Smallness of \theta_{13} and the size of the Solar Mass Splitting: Are they related?

Abstract

Compared to the other neutrino mixing angles \theta_{13} is small. The solar mass splitting is about two orders smaller than the atmospheric splitting. We show that it is possible that both are perturbative effects on a more symmetric structure. The perturbation also affects the solar mixing angle and can make alternate mixing patterns such as tribimaximal, bimaximal, or other variants equally viable. For real perturbations this can be accomplished only for normal mass ordering and with the lightest neutrino mass less than 10^{-2} eV. Both mass orderings can be accommodated by going over to complex perturbations provided the lightest neutrino is heavier. The CP-phase in the lepton sector that emerges distinguishes between different mixing models.