Are the small neutrino oscillation parameters all related?

Abstract

Neutrino oscillations reveal several small parameters, namely, $\theta_{13}$, the solar mass splitting {\em vis-\`{a}-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 $\theta_{13}$, $\Delta m^2_{solar}$, $\theta_{12}$, 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.