Gauge dependence of the quark gap equation: An exploratory study

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 <= xi <= 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.

Automated summary

In this study, we investigate the dependence of the quark propagator in quantum chromodynamics on the gauge parameter by solving the gap equation. We use a nonperturbative quark-gluon vertex that satisfies various constraints and has no kinematic singularities. Gluon propagators in renormalizable R xi gauges obtained from lattice QCD studies are employed. We find that the nonperturbative quark propagator has a gauge-dependent behavior, with the mass function increasing in the infrared domain proportional to the gauge-fixing parameter, while the wave renormalization decreases within the considered range of xi (0 <= xi <= 1). The gauge dependence of the chiral quark condensate is mild within the explored region of xi. We discuss possibilities for further research in conjunction with generalized gauge covariance relations for QCD.