# Variable Planck mass from the gauge invariant flow equation

## TL;DR

This paper uses a gauge invariant flow equation to analyze how the Planck mass varies with scale in quantum gravity, impacting predictions of Higgs parameters in the asymptotic safety scenario.

## Contribution

It introduces a method to compute the scale dependence of the Planck mass using gauge invariant flow equations, linking quantum gravity fixed points to Higgs parameter predictions.

## Key findings

- The Planck mass's fixed point value influences Higgs parameter predictions.
- The quartic Higgs coupling is irrelevant at the ultraviolet fixed point.
- The Higgs-to-top mass ratio becomes predictable in this framework.

## Abstract

Using the gauge invariant flow equation for quantum gravity we compute how the strength of gravity depends on the length or energy scale. The fixed point value of the scale-dependent Planck mass in units of the momentum scale has an important impact on the question, which parameters of the Higgs potential can be predicted in the asymptotic safety scenario for quantum gravity? For the standard model and a large class of theories with additional particles the quartic Higgs coupling is an irrelevant parameter at the ultraviolet fixed point. This makes the ratio between the Higgs boson and the top-quark mass predictable.