Unitarity analysis of a non-Abelian gauge invariant action with a mass

Abstract

In previous work done by us and coworkers, we have been able to construct a local, non-Abelian gauge invariant action with a mass parameter, based on the nonlocal gauge invariant mass dimension two operator ${F}_{\ensuremath{\mu}\ensuremath{\nu}}({D}^{2}{)}^{\ensuremath{-}1}{F}_{\ensuremath{\mu}\ensuremath{\nu}}$. The renormalizability of the resulting action was proven to all orders of perturbation theory, in the class of linear covariant gauges. We also discussed the perturbative equivalence of the model with ordinary massless Yang-Mills gauge theories when the mass is identically zero. Furthermore, we pointed out the existence of a Becchi-Rouet-Stora-Tyutin (BRST) symmetry with corresponding nilpotent charge. In this paper, we study the issue of unitarity of this massive gauge model. First, we provide a short review how to discuss the unitarity making use of the BRST charge. Afterwards we make a detailed study of the most general version of our action, and we come to the conclusion that the model is not unitary, as we are unable to remove all the negative norm states from the physical spectrum in a consistent way.