Gradient effects on false vacuum decay in gauge theory

TL;DR

This paper investigates how gauge field gradients influence false vacuum decay rates in a scalar gauge theory, incorporating radiative and gradient corrections self-consistently within the thin-wall approximation.

Contribution

It introduces a systematic method to include gradient effects and gauge field mixing in decay rate calculations, extending previous scalar or fermion loop analyses.

Findings

Gradient effects are comparable to one-loop corrections.

Radiative corrections significantly modify the bubble profile.

A covariant gradient expansion effectively constructs wave-function renormalization.

Abstract

We study false vacuum decay for a gauged complex scalar field in a polynomial potential with nearly degenerate minima. Radiative corrections to the profile of the nucleated bubble as well as the full decay rate are computed in the planar thin-wall approximation using the effective action. This allows to account for the inhomogeneity of the bounce background and the radiative corrections in a self-consistent manner. In contrast to scalar or fermion loops, for gauge fields one must deal with a coupled system that mixes the Goldstone boson and the gauge fields, which considerably complicates the numerical calculation of Green's functions. In addition to the renormalization of couplings, we employ a covariant gradient expansion in order to systematically construct the counterterm for the wave-function renormalization. The result for the full decay rate however does not rely on such an expansion and accounts for all gradient corrections at the chosen truncation of the loop expansion. The ensuing gradient effects are shown to be of the same order of magnitude as non-derivative one-loop corrections.