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Quantum Gravity on Neutrino Mass Square difference

We consider non-renormalizable interaction term as a perturbation of the neutrino mass matrix. 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}\times 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 gravitational interaction M_{X}=M_{pl}, we find that for degenerate neutrino mass spectrum, the considered perturbation term change the Δ_{21}^{'}and Δ_{31}^{'}mass square difference is unchanged above GUT scale. The nature of gravitational interaction demands that the element of this perturbation matrix should be independent of flavor indices. In this letter, we study the quantum gravity effects on neutrino mass square difference, namely modified dispersion relation for neutrino mass square differences..