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

TL;DR

This paper explores the potential connection between the smallness of the neutrino mixing angle 13 and the solar mass splitting, proposing they may both be perturbative effects of a more symmetric underlying structure.

Contribution

It demonstrates that both phenomena can originate from perturbations to a symmetric neutrino mass matrix, with implications for neutrino mass ordering and CP-phase effects.

Findings

Both effects can be explained as perturbations to a symmetric structure.

Normal mass ordering allows real perturbations for these effects.

Complex perturbations can accommodate both mass orderings with a heavier lightest neutrino.

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.