Sum rules and asymptotic behaviors of neutrino mixing and oscillations in matter

Abstract

Similar to the case in vacuum, it is straightforward to describe neutrino oscillations in matter with the effective lepton flavor mixing matrix and neutrino mass-squared differences (i, j = 1, 2, 3). By calculating two sets of sum rules of and , we have derived exact expressions of and (for α, β = e, μ, τ and i = 1, 2, 3) and discussed the asymptotic behaviors of and and in very dense matter (i.e., in the limit of the matter parameter approaching infinity).