Gravitational effects on the Higgs field within the Solar System

TL;DR

This paper investigates how gravitational fields within the Solar System can cause inhomogeneities in the Higgs field, leading to spatial variations in particle masses, and explores potential observational constraints on modified gravity theories.

Contribution

It demonstrates that gravity can influence quantum corrections to the Higgs potential, resulting in Higgs VEV inhomogeneities that are detectable through precision measurements.

Findings

Higgs VEV varies spatially in weak gravitational fields.

Inhomogeneities depend on the Eddington parameter.

Potential to constrain modified gravity theories with atomic clocks.

Abstract

The Higgs mechanism predicts, apart from the existence of a new scalar boson, the presence of a constant Higgs field that permeates all of space. The vacuum expectation value (VEV) of this field is affected by quantum corrections which are mainly generated by the self-interactions and couplings of the Higgs field to gauge bosons and heavy quarks. In this work we show that gravity can affect, in a non-trivial way, these quantum corrections through the finite parts of the one-loop contributions to the effective potential. In particular, we consider the corrections generated by the Standard Model Higgs self-interactions in slowly-varying weak gravitational backgrounds. The obtained results amount to the existence of non-negligible inhomogeneities in the Higgs VEV. Such inhomogeneities translate into spatial variations of the particle masses, and in particular of the proton-to-electron mass ratio. We find that these Higgs perturbations in our Solar System are controlled by the Eddington parameter, and are absent in pure General Relativity. Yet, they may be present in modified gravity theories. This predicted effect may be constrained by atomic clocks or high-resolution spectroscopic measurements, which could allow to improve current limits on modifications of Einstein's gravity.