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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 BRSTinvariance of the action, this mixing is not relevant at the level of thecorrelator, $\Braket {F^2_{\mu\nu}(x) F^2_{\alpha \beta}(y)}$. In contrast,when turning to the Gribov-Zwanziger action, the mixing of $F^2_{\mu\nu}$ withother $d=4$ operator does have consequences at the level of the correlator.This is due to the breaking of the BRST. We then present a possible candidatefor a physical operator in the Gribov-Zwanziger framework.

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