackers-White Formula, and Yang Formula. According to the compared results, it can be seen that the new method is of high accuracy. It could be a useful reference for the determination of sediment carrying capacity.
Efficient Cosmological Perturbation Theory with FAST-PT
Fang, Xiao; Blazek, Jonathan; McEwen, Joseph; Hirata, Christopher M.
2017-01-01
Cosmological perturbation theory is a powerful tool to model observations of large-scale structure in the weakly non-linear regime. However, even at next-to-leading order, it results in computationally expensive mode-coupling integrals. In this talk, I will focus on the physics behind our extremely efficient algorithm, FAST-PT. I will show how the algorithm can be applied to calculate 1-loop power spectra for several cosmological observables, including the matter density, galaxy bias, galaxy intrinsic alignments, the Ostriker-Vishniac effect, the secondary CMB polarization due to baryon flows, and redshift-space distortions. Our public code is written in Python and is easy to use and adapt to additional applications.
On the non-linear scale of cosmological perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-04-15
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
Perturbation treatment of symmetry breaking within random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Carvalho, J.X. de [Max-Planck-Institut fuer Physik komplexer Systeme, Noethnitzer Strasse 38, D-01187 Dresden (Germany); Instituto de Fisica, Universidade de Sao Paulo, C.P. 66318, 05315-970 Sao Paulo, S.P. (Brazil); Hussein, M.S. [Max-Planck-Institut fuer Physik komplexer Systeme, Noethnitzer Strasse 38, D-01187 Dresden (Germany); Instituto de Fisica, Universidade de Sao Paulo, C.P. 66318, 05315-970 Sao Paulo, S.P. (Brazil)], E-mail: mhussein@mpipks-dresden.mpg.de; Pato, M.P.; Sargeant, A.J. [Instituto de Fisica, Universidade de Sao Paulo, C.P. 66318, 05315-970 Sao Paulo, S.P. (Brazil)
2008-07-07
We discuss the applicability, within the random matrix theory, of perturbative treatment of symmetry breaking to the experimental data on the flip symmetry breaking in quartz crystal. We found that the values of the parameter that measures this breaking are different for the spacing distribution as compared to those for the spectral rigidity. We consider both two-fold and three-fold symmetries. The latter was found to account better for the spectral rigidity than the former. Both cases, however, underestimate the experimental spectral rigidity at large L. This discrepancy can be resolved if an appropriate number of eigenfrequencies is considered to be missing in the sample. Our findings are relevant for symmetry violation studies in general.
The Operator Product Expansion Beyond Perturbation Theory in QCD
Dominguez, C A
2010-01-01
The Operator Product Expansion (OPE) of current correlators at short distances beyond perturbation theory in QCD, together with Cauchy's theorem in the complex energy plane, are the pillars of the method of QCD sum rules. This technique provides an analytic tool to relate QCD with hadronic physics at low and intermediate energies. It has been in use for over thirty years to determine hadronic parameters, form factors, and QCD parameters such as the quark masses, and the running strong coupling at the scale of the $\\tau$-lepton. QCD sum rules provide a powerful complement to numerical simulations of QCD on the lattice. In this talk a short review of the method is presented for non experts, followed by three examples of recent applications.
Algebraic Quantum Gravity (AQG) III. Semiclassical Perturbation Theory
Giesel, K
2006-01-01
In the two previous papers of this series we defined a new combinatorical approach to quantum gravity, Algebraic Quantum Gravity (AQG). We showed that AQG reproduces the correct infinitesimal dynamics in the semiclassical limit, provided one incorrectly substitutes the non -- Abelean group SU(2) by the Abelean group $U(1)^3$ in the calculations. The mere reason why that substitution was performed at all is that in the non -- Abelean case the volume operator, pivotal for the definition of the dynamics, is not diagonisable by analytical methods. This, in contrast to the Abelean case, so far prohibited semiclassical computations. In this paper we show why this unjustified substitution nevertheless reproduces the correct physical result: Namely, we introduce for the first time semiclassical perturbation theory within AQG (and LQG) which allows to compute expectation values of interesting operators such as the master constraint as a power series in $\\hbar$ with error control. That is, in particular matrix elements...
Renormalisation and off-shell improvement in lattice perturbation theory
Capitani, S; Horsley, R; Perlt, H; Rakow, P E L; Schierholz, G; Schiller, A
2001-01-01
We discuss the improvement of flavour non-singlet point and one-link lattice quark operators, which describe the quark currents and the first moment of the DIS structure functions respectively. Suitable bases of improved operators are given, and the corresponding renormalisation factors and improvement coefficients are calculated in one-loop lattice perturbation theory, using the Sheikholeslami-Wohlert (clover) action. To this order we achieve off-shell improvement by eliminating the effect of contact terms. We use massive fermions, and our calculations are done keeping all terms up to first order in the lattice spacing, for arbitrary m^2/p^2, in a general covariant gauge. We also compare clover fermions with fermions satisfying the Ginsparg-Wilson relation, and show how to remove O(a) effects off-shell in this case too, and how this is in many aspects simpler than for clover fermions. Finally, tadpole improvement is also considered.
Exploring Perturbative Conformal Field Theory in Mellin space
Nizami, Amin A; Sarkar, Sourav; Verma, Mritunjay
2016-01-01
We explore the Mellin representation of correlation functions in conformal field theories in the weak coupling regime. We provide a complete proof for a set of Feynman rules to write the Mellin amplitude for a general tree level Feynman diagram involving only scalar operators. We find a factorised form involving beta functions associated to the propagators, similar to tree level Feynman rules in momentum space for ordinary QFTs. We also briefly consider the case where a generic scalar perturbation of the free CFT breaks conformal invariance. Mellin space still has some utility and one can consider non-conformal Mellin representations. In this context, we find that the beta function corresponding to conformal propagator uplifts to a hypergeometric function.
Exploring perturbative conformal field theory in Mellin space
Nizami, Amin A.; Rudra, Arnab; Sarkar, Sourav; Verma, Mritunjay
2017-01-01
We explore the Mellin representation of correlation functions in conformal field theories in the weak coupling regime. We provide a complete proof for a set of Feynman rules to write the Mellin amplitude for a general tree level Feynman diagram involving only scalar operators. We find a factorised form involving beta functions associated to the propagators, similar to tree level Feynman rules in momentum space for ordinary QFTs. We also briefly consider the case where a generic scalar perturbation of the free CFT breaks conformal invariance. Mellin space still has some utility and one can consider non-conformal Mellin representations. In this context, we find that the beta function corresponding to conformal propagator uplifts to a hypergeometric function.
Non-perturbative Thermodynamics in Matrix String Theory
Peñalba, J P
1999-01-01
A study of the thermodynamics in IIA Matrix String Theory is presented. The free string limit is calculated and seen to exactly reproduce the usual result. When energies are enough to excite non-perturbative objects like D-particles and specially membranes, the situation changes because they add a large number of degrees of freedom that do not appear at low energies. There seems to be a negative specific heat (even in the Microcanonical Ensemble) that moves the asymptotic temperature to zero. Besides, the mechanism of interaction and attachment of open strings to D-particles and D-membranes is analyzed. A first approach to type IIB Matrix String is carried out: its spectrum is found in the (2+1)-SYM and used to calculate an SL(2,Z) invariant partition function.
Energy Technology Data Exchange (ETDEWEB)
Vladimir Pascalutsa; Marc Vanderhaeghen
2006-01-20
We develop an extension of chiral perturbation theory to the {Delta}(1232)-resonance energy region and apply it to investigate the pion electroproduction off the nucleon (e{sup -} N {yields} e{sup -} N {pi}). We present a complete calculation of this process, in the {Delta}-resonance region, up to next-to-leading order in the {delta}-expansion. At this order, the only free parameters are the three low-energy constants corresponding to the magnetic (M1), electric (E2), and Coulomb (C2) {gamma} N {yields} {Delta} transition strength. After fitting these parameters to a few well-known data, our calculation provides a prediction for observables and multipole amplitudes of pion electroproduction. These results compare favorably with the phenomenological multipole solutions and recent experimental results from MIT-Bates and MAMI. Our prediction for the pion-mass dependence of the {gamma}N{Delta} form factors offers an explanation for the discrepancy between the recent lattice-QCD results and the experimental value for the ''C2/M1 ratio'' at low Q{sup 2}.
Jain, Shekhar; Dominik, Aleksandra; Chapman, Walter G
2007-12-28
A density functional theory based on Wertheim's first order perturbation theory is developed for inhomogeneous complex fluids. The theory is derived along similar lines as interfacial statistical associating fluid theory [S. Tripathi and W. G. Chapman, J. Chem. Phys. 122, 094506 (2005)]. However, the derivation is more general and applies broadly to a range of systems, retaining the simplicity of a segment density based theory. Furthermore, the theory gives the exact density profile for ideal chains in an external field. The general avail of the theory has been demonstrated by applying the theory to lipids near surfaces, lipid bilayers, and copolymer thin films. The theoretical results show excellent agreement with the results from molecular simulations.
Using Perturbation theory to reduce noise in diffusion tensor fields.
