On Neutrino Masses and Lepton Mixing.

A few topics pertaining to neutrino masses and lepton mixing are treated. An analysis is performed, based on an extension of the GJS model^{ [12]} to the lepton sector within the SO(10) grand unified theories. It is found that the model implied nearly degenerate masses for the two heavier neutrinos, a small nu_ {e}-nu_mu mixing with a mixing angle given by sintheta _1~eq 0.07, and a much larger nu_{mu}-nu _{tau} mixing. The computational procedure for the MSW effect ^{[3,4]} is developed for three neutrino flavors. Exemplary numerical results are presented for the adiabatic case. The evaluation of the transition probabilities between different mass levels is outlined for the non-adiabatic case. A geometric modelling of the MSW effect, originally expounded by Mikheyev and Smirnov^{[24 ]} as well as Messiah,^ {[25]} is formulated starting from the equation of motion for the neutrinos. The Kamiokande II data^{[26 ]} for the supernova 1987a is found to suggest a mass value for the heaviest neutrino of m( nu_3) = (4.7 +/- 1.8) eV, with the major assumption that the neutrinos from the neutronization burst of the supernova underwent adiabatic MSW (Mikheyev-Smirnov-Wolfenstein) transition on their voyage out. This is similar to the conclusion by Rosen^{[29] } except for a different interpretation of the mass value.