Gauge-invariant scalar and vector operators in the $SU\left(2\right)\times U\left(1\right)$ Higgs model: Ward identities and renormalization

TL;DR

This paper studies the renormalization of gauge-invariant operators in the $SU(2) imes U(1)$ Higgs model, deriving Ward identities and establishing relations between elementary and composite field correlations.

Contribution

It introduces a gauge-invariant renormalization framework for composite operators in the Higgs model using Algebraic Renormalization and Ward identities.

Findings

Derived Ward identities for the model.

Established exact relations between correlation functions.

Demonstrated renormalization consistency of composite operators.

Abstract

In this work, we investigate the renormalization of the gauge-invariant composite operators proposed in \cite{Dudal:2023jsu} to describe the $SU(2)\times U(1)$ Higgs model from a gauge-invariant perspective. To establish the relationship between the counterterms, we use the Algebraic Renormalization approach \cite{Piguet:1995er}. Therefore, we also derive the set of Ward identities of the model after introducing these composite operators. Using these Ward identities, we demonstrate important exact relations between the correlation functions of elementary fields and composite fields.