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 (\theta_1, \theta_2, \theta_3 and \delta_KM) to their effective counterparts in matter (\tilde{\theta}_1, \tilde{\theta}_2, \tilde{\theta}_3 and \tilde{\delta}_KM). We rediscover the Toshev-like relation sin \tilde{\delta}_KM sin 2\tilde{\theta}_2 = sin \delta_KM sin 2\theta_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 \nu_\mu -> \nu_e oscillations and CP-violating effects are calculated for the upcoming NOvA and Hyper-K experiments.