The neutrino parameters determined from the solar neutrino data and the antineutrino parameters determined from KamLAND reactor experiment are in good agreement with each other. However, the best fit points of the two sets differ from each other by about 10 −5 eV 2 in mass-square difference and by about 2°in the mixing angle. Future solar neutrino and reactor anti-neutrino experiments are likely to reduce the uncertainties in these measurements. This, in turn, can lead to a signal for CPT violation in terms a non-zero difference between neutrino and anti-neutrino parameters. In this paper, we propose a CPT violating mass matrix which can give rise to the above differences in both mass-squared difference and mixing angle and study the constraints imposed by the data on the parameters of the mass matrix.
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 × 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 MX = M pl , we find that for degenerate neutrino mass spectrum, the considered perturbation term change the ∆ ′ 21 and ∆ ′ 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..
The recent measurement of ∆ sol by the KamLAND experiment with very small errors, makes definitive predictions for the energy dependence of the solar neutrino survival probability P ee . We fix ∆ sol to be the KamLAND best fit value of 8 × 10 −5 eV 2 and study the energy dependence of P ee for solar neutrinos, in the framework of two flavour oscillations and also of three flavour oscillations. For the case of two flavour oscillations, P ee has a measurable slope in the 5 − 8 MeV range but the solar spectrum measurements in this range find P ee to be flat. The predicted values of P ee , even for the best fit value of θ sol , differ by 2 to 3 σ from the Super-K measured values in each of the three energy bins of the 5 − 8 MeV range. If future measurements of solar neutrinos by Super-K and SNO find a flat spectrum with reduced error bars (by a factor of 2), it will imply that two flavour oscillations can no longer explain both KamLAND data and the solar spectrum.However a flat solar neutrino spectrum and the ∆ sol measured by KamLAND can be reconciled in a three flavour oscillation framework with a moderate value of θ 13 ≃ 13 • .
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