Bansal, Ravi; Staib, Lawrence H; Xu, Dongrong; Laine, Andrew F; Liu, Jun; Peterson, Bradley S
2009-08-01
We propose the use of Perturbation theory to reduce noise in Diffusion Tensor (DT) fields. Diffusion Tensor Imaging (DTI) encodes the diffusion of water molecules along different spatial directions in a positive definite, 3 x 3 symmetric tensor. Eigenvectors and eigenvalues of DTs allow the in vivo visualization and quantitative analysis of white matter fiber bundles across the brain. The validity and reliability of these analyses are limited, however, by the low spatial resolution and low Signal-to-Noise Ratio (SNR) in DTI datasets. Our procedures can be applied to improve the validity and reliability of these quantitative analyses by reducing noise in the tensor fields. We model a tensor field as a three-dimensional Markov Random Field and then compute the likelihood and the prior terms of this model using Perturbation theory. The prior term constrains the tensor field to be smooth, whereas the likelihood term constrains the smoothed tensor field to be similar to the original field. Thus, the proposed method generates a smoothed field that is close in structure to the original tensor field. We evaluate the performance of our method both visually and quantitatively using synthetic and real-world datasets. We quantitatively assess the performance of our method by computing the SNR for eigenvalues and the coherence measures for eigenvectors of DTs across tensor fields. In addition, we quantitatively compare the performance of our procedures with the performance of one method that uses a Riemannian distance to compute the similarity between two tensors, and with another method that reduces noise in tensor fields by anisotropically filtering the diffusion weighted images that are used to estimate diffusion tensors. These experiments demonstrate that our method significantly increases the coherence of the eigenvectors and the SNR of the eigenvalues, while simultaneously preserving the fine structure and boundaries between homogeneous regions, in the smoothed tensor
Stochastic many-body perturbation theory for anharmonic molecular vibrations
Energy Technology Data Exchange (ETDEWEB)
Hermes, Matthew R. [Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801 (United States); Hirata, So, E-mail: sohirata@illinois.edu [Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801 (United States); CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012 (Japan)
2014-08-28
A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm{sup −1} and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.
Stochastic many-body perturbation theory for anharmonic molecular vibrations.
Hermes, Matthew R; Hirata, So
2014-08-28
A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm(-1) and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.
An Ultraviolet Chiral Theory of the Top for the Fundamental Composite (Goldstone) Higgs
DEFF Research Database (Denmark)
Cacciapaglia, Giacomo; Sannino, Francesco
2016-01-01
We introduce a scalar-less anomaly free chiral gauge theory that serves as natural ultraviolet completion of models of fundamental composite (Goldstone) Higgs dynamics. The new theory is able to generate the top mass and furthermore features a built-in protection mechanism that naturally suppresses...
Vector form factor of the pion in chiral effective field theory
Directory of Open Access Journals (Sweden)
D. Djukanovic
2015-03-01
Full Text Available The vector form factor of the pion is calculated in the framework of chiral effective field theory with vector mesons included as dynamical degrees of freedom. To construct an effective field theory with a consistent power counting, the complex-mass scheme is applied.
Nuclear electromagnetic charge and current operators in Chiral EFT
Energy Technology Data Exchange (ETDEWEB)
Girlanda, Luca [Università del Salento; Marcucci, Laura Elisa [Univ. Pisa; Pastore, Saori [Department of Physics and Astronomy, University of South Carolina, Columbia, SC; Piarulli, Maria [Department of Physics, Old Dominion University, Norfolk, VA; Schiavilla, Rocco [Old Dominion U., JLAB; Viviani, Michele
2013-08-01
We describe our method for deriving the nuclear electromagnetic charge and current operators in chiral perturbation theory, based on time-ordered perturbation theory. We then discuss possible strategies for fixing the relevant low-energy constants, from the magnetic moments of the deuteron and of the trinucleons, and from the radiative np capture cross sections, and identify a scheme which, partly relying on {Delta} resonance saturation, leads to a reasonable pattern of convergence of the chiral expansion.
The nucleon and Delta-resonance masses in relativistic chiral effective-field theory
Energy Technology Data Exchange (ETDEWEB)
V. Pascalutsa; M. Vanderhaeghen
2005-11-28
We study the chiral behavior of the nucleon and De-isobar masses within a manifestly covariant chiral effective-field theory, consistent with the analyticity principle. We compute the {pi} N and {pi}{Delta} one-loop contributions to the mass and field-normalization constant, and find that they can be described in terms of universal relativistic loop functions, multiplied by appropriate spin, isospin and coupling constants. We show that these relativistic one-loop corrections, when properly renormalized, obey the chiral power-counting and vanish in the chiral limit. The results including only the {pi} N-loop corrections compare favorably with the lattice QCD data for the pion-mass dependence of the nucleon and De masses, while inclusion of the {pi}/De loops tends to spoil this agreement.
Structure of chiral phase transitions at finite temperature in abelian gauge theories
Energy Technology Data Exchange (ETDEWEB)
Fukazawa, Kenji [Kure National College of Technology, Kure (Japan); Inagaki, Tomohiro [Information Media Center, Hiroshima Univ., Hiroshima (Japan); Mukaigawa, Seiji [Department of Electrical and Electronic Engineering, Faculty of Engineering, Iwate Univ., Iwate (Japan); Muta, Taizo [Department of Physics, Hiroshima Univ., Hiroshima (Japan)
2001-06-01
The mechanism of chiral symmetry breaking is investigated in strong-coupling Abelian gauge theories at finite temperature. The Schwinger-Dyson equation in the Landau gauge is employed in the real time formalism and is solved numerically within the framework of the instantaneous exchange approximation, including the effect of the thermal mass for the photon propagator. It is found that the chiral symmetry is broken below the critical temperature T for sufficiently large coupling {alpha}. The chiral phase transition is found to be of second order, and the phase diagram in the T-{alpha} plane is obtained. It is investigated how the structure of the chiral phase transition is affected by the thermal mass in the photon propagator. (author)
Structure of chiral phase transitions at finite temperature in Abelian gauge theories
Fukazawa, K; Mukaigawa, S; Muta, T; Fukazawa, Kenji; Inagaki, Tomohiro; Mukaigawa, Seiji; Muta, Taizo
1999-01-01
The mechanism of the chiral symmetry breaking is investigated in the strong-coupling Abelian gauge theories at finite temperature. The Schwinger-Dyson equation in Landau gauge is employed in the real time formalism and is solved numerically within the framework of the instantaneous exchange approximation including the effect of the hard thermal loop for the photon propagator. It is found that the chiral symmetry is broken below the critical temperature T for sufficiently large coupling. The chiral phase transition is found to be of the 2nd order and the phase diagram on the $T-\\alpha$ plane is obtained. It is investigated how the structure of the chiral phase transition is affected by the hard thermal loops in the photon propagator.
Ph.D. Thesis: Chiral Effective Field Theory Beyond the Power-Counting Regime
Hall, Jonathan M M
2011-01-01
Novel techniques are presented, which identify the power-counting regime (PCR) of chiral effective field theory, and allow the use of lattice quantum chromodynamics results that extend outside the PCR. By analyzing the renormalization of low-energy coefficients of the chiral expansion of the nucleon mass, the existence of an optimal regularization scale is realized. The techniques developed for the nucleon mass renormalization are then applied to a test case: performing a chiral extrapolation without prior phenomenological bias. The robustness of the procedure for obtaining an optimal regularization scale and performing a reliable chiral extrapolation is confirmed. The procedure developed is then applied to the magnetic moment and the electric charge radius of the nucleon. The consistency of the results for the value of the optimal regularization scale provides strong evidence for the existence of an intrinsic energy scale in the nucleon-pion interaction.
Theory of Microwave 3-WAVE Mixing of Chiral Molecules
Lehmann, Kevin
2016-06-01
The traditional spectroscopic methods to measure enantiomeric excess, based upon optical rotation or circular dichroism arise from an interference of electric and magnetic dipole contributions of an optical transitions. The later is relativisitic and gets smaller with decreasing frequency and thus these effects have not been previously observed in pure rotational spectroscopy. First introduced by the group at Harvard^1, it is possible to use a 3-wave mixing method (with one of the fields potentially a Stark Field) to distinguish enantiomers if the three wave are nonplaner. In the conceptually simplest form of this experiment, a molecule is polarized with X polarization on a a → b transition, and then the resulting ρab molecular coherence is transferred to a ρac coherence by application of a π pulse on the b → c transition. For a chiral molecule with nonzero dipole projections on the three inertial axes, this ρac coherence can radiate Z polarized emission at the frequency of the a → c transition. In this talk, I will present the full theory of such experiments, including accounting for dirrection cosine matrix elements and M degeneracy. The resulting expressions can be used to calculate the expected size of the signal as a function of the specific transitions used in the a → b → c → a cycle.^2 It will be demonstrated that the maximum size of the ρac coherence is nearly that generated by a ``π/2'' pulse on the a → c transition. However, it is not possible to phase match the emission generated by this polarization due to the requirement that the three fields be orthogonal. Given that in rotational spectroscopy the physical size of the sample produced in a pulsed supersonic jet is comparable to the wavelengths of the microwave fields, the lack of phase matching produces a substantial but not catastrophic loss in the amplitude of the emitted free induction decay field. I will present a proposal to realize an analogy of quasiphase matching to
Chiral dynamics with (non)strange quarks
Kubis, Bastian; Meißner, Ulf-G.
