Precise Calculation of the Decay Rate of False Vacuum with Multi-Field Bounce

TL;DR

This paper presents a method to accurately compute the decay rate of a false vacuum in gauge theories involving multiple scalar fields, ensuring gauge invariance and proper treatment of zero modes and renormalization.

Contribution

It introduces a gauge-invariant one-loop calculation framework for false vacuum decay involving multi-field bounces with curved trajectories in field space.

Findings

Derived a gauge-invariant expression for the decay rate.

Addressed the treatment of gauge zero modes.

Provided a systematic renormalization procedure.

Abstract

We study the decay rate of a false vacuum in gauge theory at the one-loop level. We pay particular attention to the case where the bounce consists of an arbitrary number of scalar fields. With a multi-field bounce, which has a curved trajectory in the field space, the mixing among the gauge fields and the scalar fields evolves along the path of the bounce in the field space and the one-loop calculation of the vacuum decay rate becomes complicated. We consider the one-loop contribution to the decay rate with an arbitrary choice of the gauge parameter, and obtain a gauge invariant expression of the vacuum decay rate. We also give proper treatments of gauge zero modes and renormalization.