Non-vanishing Ue3 and cos2θ23 from a broken Z2 symmetry

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.