Chiral symmetry breaking with a confining propagator and dynamically massive gluons

TL;DR

This paper investigates chiral symmetry breaking in QCD by incorporating a confining effective propagator and dynamically massive gluons, showing that confinement dominates the breaking mechanism and deriving related QCD parameters.

Contribution

It introduces a confining propagator with a specific form and analyzes its role in chiral symmetry breaking, connecting it to an effective four-fermion interaction and computing QCD parameters.

Findings

Chiral symmetry breaking primarily driven by the confining propagator.

Derived limits on the parameter m for fermion mass generation.

Obtained QCD chiral parameters consistent with experimental data.

Abstract

Chiral symmetry breaking in QCD is studied introducing a confining effective propagator, as proposed recently by Cornwall, and considering the effect of dynamically massive gluons. The effective confining propagator has the form $1/(k^2+m^2)^2$ and we study the bifurcation equation finding limits on the parameter $m$ below which a satisfactory fermion mass solution is generated. Since the coupling constant and gluon propagator are damped in the infrared, due to the presence of a dynamical gluon mass, the major part of the chiral breaking is only due to the confining propagator and related to the low momentum region of the gap equation. We study the asymptotic behavior of the gap equation containing this confinement effect and massive gluon exchange, and find that the symmetry breaking can be approximated by an effective four-fermion interaction generated by the confining propagator. We compute some QCD chiral parameters as a function of $m$, finding values compatible with the experimental data. We find a simple approximate relation between the fermion condensate and dynamical mass for a given representation as a function of the parameters appearing in the effective confining propagator.