Quantum gravity corrections to the standard model Higgs in Einstein and $R^2$ gravity

TL;DR

This paper investigates how quantum gravity corrections influence the Higgs potential at Planck-scale energies, comparing Einstein and $R^2$ gravity to assess stability and UV dependence.

Contribution

It provides a detailed analysis of quantum gravity effects on the Higgs potential using both Einstein and $R^2$ gravity frameworks, highlighting their impact on stability at high energies.

Findings

Gravity corrections significantly modify the Higgs potential near the Planck scale.

The $R^2$ gravity model reduces UV cut-off dependence compared to Einstein gravity.

Quantum gravity effects can influence the stability of the Higgs potential at high energies.

Abstract

We evaluate quantum gravity corrections to the standard model Higgs potential $V(\phi)$ a la Coleman-Weinberg and examine the stability question of $V(\phi)$ at scales of Planck mass $M_{\rm Pl}$. We compute the gravity one-loop corrections by using the momentum cut-off in Einstein gravity. The gravity corrections affect the potential in a significant manner for the value of $\Lambda= (1 - 3)M_{\rm Pl}.$ In view of reducing the UV cut-off dependence we also make a similar study in the $R^2$ gravity.