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

This proceeding gives an overview of the renormalization of $F_{\mu \nu }^2$ 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, $F_{\mu \nu }^2$ 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, $⟨F_{\mu \nu }^2(x)F_{\alpha \beta }^2(y)⟩$. In contrast, when turning to the Gribov-Zwanziger action, the mixing of $F_{\mu \nu }^2$ 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.