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

TL;DR

This paper investigates how the quark gap equation maintains gauge covariance across different quark-gluon vertex models, using the chiral condensate and pion decay constant as key tests.

Contribution

It compares gauge covariance for three vertex models, including a full vertex with transverse components, under gauge symmetry constraints.

Findings

Gauge covariance verified with chiral condensate

Gauge covariance verified with pion decay constant

Full vertex including transverse components enhances covariance

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.