Dynamical Chiral Symmetry Breaking, Goldstone's Theorem and the Consistency of the Schwinger--Dyson and Bethe--Salpeter Equations

Abstract

A proof of Goldstone's theorem is given for the case in which global chiral symmetry is dynamically broken. The proof highlights a needed consistency between the exact Schwinger--Dyson equation for the fermion propagator and the exact Bethe--Salpeter equation for fermion--antifermion bound states. A criterion, based on the Cornwall, Jackiw and Tomboulis effective action for composite operators, is provided for maintaining the consistency when the equations are modified by approximations. For gauge theories in which partial conservation of the axial current (PCAC) should hold, a constraint on the approximations to the fermion--gauge boson vertex function is discussed, and a vertex model is given which satisfies both the PCAC constraint and the vector Ward--Takahashi identity.

13 pages, LaTeX, no figures

References in corpus (3)

• Dyson-Schwinger Equations and the Application to Hadronic Physics
• Gauge independent Chiral Symmetry Breaking in Quenched QED
• Gauge covariant fermion propagator in quenched, chirally-symmetric quantum electrodynamics

Cited by in corpus (183)

• Dyson-Schwinger equations: a tool for hadron physics
• Baryons as relativistic three-quark bound states
• Goldstone Theorem and Diquark Confinement Beyond Rainbow-Ladder Approximation
• Collective perspective on advances in Dyson-Schwinger Equation QCD
• Explanation and Prediction of Observables using Continuum Strong QCD
• Sketching the Bethe-Salpeter kernel
• Interaction model for the gap equation
• Bridging a gap between continuum-QCD and ab initio predictions of hadron observables
• Hadron Properties and Dyson-Schwinger Equations
• Pion electromagnetic form factor at spacelike momenta
• Light mesons in QCD and unquenching effects from the 3PI effective action
• The quark-gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement
• Insights into the Emergence of Mass from Studies of Pion and Kaon Structure
• Aspects and consequences of a dressed-quark-gluon vertex
• The pion: an enigma within the Standard Model
• Abelian anomaly and neutral pion production
• Process-independent strong running coupling
• Aspects of Hadron Physics
• pi- and rho-mesons, and their diquark partners, from a contact interaction
• Ground-state Spectrum of Light-quark Mesons
• Survey of nucleon electromagnetic form factors
• On unifying the description of meson and baryon properties
• Commentary on rainbow-ladder truncation for excited states and exotics
• Probing the gluon self-interaction in light mesons
• Nucleon electromagnetic form factors from the covariant Faddeev equation
• Bethe-Salpeter equation and a nonperturbative quark-gluon vertex
• Pion form factor from a contact interaction
• Symmetry preserving truncations of the gap and Bethe-Salpeter equations
• Masses of ground and excited-state hadrons
• Spectrum of light- and heavy-baryons
• Symmetry, symmetry breaking, and pion parton distributions
• Basic features of the pion valence-quark distribution function
• Perspective on rainbow-ladder truncation
• Natural constraints on the gluon-quark vertex
• Spectrum of hadrons with strangeness
• Valence-quark distribution functions in the kaon and pion
• Survey of J=0,1 mesons in a Bethe-Salpeter approach
• Hadronic unquenching effects in the quark propagator
• The quark-gluon vertex in Landau gauge bound-state studies
• Pion and kaon valence-quark parton distribution functions
• Dynamical chiral symmetry breaking and the fermion--gauge-boson vertex
• Practical corollaries of transverse Ward-Green-Takahashi identities
• Spectra of heavy quarkonia in a Bethe-Salpeter-equation approach
• Masses of ground-state mesons and baryons, including those with heavy quarks
• Perspective on the origin of hadron masses
• On the Quark-Gluon Vertex and Quark-Ghost Kernel: combining Lattice Simulations with Dyson-Schwinger equations
• Empirical Consequences of Emergent Mass
• Regarding confinement and dynamical chiral symmetry breaking in QED3
• Sketching the pion's valence-quark generalised parton distribution
• Selected Science Opportunities for the EicC
• Bottomonium in a Bethe-Salpeter-equation study
• Gauge Sector Dynamics in QCD
• Flavour dependence of the pion and kaon form factors and parton distribution functions
