Gauge invariance of the vector meson mass in the Coleman-Weinberg model

TL;DR

This paper demonstrates that the pole mass of the vector meson in the Coleman-Weinberg model is gauge invariant when using dressed propagators with resummed self-energy corrections, resolving previous gauge invariance issues.

Contribution

The study shows that employing dressed propagators with resummed self-energy corrections ensures gauge invariance of the vector meson mass at one-loop in the Coleman-Weinberg model.

Findings

Pole mass is gauge invariant with dressed propagators.

Resummation of self-energy corrections is crucial.

Gauge invariance holds at the vacuum with daisy diagram resummation.

Abstract

We revisit the problem of the gauge invariance in the Coleman-Weinberg model in which a $U(1)$ gauge symmetry is driven spontaneously broken by radiative corrections. It was noticed in previous work that masses in this model are not gauge invariant at one-loop order. In our analysis, we use the dressed propagators of scalars which include a resummation of the one-loop self-energy correction to the tree-level propagator. We calculate the one-loop self-energy correction to the vector meson using these dressed propagators. We find that the pole mass of the vector meson calculated using the dressed propagator is gauge invariant at the vacuum determined using the effective potential calculated with a resummation of daisy diagrams.