The Quark Propagator in a Truncation Scheme beyond the Rainbow Approximation

TL;DR

This paper investigates the quark propagator using an advanced truncation scheme that includes non-perturbative dressing of the quark-gluon vertex, revealing significant effects of non-Abelian interactions on dynamical mass generation.

Contribution

It introduces a truncation scheme beyond the rainbow approximation by non-perturbatively dressing the quark-gluon vertex, highlighting the impact of non-Abelian contributions on chiral symmetry breaking.

Findings

Dynamical quark mass is significantly enhanced.

Quark condensate increases due to non-Abelian effects.

Critical strength for chiral symmetry breaking is lowered.

Abstract

The quark propagator is studied under a truncation scheme beyond the rainbow approximation by dressing the quark-gluon vertex non-perturbatively. It is found that, in the chiral limit with dynamical symmetry breaking, the dynamical quark mass and the quark condensate are significantly enhanced due to the non-Abelian contribution arising from the three-gluon interaction compared to those under the rainbow approximation; and the critical strength of the dynamical chiral symmetry breaking is much lowered. The Abelian contribution is much smaller than the non-Abelian contribution. A technical issue on removing the ultraviolet divergences including the overlapping divergences is discussed.