Neutrino masses, vacuum stability and quantum gravity prediction for the mass of the top quark

TL;DR

This paper explores how asymptotically safe quantum gravity predicts the top quark mass, examining the impact of intermediate-scale physics like scalar triplets and right-handed neutrinos on this prediction.

Contribution

It extends previous predictions by analyzing the effects of new physics at intermediate scales on the top quark mass within the asymptotic safety framework.

Findings

Predicted top quark mass increases to ~172.5 GeV with a scalar triplet at 10^8 GeV.

Right-handed neutrinos introduce uncertainties due to Yukawa couplings.

Vacuum stability issues can be mitigated with appropriate Yukawa couplings.

Abstract

A general prediction from asymptotically safe quantum gravity is the approximate vanishing of all quartic scalar couplings at the UV fixed point beyond the Planck scale. A vanishing Higgs doublet quartic coupling near the Planck scale translates into a prediction for the ratio between the mass of the Higgs boson $M_H$ and the top quark $M_t$. If only the standard model particles contribute to the running of couplings below the Planck mass, the observed $M_H\sim125\,{\rm GeV}$ results in the prediction for the top quark mass $M_t\sim 171\,{\rm GeV}$, in agreement with recent measurements. In this work, we study how the asymptotic safety prediction for the top quark mass is affected by possible physics at an intermediate scale. We investigate the effect of a $SU(2)$ triplet scalar and right-handed neutrinos, needed to explain the tiny mass of left-handed neutrinos. For pure seesaw II, with no or very heavy right handed neutrinos, the top mass can increase to $M_t\sim 172.5\,{\rm GeV}$ for a triplet mass of $M_\Delta\sim 10^8{\rm GeV}$. Right handed neutrino masses at an intermediate scale increase the uncertainty of the predictions of $M_t$ due to unknown Yukawa couplings of the right-handed neutrinos and a cubic interaction in the scalar potential. For an appropriate range of Yukawa couplings there is no longer an issue of vacuum stability.