Two loop MSbar Gribov mass gap equation with massive quarks

TL;DR

This paper calculates the two-loop MSbar correction to the Gribov mass gap equation in Landau gauge, incorporating massive quarks, and verifies consistency with the massless quark limit.

Contribution

It provides the first two-loop correction to the Gribov mass gap equation with massive quarks in the MSbar scheme.

Findings

Reproduces the known gap equation as quark mass approaches zero

Involves complex dilogarithm calculations

Enhances understanding of quark effects in the Gribov-Zwanziger framework

Abstract

We compute the two loop MSbar correction to the Gribov mass gap equation in the Landau gauge using the Gribov-Zwanziger Lagrangian with massive quarks included. The computation involves dilogarithms of complex arguments and reproduces the known gap equation when the quark mass tends to zero.