A candidate for the scalar glueball operator within the Gribov-Zwanziger framework

TL;DR

This paper investigates the renormalization of the $F^2_{}$ operator within the Gribov-Zwanziger framework, identifying a potential physical operator related to the scalar glueball, and discusses the impact of BRST symmetry breaking.

Contribution

It introduces a candidate for a physical scalar glueball operator in the Gribov-Zwanziger framework and analyzes the effects of BRST symmetry breaking on operator mixing.

Findings

$F^2_{}$ mixes with other operators in Faddeev-Popov theory but not at the correlator level due to BRST invariance.

In the Gribov-Zwanziger approach, BRST breaking causes $F^2_{}$ mixing to affect correlators.

A possible physical operator candidate for the scalar glueball is proposed within the Gribov-Zwanziger framework.

Abstract

This proceeding gives an overview of the renormalization of $F^2_{\mu\nu}$ using the Faddeev-Popov action and the more complicate Gribov-Zwanziger action, which deals with Gribov copies. We show that using the Faddeev-Popov action, $F^2_{\mu\nu}$ mixes with other $d=4$ operators. However, due to the BRST invariance of the action, this mixing is not relevant at the level of the correlator, $\Braket {F^2_{\mu\nu}(x) F^2_{\alpha \beta}(y)}$. In contrast, when turning to the Gribov-Zwanziger action, the mixing of $F^2_{\mu\nu}$ with other $d=4$ operator does have consequences at the level of the correlator. This is due to the breaking of the BRST. We then present a possible candidate for a physical operator in the Gribov-Zwanziger framework.