Physical unitarity for a massive Yang-Mills theory without the Higgs field: (I) A perturbative treatment

TL;DR

This paper investigates the physical unitarity of a massive Yang-Mills theory without the Higgs mechanism, introducing a new perturbative approach and highlighting unitarity violations, as a foundation for future nonperturbative studies.

Contribution

It develops a novel perturbative framework to analyze unitarity in a Higgsless massive Yang-Mills theory, clarifying unitarity violations and setting the stage for nonperturbative solutions.

Findings

Reproduces unitarity violation transparently

Establishes a perturbative framework for massive Yang-Mills theories

Prepares for nonperturbative unitarity restoration studies

Abstract

In a series of papers, we examine the physical unitarity in a massive Yang-Mills theory without the Higgs field in which the color gauge symmetry is not spontaneously broken and kept intact. For this purpose, we use a new framework proposed in the previous paper Kondo [arXiv:1208.3521] based on a nonperturbative construction of a non-Abelian field describing a massive spin-one vector boson field, which enables us to perform the perturbative and nonperturbative studies on the physical unitarity. In this paper, we present a new perturbative treatment for the physical unitarity after giving the general properties of the massive Yang-Mills theory. Then we reproduce the violation of physical unitarity in a transparent way. This paper is a preliminary work to the subsequent papers in which we present a nonperturbative framework to propose a possible scenario of restoring the physical unitarity in the Curci-Ferrari model.