Is the size of θ ₁₃ related to the smallness of the solar mass splitting?

Abstract

θ ₁₃ is small compared to the other neutrino mixing angles. The solar mass splitting is about two orders smaller than the atmospheric splitting. We indicate how both could arise from a perturbation of a more symmetric structure. The perturbation also affects the solar mixing angle and can tweak alternate mixing patterns such as tribimaximal, bimaximal, or other variants to viability. For real perturbations only normal mass ordering with the lightest neutrino mass less than 10⁻² eV can accomplish this goal. Both mass orderings can be accommodated by going over to complex perturbations if the lightest neutrino is heavier. The CP-phase in the lepton sector, fixed by θ ₁₃ and the lightest neutrino mass, distinguishes different options.