  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.
