Gauge covariance of the gap equation: from the rainbow truncation to gauge symmetry constraints

Abstract

The gauge covariance of the quark gap equation is compared for three quark-gluon vertices: the bare vertex, a Ball-Chiu like vertex constrained by the corresponding Slavnov-Taylor identity, and a full vertex including the transverse components derived from transverse Slavnov-Taylor identities. The covariance properties are verified with the chiral quark condensate and the pion decay constant in the chiral limit.

arXiv commentInvited contribution to the special edition "Chiral Symmetry, and Restoration in Nuclear Dense Matter" to appear in Symmetry. 12 pages and 5 figures, improved discussion of vertex form factor on page 5

References in corpus (31)

• Collective perspective on advances in Dyson-Schwinger Equation QCD
• Proton Mass Decomposition from the QCD Energy Momentum Tensor
• Electromagnetic Pion Form Factor and Neutral Pion Decay Width
• Lattice Gluon and Ghost Propagators, and the Strong Coupling in Pure SU(3) Yang-Mills Theory: Finite Lattice Spacing and Volume Effects
• Chiral symmetry breaking with lattice propagators
• Quark-gluon vertex in arbitrary gauge and dimension
• ONE LOOP QED VERTEX IN ANY COVARIANT GAUGE: ITS COMPLETE ANALYTIC FORM
• Dynamical chiral symmetry breaking and the fermion--gauge-boson vertex
• On the Quark-Gluon Vertex and Quark-Ghost Kernel: combining Lattice Simulations with Dyson-Schwinger equations
• The lattice gluon propagator in renormalizable $\xi$ gauges
• High Precision Statistical Landau Gauge Lattice Gluon Propagator Computation vs. the Gribov-Zwanziger approach
• On gluon and ghost propagators in linear covariant gauges
• Quark propagator with two flavors of O(a)-improved Wilson fermions
• Charmed mesons with a symmetry-preserving contact interaction
• Non-Abelian Ball-Chiu vertex for arbitrary Euclidean momenta
• Schwinger mechanism in linear covariant gauges
• Transverse Ward-Takahashi Identity, Anomaly and Schwinger-Dyson Equation
• Transverse Takahashi Identities and Their Implications for Gauge Independent Dynamical Chiral Symmetry Breaking
• Distribution Amplitudes of Heavy Mesons and Quarkonia on the Light Front
• Dynamical Fermion Masses and Constraints of Gauge Invariance in Quenched QED3
• Interplay of dynamical and explicit chiral symmetry breaking effects on a quark
• Checking the transverse Ward-Takahashi relation at one loop order in 4-dimensions
• Yang-Mills propagators in linear covariant gauges from Nielsen identities
• Transverse Symmetry Transformations and the Quark-Gluon Vertex Function in QCD
• Local Gauge Transformation for the Quark Propagator in an SU(N) Gauge Theory
• A fresh look at the (non-)Abelian Landau-Khalatnikov-Fradkin transformations
• Gauge dependence of the quark gap equation: an exploratory study
• $D^{\ast }$ and $D_s^{\ast }$ distribution amplitudes from Bethe-Salpeter wave functions
• Landau-Khalatnikov-Fradkin Transformations, Nielsen Identities, Their Equivalence and Implications for QCD
• Parton distribution functions and transverse momentum dependence of heavy mesons
• Lattice Computation of the Ghost Propagator in Linear Covariant Gauges