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

TL;DR

This paper investigates the unitarity of a gauge-invariant massive non-Abelian gauge theory, concluding that the model is not unitary due to the persistence of negative norm states.

Contribution

It provides a detailed unitarity analysis of a previously constructed gauge-invariant massive non-Abelian action, revealing its non-unitary nature.

Findings

The model is not unitary due to negative norm states.

BRST symmetry exists but does not ensure unitarity.

The analysis clarifies limitations of gauge-invariant mass terms.

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 F1/D^2F. 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 BRST symmetry with corresponding nilpotent charge. In this paper, we study the issue of unitarity of this massive gauge model. Firstly, 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.