BRST invariant scalar and vector operators in the $SU\left(2\right)\times U\left(1\right)$ Higgs model

TL;DR

This paper constructs BRST invariant operators in the $SU(2)\times U(1)$ Higgs model, enabling a gauge-invariant description of observable particles and advancing the formulation of the Standard Model spectrum.

Contribution

It introduces BRST invariant composite operators, including non-local ones localized via the Stuckelberg trick, to better understand the physical spectrum of the Higgs model.

Findings

Operators overlap with observable states

Localization preserves physical content

Advances BRST invariant formulation of the Standard Model

Abstract

We present a set of BRST invariant composite operators in the $SU\left(2\right)\times U\left(1\right)$ Higgs model which exhibit an overlap with the observable scalar and vector particle states of the theory. Some of these operators are non-local in the standard formulation of the Higgs model, however, we show that they can be localized using the Stuckelberg trick, this without changing the physical content. These operators provide thus a BRST invariant resolution of the physical spectrum of the theory, thereby giving the next step in constructing a manifestly BRST invariant formulation of the particle spectrum of the Electroweak and Standard model.