Eur. Phys. J. C (2010) 68: 283-298
https://doi.org/10.1140/epjc/s10052-010-1304-8

Regular Article - Theoretical Physics

More on the renormalization of the horizon function of the Gribov–Zwanziger action and the Kugo–Ojima Green function(s)

¹ Department of Physics and Astronomy, Ghent University, Krijgslaan 281-S9, 9000, Gent, Belgium
² 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

^* e-mail: nele.vandersickel@ugent.be

Received: 19 January 2010
Published online: 2 April 2010

Abstract

In this paper we provide strong evidence that there is no ambiguity in the choice of the horizon function underlying the Gribov–Zwanziger action. We show that there is only one correct possibility which is determined by the requirement of multiplicative renormalizability. As a consequence, this means that relations derived from other horizon functions cannot be given a consistent interpretation in terms of a local and renormalizable quantum field theory. In addition, we also discuss that the Kugo–Ojima functions u(p ²) and w(p ²) can only be defined after renormalization of the underlying Green function(s).