Pheno seminar / Joint VUB-ULB

Accurately computing the decay rate of metastable vacua in quantum field theory hinges on a precise evaluation of functional determinants arising from quantum fluctuations. In this presentation, we explore recent advances in the regularisation and evaluation of these determinants. The first part introduces a streamlined method to regularize functional determinants for fields of spin $0$, $1/2$, and $1$ in four-dimensional Euclidean space, by using familiar Feynman diagrammatic techniques with a double expansion in interactions and masses, together with dimensional regularisation in momentum space. After a Fourier transform to coordinate space, we end up with a simple regularisation prescription in terms of single integrals over the Euclidean radius of field-dependent masses and their derivatives. In the second part, we refine the electroweak vacuum decay rate by revisiting the one-loop prefactor, focusing on gauge field contributions. Using group theory, we correct an overcounting in the transverse gauge modes, leading to a $6\%$ shift in their contribution and a slightly reduced—but still cosmologically safe—vacuum lifetime. Together, these results offer improved theoretical control over vacuum decay calculations and broader insights into functional determinant techniques in gauge theories. We conclude by discussing the gravitational-wave signatures of first-order phase transitions, showing that sufficiently slow transitions can produce a linearly polarized gravitational-wave signal.