Gauge dependence of the quark gap equation: an exploratory study

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 $0\le \xi \le 1$ 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.

8 pages, 5 figures, 1 table, version accepted for publication in PRD

References in corpus (8)

• Chiral symmetry breaking with lattice propagators
• On gluon and ghost propagators in linear covariant gauges
• Schwinger mechanism in linear covariant gauges
• Quark-gluon vertex from Nf=2 lattice QCD
• Yang-Mills propagators in linear covariant gauges from Nielsen identities
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Cited by in corpus (5)

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• Parton distribution and fragmentation functions with massive gluons
• Spinning Pairs: Supporting ${}^3{P}_0$ Quark-Pair Creation from Landau Gauge Green's Functions
• Gauge covariance of the gap equation: from the rainbow truncation to gauge symmetry constraints
• Gauge invariant spectral analysis of quark hadronization dynamics