Neutrino Oscillation Probability from Tri-Bimaximality due to Planck Scale Effects

Abstract

Current neutrino experimental data on neutrino mixing are well describes by Tri-bi-maximal mixing, which is predicts sin^{2}\theta_{12}=1/3,zero U_{e3} and \theta_{23}=45^{o}. We consider the planck scale operator on neutrino mixing. We assume that the neutrino masses and mixing arise through physics at a scale intrimediate between planck scale and the electroweak braking scale. We also assume, that just above the electroweak breaking scale neutrino mass are nearly degenerate and the mixing is tri-bi-maximal. Quantum gravity (Planck scale) effects lead to an effective SU(2)_{L}\times U(1) invariant dimension-5 Lagrangian symmetry involving Standard Model. On electroweak symmetry breaking, this operator gives rise to correction to the neutrino masses and mixings these additional terms can be considered as perturbation to the tri-bimaximal neutrino mass matrix. We compute the deviation of the three mixing angles and oscillation probability. We find that the only large change in solar mixing angle and % change in maximum P_{\mu e} is about 10%.