Gauge dependence of the quark gap equation: an exploratory study

TL;DR

This study investigates how the nonperturbative quark propagator in QCD depends on gauge choice by solving the gap equation with a carefully constrained vertex, revealing gauge-dependent variations in the mass function and condensate.

Contribution

It introduces a gauge-dependent analysis of the quark propagator using a nonperturbative vertex constrained by symmetries and lattice gluon propagators, advancing understanding of gauge effects in QCD.

Findings

Mass function increases with gauge parameter in the infrared.

Wave renormalization decreases as gauge parameter increases.

Chiral quark condensate shows mild gauge dependence.

Abstract

We study the gauge dependence of the quark propagator in quantum chromodynamics by solving the gap equation with a nonperturbative quark-gluon vertex which is constrained by longitudinal and transverse Slavnov-Taylor identities, the discrete charge conjugation and parity symmetries and which is free of kinematic singularities in the limit of equal incoming and outgoing quark momenta. We employ gluon propagators in renormalizable $R_\xi$ gauges obtained in lattice QCD studies. We report the dependence of the nonperturbative quark propagator on the gauge parameter, in particular we observe an increase, proportional to the gauge-fixing parameter, of the mass function in the infrared domain, whereas the wave renormalization decreases within the range $0 \leq \xi \leq 1$ considered here. The chiral quark condensate reveals a mild gauge dependence in the region of $\xi$ investigated. We comment on how to build and improve upon this exploratory study in future in conjunction with generalized gauge covariance relations for QCD.