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

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.