Eur. Phys. J. C (2007) 52: 459-476
https://doi.org/10.1140/epjc/s10052-007-0379-3

Regular Article - Theoretical Physics

The Gribov–Zwanziger action in the presence of the gauge invariant, nonlocal mass operator Tr∫d⁴xF_μν(D²)^-1F_μν in the Landau gauge

¹ Departamento de Física Teórica, Instituto de Física, UERJ, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, 20550-013, Maracanã, Rio de Janeiro, Brasil
² Department of Mathematical Physics and Astronomy, Ghent University, Krijgslaan 281-S9, 9000, Gent, Belgium
³ CBPF, Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180, Urca, Rio de Janeiro, Brasil

^* e-mail: david.dudal@ugent.be

Received: 24 May 2007
Revised: 10 July 2007
Published online: 15 August 2007

Abstract

We prove that the nonlocal gauge invariant mass dimension 2 operator F_μν(D²)^-1F_μν 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.