The matter effects to neutrino oscillations ν_μ\to ν_e, ν_μat very long baselines and the neutrino mixing angles θ_13 and θ_23

Abstract

We study the matter effects to neutrino oscillations ν_μ\to ν_e and ν_μ\to ν_μat very long baselines. It has been observed that, for a very long baseline L~10000 km, the resonance peak for the ν_μ\to ν_e oscillation and the local minimum of the ν_μsurvival probability occurs at similar energies. With a good knowledge on the absolute value of Δm_{31}^2, measurements of the above oscillation probabilities, P_{μe} and P_{μμ}, can be performed with the neutrino energy tuned to the resonance peak of the ν_μ\to ν_e oscillations. We show that the variations of CP violating phase and the solar neutrino mixing parameters have negligible effects on P_{μe} and P_{μμ} for such a long baseline. Hence P_{μe} and P_{μμ} together determine the mixing angles θ_{13} and θ_{23}. Around the resonance peak for ν_μ\to ν_e oscillations, the dependencies of P_{μe} and P_{μμ} on the above mixing angles are worked out in detail, and the implications of such dependencies are discussed.