RG Invariant Higgs Pole Mass from the $O(\hbar)$ Expansion

TL;DR

This paper calculates the one-loop Higgs pole mass in the Standard Model, ensuring invariance under MS scheme beta functions by incorporating an $O( ext{h})$ expansion of the vacuum expectation value into the Higgs field.

Contribution

It introduces a method to derive the Higgs pole mass that remains invariant under the MS scheme beta functions using an $O( ext{h})$ expansion approach.

Findings

Derived the one-loop Higgs pole mass invariant under MS scheme beta functions.

Established a procedure linking the effective potential in unbroken phase to the broken phase.

Provided a consistent framework for Higgs mass calculations at one-loop level.

Abstract

We obtain the one-loop pole mass of the standard model Higgs which is invariant under the beta functions of the MS\ scheme by following the procedure in which the classical action in the broken symmetry phase was obtaind by adding the $O(\hbar)$ expansion of the vacuum expection value determined from the effective potential of the unbroken phase to the Higgs field $H$.