Gauge-free Coleman-Weinberg Potential

TL;DR

This paper introduces a gauge-free method to compute the Coleman-Weinberg potential in scalar electrodynamics, resolving gauge-dependence issues and providing a unique Higgs-photon mass ratio at one loop.

Contribution

It presents a gauge-free approach that avoids gauge fixing of photon fluctuations, offering a unique and gauge-invariant effective potential in scalar QED.

Findings

Achieves gauge-invariant one-loop effective potential

Determines a unique Higgs to photon mass ratio

Compares with DeWitt-Vilkovisky geometric framework

Abstract

The gauge-dependence of the one loop Coleman-Weinberg effective potential in scalar electrodynamics is resolved using a gauge-free approach not requiring any gauge-fixing of quantum fluctuations of the photon degrees of freedom. This leads to a unique dynamical ratio at one loop of the Higgs mass to the photon mass. We compare our approach and results with those obtained in geometric framework of DeWitt and Vilkovisky, which maintains invariance under field redefinitions as well as invariance under background gauge transformations, but {\it requires}, in contrast to our approach, gauge fixing of {\it fluctuating} photon fields. We also discuss possible modifications of the Coleman-Weinberg potential if we adapt the DeWitt-Vilkovisky method to our gauge-free approach for scalar QED.