Chiral symmetry breaking revisited: the gap equation with lattice ingredients

TL;DR

This paper investigates chiral symmetry breaking in QCD by incorporating recent lattice data into the quark gap equation, leading to realistic dynamical quark masses and phenomenologically consistent pion decay constants without explicitly invoking confinement.

Contribution

It introduces a non-Abelian Ansatz for the quark-gluon vertex that depends on lattice-derived ghost and gluon propagators, providing a novel approach to chiral symmetry breaking analysis.

Findings

Dynamical quark masses around 300 MeV are obtained.

Pion decay constant and quark condensate match experimental values.

Explicit confinement is not necessary for chiral symmetry breaking.

Abstract

We study chiral symmetry breaking in QCD, using as ingredients in the quark gap equation recent lattice results for the gluon and ghost propagators. The Ansatz employed for the quark-gluon vertex is purely non-Abelian, introducing a crucial dependence on the ghost dressing function and the quark-ghost scattering amplitude. The numerical impact of these quantities is considerable: the need to invoke confinement explicitly is avoided, and the dynamical quark masses generated are of the order of 300 MeV. In addition, the pion decay constant and the quark condensate are computed, and are found to be in good agreement with phenomenology.