Neutrino Mass Hierarchy Above GUT Scale

Abstract

We study the effects of neutrino mass hierarchy, above the GUT scale. We assume that the neutrino masses and mixing arise through physics at a scale intermediate between Planck scale and the electroweak breaking scale. We also assume that, just above the electroweak breaking scale, neutrino masses are nearly degenerate and their mixing is bi-maximal. Quantum gravity (Planck scale effects) lead to an effective SU(2) L × U(1) invariant dimension-5 Lagrangian involving neutrino and Higgs fields. On symmetry breaking, this operator gives rise to correction to the above masses and mixing. The nature of gravitational interaction demands that the element of this perturbation matrix should be independent of flavor indices. In this paper, we study the quantum gravity effects on neutrino mass square difference for normal and invert neutrino mass hierarchy, namely modified dispersion relation for 31 above the GUT scale.