Physical Unitarity for Massive Non-abelian Gauge Theories in the Landau Gauge: Stueckelberg and Higgs

TL;DR

This paper investigates the unitarity of massive non-abelian gauge theories in Landau gauge, establishing conditions under which the theories remain unitary, and applies the findings to both Stueckelberg and Higgs mechanisms.

Contribution

It demonstrates that unitarity in these theories depends on the absence of poles at zero momentum in the vector meson two-point function, providing a novel necessary condition for physical unitarity.

Findings

Unitarity holds if the 1-PI two-point function has no poles at p^2=0.

The proof applies to both Stueckelberg and Higgs mass generation.

The condition is crucial for defining consistent massive gauge theories.

Abstract

We discuss the problem of unitarity for Yang-Mills theory in the Landau gauge with a mass term a la Stueckelberg. We assume that the theory (non-renormalizable) makes sense in some subtraction scheme (in particular the Slavnov-Taylor identities should be respected!) and we devote the paper to the study of the space of the unphysical modes. We find that the theory is unitary only under the hypothesis that the 1-PI two-point function of the vector mesons has no poles (at p^2=0). This normalization condition might be rather crucial in the very definition of the theory. With all these provisos the theory is unitary. The proof of unitarity is given both in a form that allows a direct transcription in terms of Feynman amplitudes (cutting rules) and in the operatorial form. The same arguments and conclusions apply verbatim to the case of non-abelian gauge theories where the mass of the vector meson is generated via Higgs mechanism. To the best of our knowledge, there is no mention in the literature on the necessary condition implied by physical unitarity.