2017-01-01
We review the results and achievements of the project B.3. Topics addressed include pion photoproduction off the proton and off deuterium, three-flavor chiral perturbation theory studies, chiral symmetry tests in Goldstone boson decays, the development of unitarized chiral perturbation theory to next-to-leading order, the two-pole structure of the Λ(1405), the dynamical generation of the lowest S11 resonances, the theory of hadronic atoms and its application to various systems, precision studies in light-meson decays based on dispersion theory, the Roy-Steiner analysis of pion-nucleon scattering, a high-precision extraction of the elusive pion-nucleon σ-term, and aspects of chiral dynamics in few-nucleon systems.
Density-functional perturbation theory goes time-dependent
Directory of Open Access Journals (Sweden)
Gebauer, Ralph
2008-05-01
Full Text Available The scope of time-dependent density-functional theory (TDDFT is limited to the lowest portion of the spectrum of rather small systems (a few tens of atoms at most. In the static regime, density-functional perturbation theory (DFPT allows one to calculate response functions of systems as large as currently dealt with in ground-state simulations. In this paper we present an effective way of combining DFPT with TDDFT. The dynamical polarizability is first expressed as an off-diagonal matrix element of the resolvent of the Kohn-Sham Liouvillian super-operator. A DFPT representation of response functions allows one to avoid the calculation of unoccupied Kohn-Sham orbitals. The resolvent of the Liouvillian is finally conveniently evaluated using a newly developed non-symmetric Lanczos technique, which allows for the calculation of the entire spectrum with a single Lanczos recursion chain. Each step of the chain essentially requires twice as many operations as a single step of the iterative diagonalization of the unperturbed Kohn-Sham Hamiltonian or, for that matter, as a single time step of a Car-Parrinello molecular dynamics run. The method will be illustrated with a few case molecular applications.
Suliman, Mohamed
2016-01-01
In this supplementary appendix we provide proofs and additional simulation results that complement the paper (constrained perturbation regularization approach for signal estimation using random matrix theory).
Cutoff effects for Wilson twisted mass fermions at tree-level of perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Cichy, K.; Kujawa, A. [Poznan Univ. (Poland). Faculty of Physics; Gonzalez Lopez, J. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik]|[Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Shindler, A. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2007-10-15
We study cutoff effects at tree-level of perturbation theory for standardWilson andWilson twisted mass fermionic lattice actions with N{sub f}=2 flavour degenerate quarks. The discretization effects are investigated by computing the mass spectrum and decay amplitudes for different hadron interpolating fields and the scaling behaviour towards the continuum limit is analyzed. It is shown that the Wilson and the mass average methods are equivalent and lead to O(a) improved R{sub 5}-parity even lattice observables. We also demonstrate that automatic O(a) improvement works in case of Wilson twisted mass fermions at maximal twist and that this improvement is realized even if the condition of maximal twist is achieved only up to O(a) cutoff effects. We demonstrate that in the chiral limit standard Wilson fermions show scaling violations of O(a{sup 2}) while for maximally twisted mass fermions these violations are only of O(a{sup 4}). For our analytical calculations, lattices with sizes L=aN and periodic boundary conditions in the spatial directions have been chosen while infinite extension in the time direction, L4={infinity}, is considered. (orig.)
A stochastic perturbation theory for non-autonomous systems
Energy Technology Data Exchange (ETDEWEB)
Moon, W., E-mail: wm275@damtp.cam.ac.uk [Yale University, New Haven, Connecticut 06520-8109 (United States); Wettlaufer, J. S., E-mail: wettlaufer@maths.ox.ac.uk [Yale University, New Haven, Connecticut 06520-8109 (United States); Mathematical Institute, University of Oxford, Oxford OX2 6GG (United Kingdom)
2013-12-15
We develop a perturbation theory for a class of first order nonlinear non-autonomous stochastic ordinary differential equations that arise in climate physics. The perturbative procedure produces moments in terms of integral delay equations, whose order by order decay is characterized in a Floquet-like sense. Both additive and multiplicative sources of noise are discussed and the question of how the nature of the noise influences the results is addressed theoretically and numerically. By invoking the Martingale property, we rationalize the transformation of the underlying Stratonovich form of the model to an Ito form, independent of whether the noise is additive or multiplicative. The generality of the analysis is demonstrated by developing it both for a Brownian particle moving in a periodically forced quartic potential, which acts as a simple model of stochastic resonance, as well as for our more complex climate physics model. The validity of the approach is shown by comparison with numerical solutions. The particular climate dynamics problem upon which we focus involves a low-order model for the evolution of Arctic sea ice under the influence of increasing greenhouse gas forcing ΔF{sub 0}. The deterministic model, developed by Eisenman and Wettlaufer [“Nonlinear threshold behavior during the loss of Arctic sea ice,” Proc. Natl. Acad. Sci. U.S.A. 106(1), 28–32 (2009)] exhibits several transitions as ΔF{sub 0} increases and the stochastic analysis is used to understand the manner in which noise influences these transitions and the stability of the system.
A stochastic perturbation theory for non-autonomous systems
Moon, Woosok; Wettlaufer, John
2014-05-01
We develop a perturbation theory for a class of first order nonlinear non-autonomous stochastic ordinary differential equations that arise in climate physics. The perturbative procedure produces moments in terms of integral delay equations, whose order by order decay is characterized in a Floquet-like sense. Both additive and multiplicative sources of noise are discussed and the question of how the nature of the noise influences the results is addressed theoretically and numerically. By invoking the Martingale property, we rationalize the transformation of the underlying Stratonovich form of the model to an Ito form, independent of whether the noise is additive or multiplicative. The generality of the analysis is demonstrated by developing it both for a Brownian particle moving in a periodically forced quartic potential, which acts as a simple model of stochastic resonance, as well as for our more complex climate physics model. The validity of the approach is shown by comparison with numerical solutions. The particular climate dynamics problem upon which we focus involves a low-order model for the evolution of Arctic sea ice under the influence of increasing greenhouse gas forcing ΔF0. The deterministic model, developed by Eisenman and Wettlaufer EW09 exhibits several transitions as ΔF0 increases and the stochastic analysis is used to understand the manner in which noise influences these transitions and the stability of the system. Eisenman, I., and J. S. Wettlaufer, 'Nonlinear threshold behavior during the loss of Arctic sea ice,' Proc. Natl. Acad. Sci. USA, 106, 28-32, 2009.
The de Sitter limit of inflation and non-linear perturbation theory
DEFF Research Database (Denmark)
Jarnhus, Philip; Sloth, Martin Snoager
2008-01-01
We study the fourth order action of the comoving curvature perturbation in an inflationary universe in order to understand more systematically the de Sitter limit in nonlinear cosmological perturbation theory. We derive the action of the curvature perturbation to fourth order in the comoving gauge...
Dynamical Symmetry Breaking in Chiral Gauge Theories with Direct-Product Gauge Groups
Shi, Yan-Liang
2016-01-01
We analyze patterns of dynamical symmetry breaking in strongly coupled chiral gauge theories with direct-product gauge groups $G$. If the gauge coupling for a factor group $G_i \\subset G$ becomes sufficiently strong, it can produce bilinear fermion condensates that break the $G_i$ symmetry itself and/or break other gauge symmetries $G_j \\subset G$. Our comparative study of a number of strongly coupled direct-product chiral gauge theories elucidates how the patterns of symmetry breaking depend on the structure of $G$ and on the relative sizes of the gauge couplings corresponding to factor groups in the direct product.
Dynamical symmetry breaking in chiral gauge theories with direct-product gauge groups
Shi, Yan-Liang; Shrock, Robert
2016-09-01
We analyze patterns of dynamical symmetry breaking in strongly coupled chiral gauge theories with direct-product gauge groups G . If the gauge coupling for a factor group Gi⊂G becomes sufficiently strong, it can produce bilinear fermion condensates that break the Gi symmetry itself and/or break other gauge symmetries Gj⊂G . Our comparative study of a number of strongly coupled direct-product chiral gauge theories elucidates how the patterns of symmetry breaking depend on the structure of G and on the relative sizes of the gauge couplings corresponding to factor groups in the direct product.
Hadronic tau decays into two and three meson modes within Resonance Chiral Theory
Roig, P
2009-01-01
We study two and three meson decays of the tau lepton within the framework of the Resonance Chiral Theory, that is based on the following properties of QCD: its chiral symmetry in the massless case, its large-N_C limit, and the asymptotic behaviour it demands to the relevant form factors. Most of the couplings in the Lagrangian are determined this way rendering the theory predictive. Our outcomes can be tested thanks to the combination of a very good experimental effort (current and forthcoming, at B- and tau-charm-factories) and the very accurate devoted Monte Carlo generators.
