On the properties of the vacuum expectation value in $R_{\xi }$ gauge and $\overline{R_{\xi }}$ gauge

TL;DR

This paper examines how the vacuum expectation value (VEV) in gauge theories depends on gauge choices in $R_{\xi}$ and $ar{R}_{\xi}$ gauges within the $ar{MS}$ scheme, highlighting the gauge dependence of VEV and gauge independence of pole mass.

Contribution

It clarifies the gauge dependence of the VEV in different gauges and shows that the pole mass remains gauge independent despite VEV gauge dependence.

Findings

Gauge dependence of VEV in $R_{\xi}$ gauge requires modification due to gauge parameter.

Pole mass remains gauge independent across gauges.

Analysis within the $ar{MS}$ scheme clarifies gauge properties of VEV and mass.

Abstract

We have investigated the gauge dependence of the vacuum expectation value(VEV) both in the $R_{\xi }$ and the $\overline{R_{\xi }}$ gauge in the $\overline{MS}$ scheme. We have found that, in case of the $R_{\xi }$ gauge, the gauge dependence of the VEV should be modified due to the presence of the parameter in the gauge function that should be identified as a VEV in the broken symmetry phase. However the pole mass remains gauge independent.