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

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.