A general theory of linear cosmological perturbations: scalar-tensor and vector-tensor theories
Lagos, Macarena; Ferreira, Pedro G; Noller, Johannes
2016-01-01
We present a method for parametrizing linear cosmological perturbations of theories of gravity, around homogeneous and isotropic backgrounds. The method is sufficiently general and systematic that it can be applied to theories with any degrees of freedom (DoFs) and arbitrary gauge symmetries. In this paper, we focus on scalar-tensor and vector-tensor theories, invariant under linear coordinate transformations. In the case of scalar-tensor theories, we use our framework to recover the simple parametrizations of linearized Horndeski and "Beyond Horndeski" theories, and also find higher-derivative corrections. In the case of vector-tensor theories, we first construct the most general quadratic action for perturbations that leads to second-order equations of motion, which propagates two scalar DoFs. Then we specialize to the case in which the vector field is time-like (\\`a la Einstein-Aether gravity), where the theory only propagates one scalar DoF. As a result, we identify the complete forms of the quadratic act...
Cutoff regulators in chiral nuclear effective field theory
Long, Bingwei
2016-01-01
Three-dimensional cutoff regulators are frequently employed in multi-nucleon calculations, but they violate chiral symmetry and Lorentz invariance. A cutoff regularization scheme is proposed to compensate systematically at subleading orders for these symmetry violations caused by regulator artifacts. This is especially helpful when a soft momentum cutoff has to be used for technical reasons. It is also shown that dimensional regularization can still be used for some Feynman (sub)diagrams while cutoff regulators are used for the rest.
Cosmological Structure Formation with Augmented Lagrangian Perturbation Theory
Kitaura, Francisco-Shu
2012-01-01
We present a new fast and efficient approach to model structure formation with aug- mented Lagrangian perturbation theory (ALPT). Our method is based on splitting the dis- placement field into a long and a short range component. The long range component is computed by second order LPT (2LPT). This approximation contains a tidal nonlocal and nonlinear term. Unfortunately, 2LPT fails on small scales due to severe shell crossing and a crude quadratic behaviour in the low density regime. The spherical collapse (SC) approximation has been recently reported to correct for both effects by adding an ideal collapse truncation. However, this approach fails to reproduce the structures on large scales where it is significantly less correlated with the N-body result than 2LPT or linear LPT (the Zeldovich approximation). We propose to combine both approximations using for the short range displacement field the SC solution. A Gaussian filter with a smoothing radius r_S is used to separate between both regimes. We use the re...
Hyperfine coupling constants from internally contracted multireference perturbation theory
Shiozaki, Toru
2016-01-01
We present an accurate method for calculating hyperfine coupling constants (HFCCs) based on the complete active space second-order perturbation theory (CASPT2) with full internal contraction. The HFCCs are computed as a first-order property using the relaxed CASPT2 spin-density matrix that takes into account orbital and configurational relaxation due to dynamical electron correlation. The first-order unrelaxed spin-density matrix is calculated from one- and two-body spin-free counterparts that are readily available in the CASPT2 nuclear gradient program [M. K. MacLeod and T. Shiozaki, J. Chem. Phys. 142, 051103 (2015)], whereas the second-order part is computed directly using the newly extended automatic code generator. The relaxation contribution is then calculated from the so-called Z-vectors that are available in the CASPT2 nuclear gradient program. Numerical results are presented for the CN and AlO radicals, for which the CASPT2 values are comparable (or, even superior in some cases) to the ones computed ...
Convenient formulae for some integrals in perturbation theory
Directory of Open Access Journals (Sweden)
D. Henderson
2010-01-01
Full Text Available The free energy and pressure of a fluid, as given by perturbation theory, involve integrals of the hard sphere correlation functions and their density derivatives. In most applications a straightforward procedure would be to obtain these integrals, possibly numerically, using the formulae and computer codes for the hard sphere correlation functions, given previously [Mol. Phys., 2007, 106, 2; Condens. Matter Phys., 2009, 12, 127], followed by numerical differentiation with respect to the density and a possible compounding of errors. More sophisticated methods are given in this paper, which is the second in a planned trilogy, drawn from the author's lecture notes. Three representative model fluids are considered. They are the square-well fluid, the Yukawa fluid, and the Lennard-Jones fluid. Each model fluid is popular for theoretical and engineering calculations and can represent a simple fluid such as argon. With the methods presented here, numerical integration and differentiation are not necessary for the square-well and Yukawa fluids. Numerical integration cannot be easily avoided in the case of the Lennard-Jones fluid. However, numerical differentiation with respect to the density is not required.
Hyperfine Coupling Constants from Internally Contracted Multireference Perturbation Theory.
Shiozaki, Toru; Yanai, Takeshi
2016-09-13
We present an accurate method for calculating hyperfine coupling constants (HFCCs) based on the complete active space second-order perturbation theory (CASPT2) with full internal contraction. The HFCCs are computed as a first-order property using the relaxed CASPT2 spin-density matrix that takes into account orbital and configurational relaxation due to dynamical electron correlation. The first-order unrelaxed spin-density matrix is calculated from one- and two-body spin-free counterparts that are readily available in the CASPT2 nuclear gradient program [M. K. MacLeod and T. Shiozaki, J. Chem. Phys. 142, 051103 (2015)], whereas the second-order part is computed directly using the newly extended automatic code generator. The relaxation contribution is then calculated from the so-called Z-vectors that are available in the CASPT2 nuclear gradient program. Numerical results are presented for the CN and AlO radicals, for which the CASPT2 values are comparable (or, even superior in some cases) to the ones computed by the coupled-cluster and density matrix renormalization group methods. The HFCCs for the hexaaqua complexes with V(II), Cr(III), and Mn(II) are also presented to demonstrate the accuracy and efficiency of our code.
Construction of Perturbatively Correct Light Front Hamiltonian for (2+1)-Dimensional Gauge Theory
Malyshev, M Yu; Zubov, R A; Franke, V A
2016-01-01
In this paper we consider (2+1)-dimensional SU(N)-symmetric gauge theory within light front perturbation theory, regularized by the method analogous to Pauli-Villars regularization. This enables us to construct correct renormalized light front Hamiltonian.
Renormalization of NN Interaction with Relativistic Chiral Two Pion Exchange
Energy Technology Data Exchange (ETDEWEB)
Higa, R; Valderrama, M Pavon; Arriola, E Ruiz
2007-06-14
The renormalization of the NN interaction with the Chiral Two Pion Exchange Potential computed using relativistic baryon chiral perturbation theory is considered. The short distance singularity reduces the number of counter-terms to about a half as those in the heavy-baryon expansion. Phase shifts and deuteron properties are evaluated and a general overall agreement is observed.
Chiral symmetry breaking from Ginsparg-Wilson fermions
Hernández, Pilar; Lellouch, L P; Hernandez, Pilar; Jansen, Karl; Lellouch, Laurent
2000-01-01
We calculate the large-volume and small-mass dependences of the quark condensate in quenched QCD using Neuberger's operator. We find good agreement with the predictions of quenched chiral perturbation theory, enabling a determination of the chiral lagrangian parameter \\Sigma, up to a multiplicative renormalization.
Statistical Perturbation Theory of Cosmic Fields; 1, Basic Formalism and Second-order Theory
Matsubara, T
2000-01-01
We formulate a general method for perturbative evaluations of statistics of smoothed cosmic fields, which we call as ``Statistical Perturbation Theory''. The formalism is an extensive generalization of the method used by Matsubara (1994) who derived a weakly nonlinear formula of the genus statistic in a 3D density field. After describing the general method, we apply the formalism especially to analyses of more general genus statistics, level-crossing statistics, Minkowski functionals, and a density extrema statistic, regardless of the dimensions in which each statistic is defined. The relation between the Minkowski functionals and other geometrical statistics is clearly described. These examples are applied to some cosmic fields, including 3D density field, 3D velocity field, 2D projected density field, and 2D weak lensing field. The results are detailed for second order theory of the formalism. The reason why the genus curves etc. in CDM-like models exhibit smaller deviations from Gaussian predictions when t...
Borel summability of perturbative series in 4d N=2 and 5d N=1 theories
Honda, Masazumi
2016-01-01
We study weak coupling perturbative series in 4d N=2 and 5d N=1 supersymmetric gauge theories with Lagrangians. We prove that the perturbative series of these theories in zero instanton sector are Borel summable for various observables. We also prove Borel summability in arbitrary number of instanton sector when we know explicit expression of Nekrasov instanton partition function.
Lattice calculations for A=3,4,6,12 nuclei using chiral effective field theory
Epelbaum, Evgeny; Lee, Dean; Meißner, Ulf-G
2010-01-01
We present lattice calculations for the ground state energies of tritium, helium-3, helium-4, lithium-6, and carbon-12 nuclei. Our results were previously summarized in a letter publication. This paper provides full details of the calculations. We include isospin-breaking, Coulomb effects, and interactions up to next-to-next-to-leading order in chiral effective field theory.
Electric dipole moments of light nuclei from chiral effective field theory
de Vries, J.; Higa, R.; Liu, C. -P.; Mereghetti, E.; Stetcu, I.; Timmermans, R. G. E.; van Kolck, U.
