The Gribov-Zwanziger action in the presence of the gauge invariant, nonlocal mass operator $Tr \int d^4x F_{\mu\nu} (D^2)^{-1} F_{\mu\nu}$ in the Landau gauge

Understand

We prove that the nonlocal gauge invariant mass dimension two operator $F_{\mu\nu} (D^2)^{-1} F_{\mu\nu}$ can be consistently added to the Gribov-Zwanziger action, which implements the restriction of the path integral's domain of integration to the first Gribov region when the Landau gauge is considered.

• We identify a local polynomial action and prove the renormalizability to all orders of perturbation theory by employing the algebraic renormalization formalism.
• Furthermore, we also pay attention to the breaking of the BRST invariance, and to the consequences that this has for the Slavnov-Taylor identity.