# On the impact of Majorana masses in gravity-matter systems

## TL;DR

This paper explores how Majorana masses influence the behavior of a Higgs-Yukawa system within asymptotically safe quantum gravity, analyzing fixed points and their implications for particle physics parameters.

## Contribution

It introduces the derivation of beta functions for Majorana masses and Yukawa coupling in a gravity-matter system with higher derivative terms, revealing conditions for non-trivial fixed points.

## Key findings

- Yukawa coupling has a non-trivial fixed point under certain conditions.
- Majorana masses can render the Yukawa coupling irrelevant, making it a prediction of the theory.
- Majorana masses affect the running of the scalar quartic coupling.

## Abstract

We investigate the Higgs-Yukawa system with Majorana masses of a fermion within asymptotically safe quantum gravity. Using the functional renormalization group method we derive the beta functions of the Majorana masses and the Yukawa coupling constant and discuss the possibility of a non-trivial fixed point for the Yukawa coupling constant. In the gravitational sector we take into account higher derivative terms such as $R^2$ and $R_{\mu\nu}R^{\mu\nu}$ in addition to the Einstein-Hilbert term for our truncation. For a certain value of the gravitational coupling constants and the Majorana masses, the Yukawa coupling constant has a non-trivial fixed point value and becomes an irrelevant parameter being thus a prediction of the theory. We also discuss consequences due to the Majorana mass terms to the running of the quartic coupling constant in the scalar sector.