Noncommutative Theory in Light of Neutrino Oscillation

Solar neutrino problem and atmospheric neutrino anomaly which are both long-standing issues studied intensively by physicists in the past several decades, are reckoned to be able to be solved simultaneously in the framework of the assumption of the neutrino oscillation. For the presence of the Lorentz invariance in the Standard Model, the massless neutrino can’t have flavor mixing and oscillation. However, we exploit the q-deformed noncommutative theory to derive a general modified dispersion relation, which implies some violation of the Lorentz invariance. Then it is found that the application of the q-deformed dispersion relation to the neutrino oscillation can provide a sound explanation for the current data from the reactor and long baseline experiments. PACS numbers: 14.60.Pq, 11.10.Nx, 11.30.Cp. The current knowledge concerning high energy neutrinos mainly comes from solar, atmospheric and long baseline neutrino experiments, which all present some inconsistence with the electro-weak Standard Model. In the Super-Kamiokande (S-K) experiment [1, 2], the results of directly detecting νee scattering via the observation of the Cherenkov light in the large water Cherenkov detector, and the detection in the SNO [3]-[5] using a heavy water Cherenkov detector have significantly confirmed [email protected] [email protected]