Deviation from bimaximality due to Planck scale effects

We consider the effect of Planck scale operators on neutrino mixing. We assume that the neutrino masses and mixings 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 bimaximal. Quantum gravity (Planck scale) effects lead to an effective SU(2)LxU(1) invariant dimension-5 Lagrangian involving Standard Model lepton and Higgs fields. On electroweak symmetry breaking, this operator gives rise to corrections to the above masses and mixings. These additional terms can be considered as a perturbation to the bimaximal neutrino mass matrix. The nature of gravitational interaction demands that the elements of this perturbation matrix should be independent of flavour indices. We compute the deviations of the three neutrino mixing angles due to these Planck scale effects. We find that the changes in θ13 and θ23 are very small but the change in solar mixing angle θ12 can be as large as 3.5o