The Gribov-Zwanziger action in the presence of the gauge invariant, nonlocal mass operator $Tr \int d^4x F_{\mu\nu} (D^2)^{-1} F_{\mu\nu}$ in the Landau gauge

TL;DR

This paper demonstrates how to incorporate a nonlocal, gauge-invariant mass operator into the Gribov-Zwanziger framework in Landau gauge, establishing its renormalizability and analyzing BRST symmetry breaking effects.

Contribution

It introduces a consistent local polynomial action including the nonlocal mass operator and proves its all-order renormalizability within the Gribov-Zwanziger approach.

Findings

The nonlocal operator can be added without spoiling renormalizability.

A local polynomial action equivalent to the nonlocal operator is constructed.

BRST symmetry breaking implications are analyzed.

Abstract

We prove that the nonlocal gauge invariant mass dimension two operator $F_{\mu\nu} (D^2)^{-1} F_{\mu\nu}$ can be consistently added to the Gribov-Zwanziger action, which implements the restriction of the path integral's domain of integration to the first Gribov region when the Landau gauge is considered. We identify a local polynomial action and prove the renormalizability to all orders of perturbation theory by employing the algebraic renormalization formalism. Furthermore, we also pay attention to the breaking of the BRST invariance, and to the consequences that this has for the Slavnov-Taylor identity.