Gravitational corrections to electroweak vacuum decay: metric vs. Palatini

We consider the standard Einstein-Hilbert-Higgs action where the Higgs field couples nonminimally with gravity via the term xi h2R, and investigate the stability of the electroweak vacuum in the presence of gravitational corrections in both the metric and Palatini formulations of gravity. In order to identify the differences between the two formalisms analytically, we follow a perturbative approach in which the gravitational corrections are taken into consideration via a leading order expansion in the gravitational coupling constant. Our analysis shows that in the Palatini formalism, the well-known effect of gravity suppressing the vacuum decay probability, becomes milder in comparison with the metric case for any value of the nonminimal coupling xi. Furthermore, we have found that in the Palatini formalism, the positivity of the gravitational corrections, which is a necessary requirement for the unitarity of the theory, entails the lower bound xi > -1/12.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by/4.0/). Funded by SCOAP3.

Automated summary

This article investigates the impact of nonminimal coupling between gravity and the Higgs field on the stability of the electroweak vacuum. By analyzing the gravitational corrections in both the metric and Palatini formulations of gravity, it is found that the suppression effect of gravity on vacuum decay probability is weaker in the Palatini formalism compared to the metric case, and a lower bound of xi > -1/12 is required for the positivity of gravitational corrections.