Chiral symmetry breaking with lattice propagators

TL;DR

This paper investigates chiral symmetry breaking using lattice-derived propagators and a detailed analysis of the quark-gluon vertex, revealing significant dynamical mass generation for quarks and fermions in the adjoint representation.

Contribution

It introduces a comprehensive study of the non-abelian quark-gluon vertex and its impact on chiral symmetry breaking using lattice data and dynamical equations.

Findings

Constituent quark mass around 300 MeV.

Fermions in the adjoint representation acquire masses between 750-962 MeV.

The scalar form factor significantly influences the gap equation.

Abstract

We study chiral symmetry breaking using the standard gap equation, supplemented with the infrared-finite gluon propagator and ghost dressing function obtained from large-volume lattice simulations. One of the most important ingredients of this analysis is the non-abelian quark-gluon vertex, which controls the way the ghost sector enters into the gap equation. Specifically, this vertex introduces a numerically crucial dependence on the ghost dressing function and the quark-ghost scattering amplitude. This latter quantity satisfies its own, previously unexplored, dynamical equation, which may be decomposed into individual integral equations for its various form factors. In particular, the scalar form factor is obtained from an approximate version of the "one-loop dressed" integral equation, and its numerical impact turns out to be rather considerable. The detailed numerical analysis of the resulting gap equation reveals that the constituent quark mass obtained is about 300 MeV, while fermions in the adjoint representation acquire a mass in the range of (750-962) MeV.