Chiral symmetry breaking in QCD-like gauge theories with a confining propagator and dynamical gauge boson mass generation

TL;DR

This paper investigates how chiral symmetry breaking occurs in QCD-like theories by incorporating a confining propagator and dynamical gauge boson mass generation, showing that confinement primarily drives symmetry breaking and deriving related parameters.

Contribution

It introduces a confining effective propagator into the analysis of chiral symmetry breaking, providing new insights into the interplay between confinement and dynamical gauge boson masses.

Findings

Chiral symmetry breaking is mainly due to the confining propagator.

Derived a relation between fermion condensate and dynamical mass.

Computed QCD chiral parameters consistent with experimental data.

Abstract

We study chiral symmetry breaking in QCD-like gauge theories introducing a confining effective propagator, as proposed recently by Cornwall, and considering the effect of dynamical gauge boson mass generation. The effective confining propagator has the form $1/(k^2+m^2)^2$ and we study the bifurcation equation finding limits on $m$ below which a satisfactory fermion mass solution is generated. Since the coupling constant and gauge boson propagator are damped in the infrared, due to the presence of dynamically massive gauge bosons, the major part of the chiral breaking is only due to the confining propagator. We study the asymptotic behavior of the gap equation containing confinement and massive gauge boson exchange, and find that the symmetry breaking can be approximated at some extent 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. Within this approach we expect that lattice simulations should not see large differences between the confinement and chiral symmetry breaking scales independent of the fermionic representation and 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.