Neutrino masses and mixings in a Minimal S_3-invariant Extension of the Standard Model

Abstract

The mass matrices of the charged leptons and neutrinos, that had been derived in the framework of a Minimal S_3-invariant Extension of the Standard Model, are here reparametrized in terms of their eigenvalues. The neutrino mixing matrix, V_PMNS, is then computed and exact, explicit analytical expressions for the neutrino mixing angles as functions of the masses of the neutrinos and charged leptons are obtained. The reactor, theta_13, and the atmosferic, theta_23, mixing angles are found to be functions only of the masses of the charged leptons. The numerical values of theta_13{th} and theta_23{th} computed from our theoretical expressions are found to be in excellent agreement with the latest experimental determinations. The solar mixing angle, theta_12{th}, is found to be a function of both, the charged lepton and neutrino masses, as well as of a Majorana phase phi_nu. A comparison of our theoretical expression for the solar angle theta_12{th} with the latest experimental value theta_12{exp} ~ 34 deg allowed us to fix the scale and origin of the neutrino mass spectrum and obtain the mass values |m_nu1|=0.0507 eV, |m_nu2|=0.0499 eV and |m_nu3|=0.0193 eV, in very good agreement with the observations of neutrino oscillations, the bounds extracted from neutrinoless double beta decay and the precision cosmological measurements of the CMB.