• Nucleon axial and pseudoscalar form factors from the covariant Faddeev equation
• Leading-twist parton distribution amplitudes of S-wave heavy-quarkonia
• Sigma Terms of Light-Quark Hadrons
• Flavour symmetry breaking and meson masses
• Ward-Green-Takahashi identities and the axial-vector vertex
• Dynamical chiral symmetry breaking and a critical mass
• Parton distribution amplitudes of light vector mesons
• Phase diagram and thermal properties of strong-interaction matter
• Massless bound-state excitations and the Schwinger mechanism in QCD
• Chiral susceptibility and the scalar Ward identity
• ${\gamma }^{\ast }\gamma \to \eta ,{\eta }^{\prime }$ transition form factors
• Impressions of the Continuum Bound State Problem in QCD
• Pion distribution amplitude from lattice-QCD
• QCD Running Couplings and Effective Charges
• Three Lectures on Hadron Physics
• Mass-dependence of pseudoscalar meson elastic form factors
• Pion cloud effects on baryon masses
• Emergent Hadron Mass in Strong Dynamics
• Quark-gluon vertex dressing and meson masses beyond ladder-rainbow truncation
• Elastic electromagnetic form factors of vector mesons
• Delta and Omega masses in a three-quark covariant Faddeev approach
• Elastic and transition form factors of the Δ(1232)
• Nucleon tensor charges and electric dipole moments
• From Bethe-Salpeter Wave Functions to Generalised Parton Distributions
• Baryon and meson screening masses
• Mind the gap
• Vector-meson production and vector meson dominance
• Delta and Omega electromagnetic form factors in a Dyson-Schwinger/Bethe-Salpeter approach
• Poincaré-covariant analysis of heavy-quark baryons
• Understanding the nucleon as a Borromean bound-state
• Chemical potential and the gap equation
• Interface Effect in QCD Phase Transitions via Dyson-Schwinger Equation Approach
• Charmonia in a Contact Interaction
• Charmed mesons with a symmetry-preserving contact interaction
• Strong D* -> D+pi and B* -> B+pi couplings
• Resolving the Bethe-Salpeter kernel
• Features and flaws of a contact interaction treatment of the kaon
• Nucleon to Delta electromagnetic transition in the Dyson-Schwinger approach
• Contact-interaction Faddeev equation and, inter alia, proton tensor charges
• Contact interaction analysis of pion GTMDs
• Progress in vacuum susceptibilities and their applications to the chiral phase transition of QCD
• Beyond Rainbow-Ladder in bound state equations
• Schwinger functions and light-quark bound states, and sigma terms
• A covariant study of tensor mesons
• Proton tensor charges from a Poincaré-covariant Faddeev equation
• Masses of J^PC =1^-+ exotic quarkonia in a Bethe-Salpeter-equation approach
• Probing the quark-gluon interaction with hadrons
• Off-shell persistence of composite pions and kaons
• A new Perspective on the Scalar meson Puzzle, from Spontaneous Chiral Symmetry Breaking Beyond BCS
• Delta and Omega electromagnetic form factors in a three-body covariant Bethe-Salpeter approach
• Exploring the light-quark interaction
• Dressed-quarks and the nucleon's axial charge
• Octet and Decuplet masses: a covariant three-body Faddeev calculation
• Matrix algorithms for solving (in)homogeneous bound state equations
• Delta-baryon mass in a covariant Faddeev approach
• Vector mesons as dynamical resonances in the Bethe-Salpeter framework
• Hadronic decays of mesons and baryons in the Dyson-Schwinger approach
• Existence and stability of multiple solutions to the gap equation
• Rho-meson, Bethe-Salpeter equation, and the far infrared
• Nucleon axial-vector and pseudoscalar form factors, and PCAC relations
• Aspects of open-flavour mesons in a comprehensive DSBSE study
• Effects of a dressed quark-gluon vertex in pseudoscalar heavy-light mesons
• The role of momentum dependent dressing functions and vector meson dominance in hadronic light-by-light contributions to the muon g-2
• Form Factors of the Nucleon Axial Current
• Cold quarks in medium: an equation of state
• Bethe-Salpeter kernel and properties of strange-quark mesons
• Zero mode in a strongly coupled quark gluon plasma
• Practical scheme from QCD to phenomena via Dyson-Schwinger equations
• Unified description of hadron-photon and hadron-meson scattering in the Dyson-Schwinger approach
• Flavourful hadronic physics
• First look at heavy-light mesons with a dressed quark-gluon vertex
• Spontaneous chiral symmetry breaking in the massive Landau gauge: realistic running coupling
