Quantum gravity fluctuations flatten the Planck-scale Higgs potential

TL;DR

This paper explores how quantum gravity fluctuations can lead to a flat Higgs potential at the Planck scale, suggesting a possible asymptotic safety scenario that predicts scalar couplings and impacts dark matter models.

Contribution

It demonstrates the existence of ultraviolet fixed points in a scalar extension of the Higgs sector influenced by quantum gravity, leading to predictive scalar potentials.

Findings

Scalar couplings become irrelevant at the fixed point in certain gravitational regimes.

The infrared potential is fully predicted with no free parameters.

Quartic couplings are predicted in other gravitational regimes.

Abstract

We investigate asymptotic safety of a toy model of a singlet-scalar extension of the Higgs sector including two real scalar fields under the impact of quantum-gravity fluctuations. Employing functional renormalization group techniques, we search for fixed points of the system which provide a tentative ultraviolet completion of the system. We find that in a particular regime of the gravitational parameter space the canonically marginal and relevant couplings in the scalar sector -- including the mass parameters -- become irrelevant at the ultraviolet fixed point. The infrared potential for the two scalars that can be reached from that fixed point is fully predicted and features no free parameters. In the remainder of the gravitational parameter space, the values of the quartic couplings in our model are predicted. In light of these results, we discuss whether the singlet-scalar could be a dark-matter candidate. Furthermore, we highlight how "classical scale invariance" in the sense of a flat potential of the scalar sector at the Planck scale could arise as a consequence of asymptotic safety.