Revising the full one-loop gauge prefactor in electroweak vacuum stability

TL;DR

This paper refines the calculation of the electroweak vacuum decay rate by correcting the gauge field contribution in the one-loop prefactor, leading to a more accurate estimate of the vacuum's lifetime.

Contribution

It provides a corrected derivation of the gauge prefactor in vacuum decay calculations, addressing overcounting of transverse modes using group theory.

Findings

Gauge contribution revised by 6%

Electroweak vacuum lifetime slightly decreased

Method applicable to gauge field determinants in 4D

Abstract

We revisit the decay rate of the electroweak vacuum in the Standard Model with the full one-loop prefactor. We focus on the gauge degrees of freedom and derive the degeneracy factors appearing in the functional determinant using group theoretical arguments. Our treatment shows that the transverse modes were previously overcounted, so we revise the calculation of that part of the prefactor. The new result modifies the gauge fields' contribution by $6\%$ and slightly decreases the previously predicted lifetime of the electroweak vacuum, which remains much longer than the age of the universe. Our discussion of the transverse mode degeneracy applies to any calculation of functional determinants involving gauge fields in four dimensions.