• Hyperon elastic electromagnetic form factors in the space-like momentum region
• Semileptonic decays of $D_{(s)}$ mesons
• Vector-Interaction-Enhanced Bag Model
• Heavy-light mesons beyond ladder approximation
• On a new approach to meson phenomenology with the Bethe-Salpeter equation
• Quark anomalous magnetic moment and its effects on the $\rho$ meson properties
• Bethe-Salpeter studies of mesons beyond rainbow-ladder
• Semileptonic $B_c\to {\eta }_c,J/\psi$ transitions
• Study of Quark Propagator Solutions to the Dyson--Schwinger Equation in a Confining Model
• Vacuum pseudoscalar susceptibility
• Contact interaction analysis of octet baryon axialvector and pseudoscalar form factors
• Electric dipole moment of the rho-meson
• Distribution amplitudes of light diquarks
• Pion scalar, vector and tensor form factors from a contact interaction
• Light-quarkonium spectra and orbital-angular-momentum decomposition in a Bethe-Salpeter-equation approach
• Application of Jain and Munczek's bound-state approach to gamma gamma-processes of pi0, eta_c and eta_b
• Confinement, DCSB, Bound States, and the Quark-Gluon Vertex
• Quark-Antiquark Bound States within a Dyson-Schwinger Bethe-Salpeter Formalism
• Heavy+light pseudoscalar meson semileptonic transitions
• Light Pseudoscalar Mesons in Bethe-Salpeter Equation with Instantaneous Interaction
• Nonperturbative Aspect of Axial Vector Vertex in the Global Color Symmetry Model
• Theory and Phenomenology of Hadrons
• Hadronic bound-states in SU(2) from Dyson--Schwinger Equations
• Symmetry-preserving contact interaction model for heavy-light mesons
• Impact of the Nuclear Equation of State on the Stability of Hybrid Neutron Stars
• The Quark Propagator in a Truncation Scheme beyond the Rainbow Approximation
• Diquark bound states with a completely crossed ladder truncation
• Emergent phenomena and partonic structure in hadrons
• Chiral symmetry restoration and properties of Goldstone bosons at finite temperature
• New insight on the quark condensate beyond chiral limit
• Dressed Quark Tensor Vertex and Nucleon Tensor Charge
• Meson spectroscopy and properties using Dyson-Schwinger equations
• Quasi-exotic open-flavor mesons
• QCD phase transition and equation of state of stellar strong interaction matter via Dyson-Schwinger equation approach
• Radially excited pion: electromagnetic form factor and the box contribution to the muon's $g-2$
• A comprehensive approach to the physics of mesons
• Extending the truncated Dyson-Schwinger equation to finite temperatures
• Dynamical Chiral Symmetry Breaking in Effective Models of QCD in the Bethe-Salpeter Approach
• DSE inspired model for the pion's valence dressed-quark GPD
• On the low-energy spectrum of an SU(2) gauge theory with dynamical fermions
• Pseudo-scalar {\boldm $q\bar{q}$} bound states at finite temperatures within a Dyson-Schwinger--Bethe-Salpeter approach
• Calculation of tensor susceptibility beyond rainbow-ladder approximation of Dyson-Schwinger equations approach
• Non-perturbative Analysis of Various Mass Generation by Gluonic Dressing Effect with the Schwinger-Dyson Formalism in QCD
• Distribution amplitudes of heavy-light pseudo-scalar and vector mesons from Dyson-Schwinger equations framework
• On aspects of self-consistency in the Dyson-Schwinger approach to QED and λ(ϕ^\star ϕ)^2 theories
• Mass-dependence of pseudocritical temperature in mean field approximation
• Hadron phenomenology from first-principle QCD studies
• Partial wave analysis for the in-hadron condensate
• Derivation of the gap and Bethe-Salpeter equations at large $N_c$ limit and symmetry preserving truncations
• Approximation of the Schwinger--Dyson and the Bethe--Salpeter Equations and Chiral Symmetry of QCD
• Gauge invariant formulation of 3$\gamma$ decay of particle-antiparticle bound states
• S- and D-wave vector charmonia
• Bethe-Salpeter equations: mesons beyond the rainbow-ladder truncation
• Perturbative method to estimate meson masses in the framework of Bethe-Salpeter equation beyond its dominant interaction
• Images of the Origin of Mass
• $D^{\ast }D\pi$ and $B^{\ast }B\pi$ couplings from Dyson-Schwinger equations framework
• Unified analysis of screening masses for vector and axial-vector mesons and their diquark partners in the Contact Interaction model
• Exploring the In-Medium Momentum Dependence of the Dynamical Quark Mass