Functional Determinants for False Vacuum Decay

TL;DR

This paper presents a simplified method to regularise functional determinants for fluctuations of various fields, crucial for accurately calculating false vacuum decay rates in quantum field theories.

Contribution

It introduces a straightforward regularisation prescription for functional determinants involving fields of different spins, applicable to complex models like the Standard Model.

Findings

Derived simple regularisation expressions for functional determinants.

Applied method to the Standard Model for decay rate calculations.

Streamlined the renormalisation and divergence isolation process.

Abstract

We derive simple expressions to regularise functional determinants from fluctuations of fields with spin 0, 1/2, and 1. These are important for the precise dimensionful determination of false vacuum decay rates. We work in $D = 4$ Euclidean dimensions and use familiar Feynman diagrammatic techniques with a double expansion in interactions and masses, together with dimensional regularisation in momentum space. We Fourier transform to coordinate space and end up with a simple regularisation prescription in terms of single integrals over the Euclidean radius of field-dependent masses and their derivatives. Our results apply to models with an arbitrary scalar potential and with any number of scalars, fermions, gauge bosons and associated ghosts. We exemplify this approach on the Standard Model with a streamlined calculation of the renormalisation and isolation of divergences in fluctuation determinants.