# On Shell Renormalization Scheme From the Loopwise Expansion of the Pole Mass

## TL;DR

This paper proposes an on-shell renormalization scheme replacing the MS scheme's mass parameter with the pole mass, maintaining the quartic coupling and ensuring RG invariance of the pole mass.

## Contribution

It introduces a novel on-shell renormalization scheme based on the loop expansion of the pole mass, preserving key parameters and invariance properties.

## Key findings

- The quartic coupling remains unchanged from the MS scheme.
- The vacuum expectation value receives contributions from 1PI diagrams.
- The pole mass is shown to be renormalization group invariant.

## Abstract

We introduce an on shell renormalization scheme in which the mass parameter of minimal MS scheme is replaced with the pole mass obtained from the loop order expansion of the pole mass in the MS scheme. As a consequence, the quartic coupling constant remains same as that of the MS scheme and the vacuum expectation value gets contributions from the one-particle-irreducible diagrams. We also show the renormalization group invariance of the pole mass in this scheme.