Relating small neutrino masses and mixing

Abstract

Experiments on neutrino oscillations have uncovered several small parameters, $\theta_{13}$ being a prominent one. Others are the solar mass splitting {\em vis-\`{a}-vis} the atmospheric one and the deviation of $\theta_{23}$ from maximal mixing. In this talk we elaborate on a neutrino mass model based on the see-saw mechanism in which the mixing angles to start with are either vanishing ($\theta_{13}$ and $\theta_{12}$) or $\pi/4$ ($\theta_{23}$). The atmospheric mass splitting is taken as a part of this initial structure but the solar splitting is absent. A perturbative contribution, originating from a Type-I see-saw, results in non-zero values of $\theta_{13}$, $\theta_{12}$, $\Delta m^2_{solar}$, and shifts $\theta_{23}$ slightly from $\pi/4$, interrelating them all. The model incorporates CP-violation, the phase $\delta$ being close to 3$\pi$/2 for (a) quasi-degeneracy or (b) inverted mass ordering. It will be put to test as the neutrino parameters get better determined.