2011-01-01
We set up the framework for the calculation of electric dipole moments (EDMs) of light nuclei using the systematic expansion provided by chiral effective field theory (EFT). We take into account parity (P) and timer-reversal (T) violation which, at the quark-gluon level, originates from the QCD vacu
Chiral Rings and Physical States in c<1 String Theory
Govindarajan, S; John, V
1993-01-01
We show how the double cohomology of the String and Felder BRST charges naturally leads to the ring structure of $c<1$ strings. The chiral ring is a ring of polynomials in two variables modulo an equivalence relation of the form $x^p \\simeq y^{p+1}$ for the (p+1,p) model. We also study the states corresponding to the edges of the conformal grid whose inclusion is crucial for the closure of the ring. We introduce candidate operators that correspond to the observables of the matrix models. Their existence is motivated by the relation of one of the screening operators of the minimal model to the zero momentum dilaton.
Bogdan, V. M.; Bond, V. B.
1980-01-01
The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.
Full simulation of chiral Random Matrix Theory at non-zero chemical potential by Complex Langevin
Mollgaard, A
2014-01-01
It is demonstrated that the complex Langevin method can simulate chiral random matrix theory at non-zero chemical potential. The successful match with the analytic prediction for the chiral condensate is established through a shift of matrix integration variables and choosing a polar representation for the new matrix elements before complexification. Furthermore, we test the proposal to work with a Langevin-time dependent quark mass and find that it allows us to control the fluctuations of the phase of the fermion determinant throughout the Langevin trajectory.
Full simulation of chiral random matrix theory at nonzero chemical potential by complex Langevin
Mollgaard, A.; Splittorff, K.
2015-02-01
It is demonstrated that the complex Langevin method can simulate chiral random matrix theory at nonzero chemical potential. The successful match with the analytic prediction for the chiral condensate is established through a shift of matrix integration variables and choosing a polar representation for the new matrix elements before complexification. Furthermore, we test the proposal to work with a Langevin-time-dependent quark mass and find that it allows us to control the fluctuations of the phase of the fermion determinant throughout the Langevin trajectory.
Random matrix theory and higher genus integrability: the quantum chiral Potts model
Energy Technology Data Exchange (ETDEWEB)
Angles d' Auriac, J.Ch. [Centre de Recherches sur les Tres Basses Temperatures, BP 166, Grenoble (France)]. E-mail: dauriac@polycnrs-gre.fr; Maillard, J.M.; Viallet, C.M. [LPTHE, Tour 16, Paris (France)]. E-mails: maillard@lpthe.jussieu.fr; viallet@lpthe.jussieu.fr
2002-06-14
We perform a random matrix theory (RMT) analysis of the quantum four-state chiral Potts chain for different sizes of the chain up to size L 8. Our analysis gives clear evidence of a Gaussian orthogonal ensemble (GOE) statistics, suggesting the existence of a generalized time-reversal invariance. Furthermore, a change from the (generic) GOE distribution to a Poisson distribution occurs when the integrability conditions are met. The chiral Potts model is known to correspond to a (star-triangle) integrability associated with curves of genus higher than zero or one. Therefore, the RMT analysis can also be seen as a detector of 'higher genus integrability'. (author)
Aoki, Ken-Ichi; Sato, Daisuke
2016-01-01
We analyze the dynamical chiral symmetry breaking in gauge theory with the nonperturbative renormalization group equation (NPRGE), which is a first order nonlinear partial differential equation (PDE). In case that the spontaneous chiral symmetry breaking occurs, the NPRGE encounters some non-analytic singularities at the finite critical scale even though the initial function is continuous and smooth. Therefore there is no usual solution of the PDE beyond the critical scale. In this paper, we newly introduce the notion of a weak solution which is the global solution of the weak NPRGE. We show how to evaluate the physical quantities with the weak solution.
On Invariants and Scalar Chiral Correlation Functions in { n} = 1 Superconformal Field Theories
Knuth, Holger
A general expression for the four-point function with vanishing total R-charge of antichiral and chiral superfields in { N} = 1 superconformal theories is given. It is obtained by applying the exponential of a simple universal nilpotent differential operator to an arbitrary function of two cross-ratios. To achieve this the nilpotent superconformal invariants according to Park are focused. Several dependencies between these invariants are presented, so that eight nilpotent invariants and 27 monomials of these invariants of degree d > 1 are left being linearly independent. It is analyzed, how terms within the four-point function of general scalar superfields cancel in order to fulfill the chiral restrictions.
Chiral behavior of light meson form factors in 2+1 flavor QCD with exact chiral symmetry
Kaneko, T; Cossu, G; Feng, X; Fukaya, H; Hashimoto, S; Noaki, J; Onogi, T
2016-01-01
We present a study of chiral behavior of light meson form factors in QCD with three flavors of overlap quarks. Gauge ensembles are generated at single lattice spacing 0.12 fm with pion masses down to 300 MeV. The pion and kaon electromagnetic form factors and the kaon semileptonic form factors are precisely calculated using the all-to-all quark propagator. We discuss their chiral behavior using the next-to-next-to-leading order chiral perturbation theory.
A new chiral two-matrix theory for Dirac spectra with imaginary chemical potential
Energy Technology Data Exchange (ETDEWEB)
Akemann, G. [Department of Mathematical Sciences, Brunel University West London, Uxbridge UB8 3PH (United Kingdom); Damgaard, P.H. [Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen O (Denmark)]. E-mail: phdamg@nbi.dk; Osborn, J.C. [Physics Department and Center for Computational Science, Boston University, Boston, MA 02215 (United States); Splittorff, K. [Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen O (Denmark)
2007-03-26
We solve a new chiral random two-matrix theory by means of biorthogonal polynomials for any matrix size N. By deriving the relevant kernels we find explicit formulas for all (n,k)-point spectral (mixed or unmixed) correlation functions. In the microscopic limit we find the corresponding scaling functions, and thus derive all spectral correlators in this limit as well. We extend these results to the ordinary (non-chiral) ensembles, and also there provide explicit solutions for any finite size N, and in the microscopic scaling limit. Our results give the general analytical expressions for the microscopic correlation functions of the Dirac operator eigenvalues in theories with imaginary baryon and isospin chemical potential, and can be used to extract the tree-level pion decay constant from lattice gauge theory configurations. We find exact agreement with previous computations based on the low-energy effective field theory in the two special cases where comparisons are possible.
Equation-of-motion coupled cluster perturbation theory revisited
DEFF Research Database (Denmark)
Eriksen, Janus Juul; Jørgensen, Poul; Olsen, Jeppe;
2014-01-01
The equation-of-motion coupled cluster (EOM-CC) framework has been used for deriving a novel series of perturbative corrections to the coupled cluster singles and doubles energy that formally con- verges towards the full configuration interaction energy limit. The series is based on a Møller-Ples......-Plesset partitioning of the Hamiltonian and thus size extensive at any order in the perturbation, thereby rem- edying the major deficiency inherent to previous perturbation series based on the EOM-CC ansatz. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4873138]...
Chiral observables and S-duality in N = 2* U(N) gauge theories
Ashok, S K; Dell'Aquila, E; Frau, M; Lerda, A; Moskovic, M; Raman, M
2016-01-01
We study N = 2* theories with gauge group U(N) and use equivariant localization to calculate the quantum expectation values of the simplest chiral ring elements. These are expressed as an expansion in the mass of the adjoint hypermultiplet, with coefficients given by quasi-modular forms of the S-duality group. Under the action of this group, we construct combinations of chiral ring elements that transform as modular forms of definite weight. As an independent check, we confirm these results by comparing the spectral curves of the associated Hitchin system and the elliptic Calogero-Moser system. We also propose an exact and compact expression for the 1-instanton contribution to the expectation value of the chiral ring elements.
Perturbation theory, effective field theory, and oscillations in the power spectrum
Vlah, Zvonimir; Chu, Man Yat; Feng, Yu
2015-01-01
We explore the relationship between the nonlinear matter power spectrum and the various Lagrangian and Standard Perturbation Theories (LPT and SPT). We first look at it in the context of one dimensional (1-d) dynamics, where 1LPT is exact at the perturbative level and one can exactly resum the SPT series into the 1LPT power spectrum. Shell crossings lead to non-perturbative effects, and the PT ignorance can be quantified in terms of their ratio, which is also the transfer function squared in the absence of stochasticity. At the order of PT we work, this parametrization is equivalent to the results of effective field theory (EFT), and can thus be expanded in terms of the same parameters. We find that its radius of convergence is larger than the SPT loop expansion. The same EFT parametrization applies to all SPT loop terms and, if stochasticity can be ignored, to all N-point correlators. In 3-d, the LPT structure is considerably more complicated, and we find that LPT models with parametrization motivated by the...
