# Interplay of dynamical and explicit chiral symmetry breaking effects on a quark

## TL;DR

This paper investigates how explicit and dynamical chiral symmetry breaking contribute to quark mass generation in QCD, using advanced models and lattice QCD data, revealing their relative importance varies with quark mass.

## Contribution

It extends the analysis of chiral symmetry breaking effects in the quark-gap equation by incorporating a beyond-Abelian quark-gluon vertex and lattice QCD data, providing new insights into their interplay.

## Key findings

- The ratio of explicit to dynamical chiral symmetry breaking is largely independent of interaction models for light to heavy quarks.
- Explicit and dynamical contributions are equal at a quark mass of approximately 400 MeV.
- For solutions with lattice propagators, this equality occurs at about 200 MeV.

## Abstract

The relative contributions of explicit and dynamical chiral symmetry breaking in QCD models of the quark-gap equation are studied in dependence of frequently employed ans\"atze for the dressed interaction and quark-gluon vertex. The explicit symmetry breaking contributions are defined by a constituent-quark sigma term whereas the combined effects of explicit and dynamical symmetry breaking are described by a Euclidean constituent-mass solution. We extend this study of the gap equation to a quark-gluon vertex beyond the Abelian approximation complemented with numerical gluon- and ghost-dressing functions from lattice QCD. We find that the ratio of the sigma term over the Euclidean mass is largely independent of nonperturbative interaction and vertex models for current-quark masses, $m_{u,d}(\mu) \leq m(\mu) \leq m_b(\mu)$, and equal contributions of explicit and dynamical chiral symmetry breaking occur at $m(\mu) \approx 400$~MeV. For massive solutions of the gap equation with lattice propagators this value decreases to about 200~MeV.