Vacuum Decay Rate in D-dimensional Electroweak theories

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 ${\log }_{10}({\mathrm{\Gamma }}_T\times \text{Gyr}\times {\text{Gpc}}^3)=42.4$ 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.