Compton scattering from chiral dynamics with unitarity and causality
Energy Technology Data Exchange (ETDEWEB)
Gasparyan, A.M. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Planckstrasse 1, 64291 Darmstadt (Germany); SSC RF ITEP, Bolshaya Cheremushkinskaya 25, 117218 Moscow (Russian Federation); Lutz, M.F.M., E-mail: m.lutz@gsi.de [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Planckstrasse 1, 64291 Darmstadt (Germany); Pasquini, B. [Dipartimento di Fisica Nucleare e Teorica, Universita degli Studi di Pavia and INFN, Sezione di Pavia, Pavia (Italy)
2011-09-15
Proton Compton scattering is analyzed with the chiral Lagrangian. Partial-wave amplitudes are obtained by an analytic extrapolation of subthreshold reaction amplitudes computed in chiral perturbation theory, where the constraints set by electromagnetic-gauge invariance, causality and unitarity are used to stabilize the extrapolation. We present and discuss predictions for various spin observables and polarizabilities of the proton. While for the transition polarizabilities {gamma}{sub E1M2}, {gamma}{sub M1E2} we recover the results of strict chiral perturbation theory, for the diagonal {gamma}{sub E1E1}, {gamma}{sub M1M1} elements we find significant effects from rescattering.
From enemies to friends chiral symmetry on the lattice
Hernández, Pilar; Lellouch, L P; Hernandez, Pilar; Jansen, Karl; Lellouch, Laurent
2002-01-01
The physics of strong interactions is invariant under the exchange of left-handed and right-handed quarks, at least in the massless limit. This invariance is reflected in the chiral symmetry of quantum chromodynamics. Surprisingly, it has become clear only recently how to implement this important symmetry in lattice formulations of quantum field theories. We will discuss realizations of exact lattice chiral symmetry and give an example of the computation of a physical observable in quantum chromodynamics where chiral symmetry is important. This calculation is performed by relying on finite size scaling methods as predicted by chiral perturbation theory.
Chiral effective field theory beyond the power-counting regime
Hall, Jonathan M M; Young, Ross D
2011-01-01
Novel techniques are presented, which identify the chiral power-counting regime (PCR), and realize the existence of an intrinsic energy scale embedded in lattice QCD results that extend outside the PCR. The nucleon mass is considered as a benchmark for illustrating this new approach. Using finite-range regularization, an optimal regularization scale can be extracted from lattice simulation results by analyzing the renormalization of the low energy coefficients. The optimal scale allows a description of lattice simulation results that extend beyond the PCR by quantifying and thus handling any scheme-dependence. Preliminary results for the nucleon magnetic moment are also examined, and a consistent optimal regularization scale is obtained. This indicates the existence of an intrinsic scale corresponding to the finite size of the source of the pion cloud.
An Ultraviolet Chiral Theory of the Top for the Fundamental Composite (Goldstone) Higgs
Cacciapaglia, Giacomo
2015-01-01
We introduce a scalar-less anomaly free chiral gauge theory that serves as natural ultraviolet completion of models of fundamental composite (Goldstone) Higgs dynamics. The new theory is able to generate the top mass and furthermore features a built-in protection mechanism that naturally suppresses the bottom mass. At low energies the theory predicts new fractionally charged fermions, and a number of four-fermion operators that, besides being relevant for the generation of the top mass, also lead to an intriguing phenomenology for the new states predicted by the theory.
An ultraviolet chiral theory of the top for the fundamental composite (Goldstone) Higgs
Energy Technology Data Exchange (ETDEWEB)
Cacciapaglia, Giacomo, E-mail: g.cacciapaglia@ipnl.in2p3.fr [Univ Lyon, Université Lyon 1, CNRS/IN2P3, IPNL, 4 rue Enrico Fermi, F-69622 Villeurbanne Cedex (France); Sannino, Francesco, E-mail: sannino@cp3.dias.sdu.dk [CP" 3-Origins and the Danish IAS, University of Southern Denmark, Campusvej 55, DK-5230 Odense M (Denmark)
2016-04-10
We introduce a scalar-less anomaly free chiral gauge theory that serves as natural ultraviolet completion of models of fundamental composite (Goldstone) Higgs dynamics. The new theory is able to generate the top mass and furthermore features a built-in protection mechanism that naturally suppresses the bottom mass. At low energies the theory predicts new fractionally charged fermions, and a number of four-fermion operators that, besides being relevant for the generation of the top mass, also lead to an intriguing phenomenology for the new states predicted by the theory.
An Ultraviolet Chiral Theory of the Top for the Fundamental Composite (Goldstone) Higgs
DEFF Research Database (Denmark)
Cacciapaglia, Giacomo; Sannino, Francesco
2016-01-01
We introduce a scalar-less anomaly free chiral gauge theory that serves as natural ultraviolet completion of models of fundamental composite (Goldstone) Higgs dynamics. The new theory is able to generate the top mass and furthermore features a built-in protection mechanism that naturally suppresses...... the bottom mass. At low energies the theory predicts new fractionally charged fermions, and a number of four-fermion operators that, besides being relevant for the generation of the top mass, also lead to an intriguing phenomenology for the new states predicted by the theory....
Energy Technology Data Exchange (ETDEWEB)
Scherrer, Arne [Martin-Luther-University Halle-Wittenberg, von-Danckelmann-Platz 4, D-06120 Halle (Germany); UMR 8640 ENS-CNRS-UPMC, Département de Chimie, 24 rue Lhomond, École Normale Supérieure, 75005 Paris (France); UPMC Université Paris 06, 4, Place Jussieu, 75005 Paris (France); Agostini, Federica; Gross, E. K. U. [Max-Planck-Institute of Microstructure Physics, Weinberg 2, D-06120 Halle (Germany); Sebastiani, Daniel [Martin-Luther-University Halle-Wittenberg, von-Danckelmann-Platz 4, D-06120 Halle (Germany); Vuilleumier, Rodolphe [UMR 8640 ENS-CNRS-UPMC, Département de Chimie, 24 rue Lhomond, École Normale Supérieure, 75005 Paris (France); UPMC Université Paris 06, 4, Place Jussieu, 75005 Paris (France)
2015-08-21
The nuclear velocity perturbation theory (NVPT) for vibrational circular dichroism (VCD) is derived from the exact factorization of the electron-nuclear wave function. This new formalism offers an exact starting point to include correction terms to the Born-Oppenheimer (BO) form of the molecular wave function, similar to the complete-adiabatic approximation. The corrections depend on a small parameter that, in a classical treatment of the nuclei, is identified as the nuclear velocity. Apart from proposing a rigorous basis for the NVPT, we show that the rotational strengths, related to the intensity of the VCD signal, contain a new contribution beyond-BO that can be evaluated with the NVPT and that only arises when the exact factorization approach is employed. Numerical results are presented for chiral and non-chiral systems to test the validity of the approach.
Kampf, Karol; Trnka, Jaroslav
2009-01-01
We study in detail various aspects of the renormalization of the spin-1 resonance propagator in the effective field theory framework. First, we briefly review the formalisms for the description of spin-1 resonances in the path integral formulation with the stress on the issue of propagating degrees of freedom. Then we calculate the one-loop 1-- meson self-energy within the Resonance chiral theory in the chiral limit using different methods for the description of spin-one particles, namely the Proca field, antisymmetric tensor field and the first order formalisms. We discuss in detail technical aspects of the renormalization procedure which are inherent to the power-counting non-renormalizable theory and give a formal prescription for the organization of both the counterterms and one-particle irreducible graphs. We also construct the corresponding propagators and investigate their properties. We show that the additional poles corresponding to the additional one-particle states are generated by loop corrections...
Domain walls and perturbation theory in high temperature gauge theory SU(2) in 2+1 dimensions
Korthals-Altes, C P; Stephanov, M A; Teper, M; Altes, C Korthals
1997-01-01
We study the detailed properties of Z_2 domain walls in the deconfined high temperature phase of the d=2+1 SU(2) gauge theory. These walls are studied both by computer simulations of the lattice theory and by one-loop perturbative calculations. The latter are carried out both in the continuum and on the lattice. We find that leading order perturbation theory reproduces the detailed properties of these domain walls remarkably accurately even at temperatures where the effective dimensionless expansion parameter, g^2/T, is close to unity. The quantities studied include the surface tension, the action density profiles, roughening and the electric screening mass. It is only for the last quantity that we find an exception to the precocious success of perturbation theory. All this shows that, despite the presence of infrared divergences at higher orders, high-T perturbation theory can be an accurate calculational tool.
Perturbation Theory for Interacting Electrons in a Quantum Dot under Strong Magnetic Field
Institute of Scientific and Technical Information of China (English)
GU Yun-Ting; RUAN Wen-Ying; LI Quan; CAI Min; CHAN Kok-Sam
2001-01-01
The quantum spectrum of interacting electrons confined in a parabolic dot in two dimensions is obtained by employing the perturbation theory. Comparison with the existing analytical results has been made. We show that while the widely used second-order perturbation significantly underestimates the ground state energies, the results including higher orders of perturbation are highly accurate within the B-field range of experimental interest.
Lattice quantum chromodynamics with approximately chiral fermions
Energy Technology Data Exchange (ETDEWEB)
Hierl, Dieter
2008-05-15
In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the {theta}{sup +} pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)
Application of Perturbation Theory to a Master Equation
Directory of Open Access Journals (Sweden)
B. M. Villegas-Martínez
2016-01-01
Full Text Available We develop a matrix perturbation method for the Lindblad master equation. The first- and second-order corrections are obtained and the method is generalized for higher orders. The perturbation method developed is applied to the problem of a lossy cavity filled with a Kerr medium; the second-order corrections are estimated and compared with the known exact analytic solution. The comparison is done by calculating the Q-function, the average number of photons, and the distance between density matrices.
