Multivacuum States in a Fermionic Gap Equation with massive gluons and confinement

TL;DR

This paper investigates the solutions of the QCD fermionic gap equation considering massive gluons and confinement, revealing conditions for multiple vacuum states and their absence under various scenarios.

Contribution

It provides a comprehensive analysis of multivacuum solutions in the fermionic gap equation with massive gluons and confinement, clarifying when such solutions occur or are absent.

Findings

Multivacuum solutions exist with non-running gluon mass.

Vacuum replicas are absent with running gluon mass.

Pure confinement sector has only one stable solution.

Abstract

We study the nontrivial solutions of the QCD fermionic gap equation including the contribution of dynamically massive gluons and the confining propagator proposed by Cornwall. Without the confining propagator, in the case of non-running gluon mass (mg), we found the multivacuum solutions (replicas) reported in the literature and we were able to define limits on mg for dynamical chiral symmetry breaking. On the other side, when considering the running in the gluon mass the vacuum replicas are absent in the limits on mg where the chiral symmetry is broken. In the pure confining sector, the multivacuum states are always absent so it is said that only one stable solution for the gap equation is found as claimed in previous analysis using different approaches. Finally in the case of the complete gap equation i.e. with both contributions, the vacuum replicas are also absent in both cases; with constant and with running gluon mass.