Neutrino masses and mixing from hierarchy and symmetry

Abstract

We construct a model that allows us to determine the three neutrino masses and the mass matrix directly from the experimental mass squared differences delta atm and delta sol, using the assumptions of rational hierarchy (m1/m2 = m2/m3) and of S3-S2 symmetry for the mixing matrix. We find that both the mass ratios and mixing angles are dominated by the same parameter. For the mixing angles, this parameter=sq rt (1/6)=0.41, is a Clebsch-Gordan coefficient. For the masses, the mass ratios depend on the experimental mass squared differences and with most recent data, remarkably, we obtain sq rt (m1/m2)=sq rt (m2/m3)=0.41. This possibly coincidental equality gives a simple mass matrix. We obtain the masses m1,m2 and m3. We also obtain the mass matrix M and evaluate its elements numerically for the presently 'best fit' solution.