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-à-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 ${\theta }_{13}$, ${\theta }_{12}$, $\Delta m_{solar}^2$, 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.

Comments: Talk given by A. Raychaudhuri at the International Conference on Massive Neutrinos, IAS, NTU, Singapore, February 2015; to appear in the Proceedings; based closely on arXiv:1411:0320, v2: One typo fixed, v3: Published version, minor typographical changes, references updated