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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 theGribov-Zwanziger action, which implements the restriction of the pathintegral's domain of integration to the first Gribov region when the Landaugauge is considered. We identify a local polynomial action and prove therenormalizability to all orders of perturbation theory by employing thealgebraic renormalization formalism. Furthermore, we also pay attention to thebreaking of the BRST invariance, and to the consequences that this has for theSlavnov-Taylor identity.

european physical journal. c, particles and fields

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