Derivation of the gap and Bethe-Salpeter equations at large $N_c$ limit and symmetry preserving truncations

Abstract

We develop a framework for deriving Dyson-Schwinger Equations (DSEs) and Bethe-Salpeter Equation (BSE) in QCD at large $N_c$ limit. The starting point is a modified form (with auxiliary fields) of QCD generating functional. This framework provides a natural order-by-order truncation scheme for DSEs and BSE, and the kernels of the equations up to any order are explicitly given. Chiral symmetry (at chiral limit) is preserved in any order truncation, so it exemplifies the symmetry preserving truncation scheme. It provides a method to study DSEs and BSE beyond the Rainbow-Ladder truncation, and is especially useful to study contributions from non-Abelian dynamics (those arise from gluon self-interactions). We also derive the equation for the quark-ghost scattering kernel, and discuss the Slavnov-Taylor identity connecting the quark-gluon vertex, the quark propagator and the quark-ghost scattering kernel.

arXiv comment19 pages, 2 figures

References in corpus (34)

• pi- and K-meson Bethe-Salpeter Amplitudes
• Bethe-Salpeter Study of Vector Meson Masses and Decay Constants
• Goldstone Theorem and Diquark Confinement Beyond Rainbow-Ladder Approximation
• Non-perturbative Propagators, Running Coupling and Dynamical Quark Mass of Landau gauge QCD
• Dynamical Chiral Symmetry Breaking, Goldstone's Theorem and the Consistency of the Schwinger--Dyson and Bethe--Salpeter Equations
• Hadron Physics from the Global Color Model of QCD
• The quark-gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement
• Aspects and consequences of a dressed-quark-gluon vertex
• Ground-state Spectrum of Light-quark Mesons
• Probing the gluon self-interaction in light mesons
• Bethe-Salpeter equation and a nonperturbative quark-gluon vertex
• Chiral symmetry breaking with lattice propagators
• Symmetry preserving truncations of the gap and Bethe-Salpeter equations
• Survey of J=0,1 mesons in a Bethe-Salpeter approach
• Hadronic unquenching effects in the quark propagator
• Beyond the rainbow: effects from pion back-coupling
• Practical corollaries of transverse Ward-Green-Takahashi identities
• Spectra of heavy quarkonia in a Bethe-Salpeter-equation approach
• On the Quark-Gluon Vertex and Quark-Ghost Kernel: combining Lattice Simulations with Dyson-Schwinger equations
• Quark-gluon vertex model and lattice-QCD data
• On Gribov's supercriticality picture of quark confinement
• Quark-gluon vertex dressing and meson masses beyond ladder-rainbow truncation
• Bethe-Salpeter Meson Masses Beyond Ladder Approximation
• Facets of confinement and dynamical chiral symmetry breaking
• QCD based quark description of pi-pi scattering up to the sigma and rho region
• Hadron Physics and the Dyson--Schwinger Equations of QCD
• Probing the quark-gluon interaction with hadrons
• Hadronic decays of mesons and baryons in the Dyson-Schwinger approach
• Derivation of the Effective Chiral Lagrangian for Pseudoscalar Mesons from QCD
• Transverse Symmetry Transformations and the Quark-Gluon Vertex Function in QCD
• First look at heavy-light mesons with a dressed quark-gluon vertex
• Bethe-Salpeter studies of mesons beyond rainbow-ladder
• Confinement, Diquarks and Goldstone's theorem
• The Quark Propagator in a Truncation Scheme beyond the Rainbow Approximation

Cited by in corpus (2)

• Masses of positive- and negative-parity hadron ground-states, including those with heavy quarks
• Practical scheme from QCD to phenomena via Dyson-Schwinger equations