Phenomenology of Neutrino Oscillations at a Neutrino Factory

There have been several experiments 1,2,3,4,5,6,7,8,9,10,11 which suggest neutrino oscillations. It has been known in the two flavor framework that the solar neutrino deficit can be explained by neutrino oscillation with the set of parameters (∆m⊙, sin 2 2θ⊙) ≃ (O(10−5eV),O(10−2)) (small angle MSW solution), (O(10−5eV),O(1)) (large angle MSW solution), or (O(10−10eV),O(1)) (vacuum oscillation solution), and the atmospheric neutrino anomaly can be accounted for by (∆m2atm, sin 2 2θatm) ≃ (10−2.5eV, 1.0). In the three flavor framework there are two independent mass squared differences and it is usually assumed that these two mass differences correspond to ∆m⊙ and ∆m2atm. Throughout this talk I will assume three neutrino species which can account for only the solar neutrino deficit and the atmospheric neutrino anomaly . Without loss of generality I assume |∆m21| < |∆m32| < |∆m31| where ∆mij ≡ mi −mj . The flavor eigenstates are related to the mass eigenstates by Uαj (α = e, μ, τ), where Uαj are the elements of the MNS mixing matrix U :