Higgs scalar potential coupled to gravity in the exponential parametrization in arbitrary gauge

TL;DR

This paper investigates the gauge and parametrization dependence of the Higgs potential coupled to gravity within the asymptotic safety framework, using exponential parametrization and analyzing fixed points and stability.

Contribution

It introduces the exponential parametrization approach to study gauge dependence in Higgs-gravity coupling and compares it with the linear split, revealing stability regions for fixed points.

Findings

Gauge dependence of Higgs potential beta functions is minimized with redefined Planck mass.

Stable fixed points and critical exponents are found for certain gauge parameter regions.

Higgs coupling is confirmed to be irrelevant for typical gauge choices.

Abstract

We study the parametrization and gauge dependences in the Higgs field coupled to gravity in the context of asymptotic safety. We use the exponential parametrization to derive the fixed points for the cosmological constant, Planck mass, Higgs mass and its coupling, keeping arbitrary gauge parameters $\alpha$ and $\beta$, and compare the results with the linear split. We find that the beta functions for the Higgs potential are expressed in terms of redefined Planck mass such that the apparent gauge dependence is absent. Only the trace mode of the gravity fluctuations couples to the Higgs potential and it tends to decouple in the large $\beta$ limit, but the anomalous dimension becomes large, invalidating the local potential approximation. This gives the limitation of the exponential parametrization. There are also singularities for some values of the gauge parameters but well away from these, we find rather stable fixed points and critical exponents. We thus find that there are regions for the gauge parameters to give stable fixed points and critical exponents against the change of gauge parameters. The Higgs coupling is confirmed to be irrelevant for the reasonable choice of gauge parameters.