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

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 similar to 125 GeV results in the prediction for the top quark mass M-t similar to 171 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 an 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 similar to 172.5 GeV for a triplet mass of M similar to 10(8)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.