Does CP Phase Exist Above the GUT Scale

Abstract

We consider non-reormalizable interaction term as a perturbation of the conventional neutrino mass matrix. Quantum gravitational (Planck scale )effects lead to an effective SU(2)L×U(1) invariant dimension-5 Lagrangian involving neutrino and Higgs fields, which gives rise to additional terms in neutrino mass matrix. There additional term can be considered to be perturbation of the GUT scale bi-maximal neutrino mass matrix. In particular, for the \(\theta_{13}'\) range 0.00005–0.28, indicates the existence of CP violating phase above the GUT scale. We assume that the gravitational interaction is flavor blind. In this paper, we further investigate the possibility of CP phase exist from Quantum gravity.