Dalgarno-Lewis perturbation theory for scattering states
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima, Colima Mexico (Mexico)]. E-mail: paolo@ucol.mx; Fernandez, Francisco M. [INIFTA (Conicet, UNLP), Division Quimica Teorica, Diag. 113 y 64 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)]. E-mail: fernande@quimica.unlp.edu.ar
2007-07-23
We apply the method of Dalgarno and Lewis to scattering states and discuss the choice of the unperturbed model in order to have a convergent perturbation series for the phase shift. We show that a recently proposed approach is a particular case of the method of Dalgarno and Lewis.
Molecular Interactions with Many-Body Perturbation Theory.
1981-09-11
Medcine , Ne. York, York, June 4, 1979. R. J. Bartlett, "Many-Body Perturbation Thery", Aarhus University, Aarhus, Denmark, June 18, 1979. R. J. Bartlett...editor can be accepted for speedy publication. Permission is granted to authors of scientific articles and books to quote from this journal provided
The theory and phenomenology of perturbative QCD based jet quenching
Majumder, A.; van Leeuwen, M.
2010-01-01
The study of the structure of strongly interacting dense matter via hard jets is reviewed. High momentum partons produced in hard collisions produce a shower of gluons prior to undergoing the non-perturbative process of hadronization. In the presence of a dense medium this shower is modified due to
BLOCKWISE PERTURBATION THEORY FOR 2 × 2 BLOCK MARKOV CHAINS
Institute of Scientific and Technical Information of China (English)
Jun-gong Xue; Wei-guo Gao
2000-01-01
Let P be a transition matrix of a Markov chain and be of the form The stationary distribution πT is partitioned conformally in the form (π1T, π2T).This paper establish the relative error bound in πiT (i ＝ 1, 2) when each block Pij get a small relative perturbation.
A non—perturbation approach in temperature Green function theory
Institute of Scientific and Technical Information of China (English)
ZuoWei; WangShun－Jin
1997-01-01
A set of differo-integral equations for many-body connected temperature Green's functions is established which is non-perturbative in nature and provides a reasonable truncation scheme with respect to the order of many-body correlations.The method can be applied to nuclear systems at finite temperature.
6d strings from new chiral gauge theories
Kim, Hee-Cheol; Park, Jaemo
2016-01-01
We study the 6d $\\mathcal{N}=(1,0)$ superconformal field theory with smallest non-Higgsable gauge symmetry $SU(3)$. In particular, we propose new 2d gauge theory descriptions of its self-dual strings in the tensor branch. We use our gauge theories to compute the elliptic genera of the self-dual strings, which completely agree with the partial data known from topological strings. We further study the strings of the $(E_6,E_6)$ conformal matter by generalizing our 2d gauge theories. We also show that anomalies of all our gauge theories agree with the self-dual string anomalies computed by inflows from 6d.
Institute of Scientific and Technical Information of China (English)
GAO TIAN-LING; LIU QIANG; Ma Fu-ming
2012-01-01
This paper is concerned with the electromagnetic scattering by a nonperfectly conductor obstacle in chiral environment.A two-dimensional mathematical model is established.The existence and uniqueness of the problem are discussed by potential theory.
CHIRAL RING OF Sp(N) AND SO(N) SUPERSYMMETRIC GAUGE THEORY IN FOUR DIMENSIONS
Institute of Scientific and Technical Information of China (English)
E. WITTEN
2003-01-01
The chiral ring of classical supersymmetric Yang-Mills theory with gauge group Sp(N) or SO(N) is computed, extending previous work (of Cachazo, Douglas, Seiberg, and the author)for SU(N). The result is that, as has been conjectured, the ring is generated by the usualglueball superfield S ～ Tr WαWα, with the relation Sh = 0, h being the dual Coxeter number.Though this proposition has important implications for the behavior of the quantum theory,the statement and (for the most part) the proofs amount to assertions about Lie groups withno direct reference to gauge theory.
Constrained Perturbation Regularization Approach for Signal Estimation Using Random Matrix Theory
Suliman, Mohamed; Ballal, Tarig; Kammoun, Abla; Al-Naffouri, Tareq Y.
2016-12-01
In this supplementary appendix we provide proofs and additional extensive simulations that complement the analysis of the main paper (constrained perturbation regularization approach for signal estimation using random matrix theory).
Perturbation theory, effective field theory, and oscillations in the power spectrum
Vlah, Zvonimir; Seljak, Uroš; Yat Chu, Man; Feng, Yu
2016-03-01
We explore the relationship between the nonlinear matter power spectrum and the various Lagrangian and Standard Perturbation Theories (LPT and SPT). We first look at it in the context of one dimensional (1-d) dynamics, where 1LPT is exact at the perturbative level and one can exactly resum the SPT series into the 1LPT power spectrum. Shell crossings lead to non-perturbative effects, and the PT ignorance can be quantified in terms of their ratio, which is also the transfer function squared in the absence of stochasticity. At the order of PT we work, this parametrization is equivalent to the results of effective field theory (EFT), and can thus be expanded in terms of the same parameters. We find that its radius of convergence is larger than the SPT loop expansion. The same EFT parametrization applies to all SPT loop terms and if stochasticity can be ignored, to all N-point correlators. In 3-d, the LPT structure is considerably more complicated, and we find that LPT models with parametrization motivated by the EFT exhibit running with k and that SPT is generally a better choice. Since these transfer function expansions contain free parameters that change with cosmological model their usefulness for broadband power is unclear. For this reason we test the predictions of these models on baryonic acoustic oscillations (BAO) and other primordial oscillations, including string monodromy models, for which we ran a series of simulations with and without oscillations. Most models are successful in predicting oscillations beyond their corresponding PT versions, confirming the basic validity of the model. We show that if primordial oscillations are localized to a scale q, the wiggles in power spectrum are approximately suppressed as exp[-k2Σ2(q)/2], where Σ(q) is rms displacement of particles separated by q, which saturates on large scales, and decreases as q is reduced. No oscillatory features survive past k ~ 0.5h/Mpc at z = 0.
Mesonic Chiral Rings in Calabi-Yau Cones from Field Theory
Grant, L; Grant, Lars
2007-01-01
We study the half-BPS mesonic chiral ring of the N=1 superconformal quiver theories arising from N D3-branes stacked at Y^pq and L^abc Calabi-Yau conical singularities. We map each gauge invariant operator represented on the quiver as an irreducible loop adjoint at some node, to an invariant monomial, modulo relations, in the gauged linear sigma model describing the corresponding bulk geometry. This map enables us to write a partition function at finite N over mesonic half-BPS states. It agrees with the bulk gravity interpretation of chiral ring states as cohomologically trivial giant gravitons. The quiver theories for L^aba, which have singular base geometries, contain extra operators not counted by the naive bulk partition function. These extra operators have a natural interpretation in terms of twisted states localized at the orbifold-like singularities in the bulk.
The de Sitter limit of inflation and non-linear perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Jarnhus, Philip R; Sloth, Martin S, E-mail: pjarn@phys.au.dk, E-mail: sloth@phys.au.dk [Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C (Denmark)
2008-02-15
We study the fourth-order action of the comoving curvature perturbation in an inflationary universe in order to understand more systematically the de Sitter limit in non-linear cosmological perturbation theory. We derive the action of the curvature perturbation to fourth order in the comoving gauge, and show that it vanishes sufficiently fast in the de Sitter limit. By studying the de Sitter limit, we then extrapolate to the nth-order action of the comoving curvature perturbation and discuss the slow-roll order of the n-point correlation function.
Interaction Between Massive and Massless Gravitons by Perturbing Topological Field Theory
Institute of Scientific and Technical Information of China (English)
E. Koorambas
2012-01-01
We test the Wu gauge theory of gravity with massive gravitons in the perturbing topological field theory framework. We show that the computation of the correlation function between massive and massless gravitons is reported up to 4-loop and appears to be unaffected by radiative correction. This result ensures the stability of the linking number between massive and massless gravitons with respect to the local perturbation, a result with potential wider applications in cosmology.
Perturbation theory of solid-liquid interfacial free energies of bcc metals.
Warshavsky, Vadim B; Song, Xueyu
2012-09-01
A perturbation theory is used to calculate bcc solid-liquid interfacial free energies of metallic systems with embedded-atom model potentials. As a reference system for bcc crystals we used a single-occupancy cell, hard-sphere bcc system. Good agreements between the perturbation theory results and the corresponding results from simulations are found. The strategy to extract hard-sphere bcc solid-liquid interfacial free energies may have broader applications for other crystal lattices.
