Are the small neutrino oscillation parameters all related?

Abstract

Neutrino oscillations reveal several small parameters, namely, ${\theta }_{13}$, the solar mass splitting {\em vis-à-vis} the atmospheric one, and the deviation of ${\theta }_{23}$ from maximal mixing. Can these small quantities all be traced to a single source and, if so, how could that be tested? Here a see-saw model for neutrino masses is presented wherein a dominant term generates the atmospheric mass splitting with maximal mixing in this sector, keeping ${\theta }_{13}=0$ and zero solar splitting. A Type-I see-saw perturbative contribution results in non-zero values of ${\theta }_{13}$, $\Delta m_{solar}^2$, ${\theta }_{12}$, as well as allows ${\theta }_{23}$ to deviate from $\pi /4$ in consistency with the data while interrelating them all. CP-violation is a natural consequence and is large ($\delta \sim \pi /2,3\pi /2$) for inverted mass ordering. The model will be tested as precision on the neutrino parameters is sharpened.

Comments: v1: 8 pages, 2 Figures, v2: Published version, Journal title different, minor typographical changes, presentation improved, references added and updated. 9 pages, 3 Figures, Fig. 2 split into Fig. 2 and Fig. 3 for clarity