Local gauge-invariant vector operators in the adjoint $SU(2)$ Higgs model

TL;DR

This paper investigates local gauge-invariant vector operators in the adjoint SU(2) Higgs model, using theoretical tools to identify which operators can propagate as fundamental excitations, supported by explicit one-loop calculations.

Contribution

It introduces a method combining equations of motion and BRST symmetry to determine operator propagation, validated by explicit one-loop computations.

Findings

Identifies conditions for operator propagation in the model

Derives a Ward identity linking operators and their propagating nature

Performs explicit one-loop calculations confirming theoretical predictions

Abstract

In this work, we scrutinize local gauge-invariant vector operators of dimension four in the adjoint $SU(2)$ Higgs model, which are candidates for interpolating fields of the fundamental excitations of the model due to the so-called FMS mechanism. We use the equations of motion and the properties of the BRST operator to derive a Ward identity that allows us to determine whether a given operator can propagate. To corroborate this analysis, we explicitly compute the two-point function of the non-propagating operator at the one-loop level.