The unitarity of a spontaneously broken SU(2) theory using unitary-gauge diagrams

TL;DR

This paper provides a diagrammatic proof of tree-level unitarity in a spontaneously broken SU(2) gauge theory using only physical fields, employing a new Ward-like identity to control high-energy behavior.

Contribution

It introduces a novel Ward-like identity and a diagrammatic approach to prove unitarity in a non-Abelian gauge theory with spontaneous symmetry breaking.

Findings

High-energy amplitudes grow at most quadratically

Unitarity is maintained at tree level in the model

Diagrammatic proof confirms physical consistency of the theory

Abstract

A spontaneously broken SU(2) theory is the simplest generalization of the Abelian Higgs model, containing three equally massive vector bosons and a single Higgs scalar. A strictly diagrammatic proof is presented of the tree-level unitarity of this model in the unitary gauge, i.e. employing only physical fields. A new Ward-like identity is used to show that the high-energy behaviour of all amplitudes cannot be more than quadratic; the use of generating functions for all off-shell amplitudes then leads to the unitarity proof.