Quark model with chiral-symmetry breaking and confinement in the Covariant Spectator Theory
Energy Technology Data Exchange (ETDEWEB)
Biernat, Elmer P. [CFTP, Instituto Superior TÃ©cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal; Pena, Maria Teresa [CFTP, Instituto Superior TÃ©cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal; Departamento de FÃsica, Instituto Superior TÃ©cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal; Ribiero, Jose' Emilio F. [CeFEMA, Instituto Superior TÃ©cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal; Stadler, Alfred [Departamento de FÃsica, Universidade de Ãvora, 7000-671 Ãvora, Portugal; Gross, Franz L. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
2016-03-01
We propose a model for the quark-antiquark interaction in Minkowski space using the Covariant Spectator Theory. We show that with an equal-weighted scalar-pseudoscalar structure for the confining part of our interaction kernel the axial-vector Ward-Takahashi identity is preserved and our model complies with the Adler-zero constraint for pi-pi-scattering imposed by chiral symmetry.
Role of center vortices in chiral symmetry breaking in SU(3) gauge theory
2011-01-01
We study the behavior of the AsqTad quark propagator in Landau gauge on SU(3) Yang-Mills gauge configurations under the removal of center vortices. In SU(2) gauge theory, center vortices have been observed to generate chiral symmetry breaking and dominate the infrared behavior of the quark propagator. In contrast, we report a weak dependence on the vortex content of the gauge configurations, including the survival of dynamical mass generation on configurations with vanishing string tension.
Electric Dipole Moments of Light Nuclei From Chiral Effective Field Theory
Higa, R.
2013-08-01
Recent calculations of EDMs of light nuclei in the framework of chiral effective field theory are presented. We argue that they can be written in terms of the leading six low-energy constants encoding CP-violating physics. EDMs of the deuteron, triton, and helion are explicitly given in order to corroborate our claim. An eventual non-zero measurement of these EDMs can be used to disentangle the different sources and strengths of CP-violation.
Chiral logarithms in the massless limit tamed.
Kivel, Nikolai; Polyakov, Maxim V; Vladimirov, Alexei
2008-12-31
We derive nonlinear recursion relations for the leading chiral logarithms (LLs) in massless theories. These relations not only provide a very efficient method of computation of LLs (e.g., the 33-loop contribution is calculated in a dozen of seconds on a PC) but also equip us with a powerful tool for the summation of the LLs. Our method is not limited to chiral perturbation theory only; it is pertinent to any nonrenormalizable effective field theory such as, for instance, the theory of critical phenomena, low-energy quantum gravity, etc.
Evidence for hard chiral logarithms in quenched lattice QCD
Kim, S; Kim, Seyong; Sinclair, D K
1995-01-01
We present the first direct evidence that quenched QCD differs from full QCD in the chiral (m_q \\rightarrow 0) limit, as predicted by chiral perturbation theory, from our quenched lattice QCD simulations at \\beta = 6/g^2 = 6.0. We measured the spectrum of light hadrons on 16^3 \\times 64, 24^3 \\times 64 and 32^3 \\times 64, using staggered quarks of masses m_q=0.01, m_q=0.005 and m_q=0.0025. The pion masses showed clear evidence for logarithmic violations of the PCAC relation m_{\\pi}^2 \\propto m_q, as predicted by quenched chiral perturbation theory. The dependence on spatial lattice volume precludes this being a finite size effect. No evidence was seen for such chiral logarithms in the behaviour of the chiral condensate \\langle\\bar{\\psi}\\psi\\rangle.
The supersymmetry method for chiral random matrix theory with arbitrary rotation-invariant weights
Kaymak, Vural; Kieburg, Mario; Guhr, Thomas
2014-07-01
In the past few years, the supersymmetry method has been generalized to real symmetric, Hermitian, and Hermitian self-dual random matrices drawn from ensembles invariant under the orthogonal, unitary, and unitary symplectic groups, respectively. We extend this supersymmetry approach to chiral random matrix theory invariant under the three chiral unitary groups in a unifying way. Thereby we generalize a projection formula providing a direct link and, hence, a ‘short cut’ between the probability density in ordinary space and that in superspace. We emphasize that this point was one of the main problems and shortcomings of the supersymmetry method, since only implicit dualities between ordinary space and superspace were known before. To provide examples, we apply this approach to the calculation of the supersymmetric analogue of a Lorentzian (Cauchy) ensemble and an ensemble with a quartic potential. Moreover, we consider the partially quenched partition function of the three chiral Gaussian ensembles corresponding to four-dimensional continuum quantum chromodynamics. We identify a natural splitting of the chiral Lagrangian in its lowest order into a part for the physical mesons and a part associated with source terms generating the observables, e.g. the level density of the Dirac operator.
Reina, Borja
2014-01-01
Hartle's model describes the equilibrium configuration of a rotating isolated compact body in perturbation theory up to second order in General Relativity. The interior of the body is a perfect fluid with a barotropic equation of state, no convective motions and rigid rotation. That interior is matched across its surface to an asymptotically flat vacuum exterior. Perturbations are taken to second order around a static and spherically symmetric background configuration. Apart from the explicit assumptions, the perturbed configuration is constructed upon some implicit premises, in particular the continuity of the functions describing the perturbation in terms of some background radial coordinate. In this work we revisit the model within a modern general and consistent theory of perturbative matchings to second order, which is independent of the coordinates and gauges used to describe the two regions to be joined. We explore the matching conditions up to second order in full. The main particular result we presen...
Hamiltonian cosmological perturbation theory with loop quantum gravity corrections
Bojowald, M; Kagan, M; Singh, P; Skirzewski, A; Bojowald, Martin; Hern\\'andez, Hector H.; Kagan, Mikhail; Singh, Parampreet; Skirzewski, Aureliano
2006-01-01
Cosmological perturbation equations are derived systematically in a canonical scheme based on Ashtekar variables. A comparison with the covariant derivation and various subtleties in the calculation and choice of gauges are pointed out. Nevertheless, the treatment is more systematic when correction terms of canonical quantum gravity are to be included. This is done throughout the paper for one characteristic modification expected from loop quantum gravity.
Reciprocity theorem and perturbation theory for photonic crystal waveguides.
Michaelis, D; Peschel, U; Wächter, C; Bräuer, A
2003-12-01
Starting from Maxwell's equations we derive a reciprocity theorem for photonic crystal waveguides. A set of strongly coupled discrete equations results, which can be applied to the simulation of perturbed photonic crystal waveguides. As an example we analytically study the influence of the dispersion of a two level system on the band structure of a photonic crystal waveguide. In particular, the formation of polariton gaps is discussed.
Some Applications of Hard Thermal Loop Perturbation Theory in Quark Gluon Plasma
Haque, Najmul
2014-01-01
This thesis is mainly devoted to the study of thermodynamics for quantum Chromodynamics. In this thesis I apply hard-thermal-loop perturbation theory, which is a gauge-invariant reorganization of the conventional perturbative expansion for quantum gauge theories to study the thermodynamics of QCD in leading-order, next-to-leading-order and next-to-next-to-leading order at finite temperature and finite chemical potential. I also discuss about various order diagonal and off-diagonale quark number susceptibilities in leading order as well as beyond leading order. For all the observables, I compare our results with available lattice QCD data and we find good agreement. Along-with the computation of thermodynamic quantities of hot and dense matter, I also discuss about low mass dilepton rate from hot and dense medium using both perturbative and non-perturbative models and compare them with those from lattice gauge theory and in-medium hadron gas.
Many-body quantum chemistry for the electron gas: convergent perturbative theories
Shepherd, James J
2013-01-01
We investigate the accuracy of a number of wavefunction based methods at the heart of quantum chemistry for metallic systems. Using Hartree-Fock as a reference, perturbative (M{\\o}ller-Plesset, MP) and coupled cluster (CC) theories are used to study the uniform electron gas model. Our findings suggest that non-perturbative coupled cluster theories are acceptable for modelling electronic interactions in metals whilst perturbative coupled cluster theories are not. Using screened interactions, we propose a simple modification to the widely-used coupled-cluster singles and doubles plus perturbative triples method (CCSD(T)) that lifts the divergent behaviour and is shown to give very accurate correlation energies for the homogeneous electron gas.
A time-dependent formulation of multi-reference perturbation theory.
Sokolov, Alexander Yu; Chan, Garnet Kin-Lic
2016-02-14
We discuss the time-dependent formulation of perturbation theory in the context of the interacting zeroth-order Hamiltonians that appear in multi-reference situations. As an example, we present a time-dependent formulation and implementation of second-order n-electron valence perturbation theory. The resulting time-dependent n-electron valence second-order perturbation theory (t-NEVPT2) method yields the fully uncontracted n-electron valence perturbation wavefunction and energy, but has a lower computational scaling than the usual contracted variants, and also avoids the construction of high-order density matrices and the diagonalization of metrics. We present results of t-NEVPT2 for the water, nitrogen, carbon, and chromium molecules and outline directions for the future.
Chiral field theories as models for hadron substructure
Energy Technology Data Exchange (ETDEWEB)
Kahana, S.H.
1987-03-01
A model for the nucleon as soliton of quarks interacting with classical meson fields is described. The theory, based on the linear sigma model, is renormalizable and capable of including sea quarks straightforwardly. Application to nuclear matter is made in a Wigner-Seitz approximation.