Non-vanishing Ue3 and cos2θ₂₃ from a broken Z₂ symmetry

Abstract

It is shown that the neutrino mass matrices in the flavour basis yielding a vanishing Ue3 are characterized by invariance under a class of Z₂ symmetries. A specific Z₂ in this class also leads to a maximal atmospheric mixing angle θ₂₃. The breaking of that Z₂ can be parameterized by two dimensionless quantities, ε and ε'; the effects of ε,ε'≠0 are studied perturbatively and numerically. The induced value of |Ue3| strongly depends on the neutrino mass hierarchy. We find that |Ue3| is less than 0.07 for a normal mass hierarchy, even when ε,ε'~30%. For an inverted mass hierarchy |Ue3| tends to be around 0.1 but can be as large as 0.17. In the case of quasi-degenerate neutrinos, |Ue3| could be close to its experimental upper bound 0.2. In contrast, |cos2θ₂₃| can always reach its experimental upper bound 0.28. We propose a specific model, based on electroweak radiative corrections in the MSSM, for ε and ε'. In that model, both |Ue3| and |cos2θ₂₃|, could be close to their respective experimental upper bounds if neutrinos are quasi-degenerate.