Vacuum Decay Rate in D-dimensional Electroweak theories

TL;DR

This paper introduces a unified and efficient framework for calculating vacuum decay rates in D-dimensional electroweak theories, applicable to various fields and temperature conditions, with precise results for standard model scenarios.

Contribution

It develops a systematic method combining WKB expansion and dimensional regularization for vacuum decay calculations across dimensions, improving convergence and applicability.

Findings

Calculated decay rates for 4D and 3D standard model effective theories.

Provided precise logarithmic decay rate values at different loop orders.

Demonstrated the method's efficiency and generality for vacuum stability analysis.

Abstract

We present a systematic framework for calculating the vacuum decay rate in D-dimensional electroweak theories, providing a unified treatment of quantum fluctuations for scalar, fermion, and gauge boson fields via a combined WKB expansion and dimensional regularization. This method ensures rapid convergence even at large angular momenta. Application to a $D=4$ standard model effective field theory gives $\log_{10}(\gamma \times \text{Gyr} \times \text{Gpc}^3)=183$. In the finite-temperature, dimensionally reduced standard model effective field theory with $D=3$, the values are $\log_{10}(\Gamma_T \times \text{Gyr} \times \text{Gpc}^3)=42.4$ at tree level and $116.1$ at two-loop order. The approach offers a general and efficient tool for analyzing vacuum stability and decay across dimensions.