A complete solution to neutrino mixing

Abstract

Deviations from expectations have been claimed for solar, atmospheric and high energy prompt neutrinos from charm decay. This information, supplemented only by the existing very good upper limits for oscillations of the $ν_μ$ at accelerator energies, is used as input to a phenomenological three-flavour analysis of neutrino mixing. The solution found is unique and completely determines the mass eigenstates as well as the mixing matrix relating mass and flavour eigenstates. Assuming the mass eigenstates to follow the hierarchy $m_{1} \ll m_{2} \ll m_{3}$, their values are found to be $m_{1} \ll 10^{-2}$ eV, $m_{2} = (0.18 \pm 0.06)$ eV, $m_{3} = (19.4 \pm 0.7)$ eV. These masses are in agreement with the leptonic quadratic hierarchy of the see-saw model and large enough to render energy-independent any oscillation-induced phenomenon in solar neutrino physics observable on Earth. This possibility is not excluded by the present knowledge of solar neutrino physics. The mixing angles are determined to be $θ_{12} = 0.55 \pm 0.08$, $θ_{13} = 0.38 \pm 0.06$, $θ_{23} < 0.03$. Small values of $θ_{23}$ are typical of any solution in which $m_{3}$ lies in the cosmological interesting region. The solution found is not in serious contradiction with any of the present limits to the existence of neutrino oscillations. The most relevant implications in particle physics, astrophysics and cosmology are discussed.