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The Kobayashi-Maskawa Parametrization of Lepton Flavor Mixing and Its Application to Neutrino Oscillations in Matter

We show that the Kobayashi-Maskawa (KM) parametrization of the 3 X 3 lepton flavor mixing matrix is a useful language to describe the phenomenology of neutrino oscillations. In particular, it provides us with a convenient way to link the genuine flavor mixing parameters (θ_1, θ_2, θ_3 and δ_KM) to their effective counterparts in matter (\tildeθ_1, \tildeθ_2, \tildeθ_3 and \tildeδ_KM). We rediscover the Toshev-like relation sin \tildeδ_KM sin 2\tildeθ_2 = sin δ_KM sin 2θ_2 in the KM parametrization. We make reasonable analytical approximations to the exact relations between the genuine and matter-corrected flavor mixing parameters in two different experimental scenarios: (a) the neutrino beam energy E is above O(1) GeV and (b) E is below O(1) GeV. As an example, the probability of ν_μ-> ν_e oscillations and CP-violating effects are calculated for the upcoming NOvA and Hyper-K experiments.