Abstract
Three-flavor neutrino oscillations in matter can be described by three effective neutrino masses mi (for i = 1, 2, 3) and the effective mixing matrix Vαi (for α = e, µ, τ and i = 1, 2, 3). When the matter parameter a ≡ 2√2GFNeE is taken as an independent variable, a complete set of first-order ordinary differential equations for m2
i and |Vαi|2have been derived in the previous works. In the present paper, we point out that such a system of differential equations possesses both the continuous symmetries characterized by one-parameter Lie groups and the discrete symmetry associated with the permutations of three neutrino mass eigenstates. The implications of these symmetries for solving the differential equations and looking for differential invariants are discussed.
Flavor Mixing, Neutrino Masses and Neutrino Oscillations
