Absolute values of three neutrino masses from atmospheric mixing and an ansatz for the mixing-matrix elements

Abstract

Using data from atmospheric neutrino mixing, and a simple functional form for mixing angles, the absolute values of three neutrino masses are calculated: $m_3\cong 5.37\times 10^{-2} eV$, $m_2\cong 1.94\times 10^{-2} eV$, $m_1\cong 1.46\times 10^{-2} eV$. The quantities relevant for solar neutrino mixing are calculated: $(m_2^2-m_1^2) \cong 1.63\times 10^{-4} eV^2$, with non-maximal mixing $\tan^2\theta_\sol \cong 0.56$. The analysis gives a suggestion of a dynamical origin for the empirical, large CP-violating phase associated with an intrinsically, very small mixing angle in the quark sector.