Gravitational corrections to Higgs potentials

TL;DR

This paper demonstrates that the Higgs potential at high energies can be derived independently of conformal frame choices, clarifying vacuum stability questions and establishing new relations between beta functions.

Contribution

It introduces a frame-independent method to analyze the Higgs potential and derives improved stability limits and relations between beta functions.

Findings

Frame independence leads to new relations between beta functions.

Improved limits on Higgs curvature coupling for stability.

Unambiguous analysis of vacuum stability at high energies.

Abstract

Understanding the Higgs potential at large field values corresponding to scales in the range above $10^{10}{\rm GeV}$ is important for questions of vacuum stability, particularly in the early universe where survival of the Higgs vacuum can be an issue. In this paper we show that the Higgs potential can be derived in away which is independent of the choice of conformal frame for the spacetime metric. Questions about vacuum stability can therefore be answered unambiguously. We show that frame independence leads to new relations between the beta functions of the theory and we give improved limits on the allowed values of the Higgs curvature coupling for stability.