Implications of the Topological Chern-Simons mass in the Gap Equation

TL;DR

This paper investigates how the topological Chern-Simons mass influences the solutions of the gap equation in a modified Yang-Mills theory, revealing three distinct solutions and new insights into the theory's regime.

Contribution

It introduces a first-order analysis of the Chern-Simons mass in the gap equation, identifying three possible Gribov parameters and contrasting with previous results.

Findings

Three solutions to the gap equation with different Gribov parameters

Distinct regimes of the theory for each Gribov parameter

Results differ from existing literature on the topic

Abstract

In this paper, we solve the gap equation of the Yang-Mills-Gribov-Zwanziger-Chern-Simon theory by considering the first order in the Chern-Simon topological mass term, $M$. As a result, we find three possible solutions to the gap equation, i.e. three different Gribov parameters. In addition, we analyze the regime of the theory for each of these Gribov parameters and we obtain a different result from the literature.