Non-vanishing Ue3 and cos 2θ23 from a broken Z2 symmetry

It is shown that the neutrino mass matrices in the flavour basis yielding a vanishing U-e3 are characterized by invariance under a class of Z(2) symmetries. A specific Z(2) in this class also leads to a maximal atmospheric mixing angle theta(23). The breaking of that Z(2) can be parameterized by two dimensionless quantities, is an element of and is an element of'; the effects of is an element of, is an element of' not equal 0 are studied perturbatively and numerically. The induced value Of vertical bar U(e3)vertical bar strongly depends on the neutrino mass hierarchy. We find that vertical bar U(e3)vertical bar is less than 0.07 for a normal mass hierarchy, even when is an element of, is an element of' similar to 30%. For an inverted mass hierarchy vertical bar U(e3)vertical bar tends to be around 0.1 but can be as large as 0.17. In the case of quasi-degenerate neutrinos, vertical bar U(e3)vertical bar could be close to its experimental upper bound 0.2. In contrast, vertical bar cos2 theta 23 vertical bar can always reach its experimental upper bound 0.28. We propose a specific model, based on electroweak radiative corrections in the MSSM, for is an element of and is an element of'. In that model, both vertical bar U(e3)vertical bar and vertical bar cos2 theta(23)vertical bar, could be close to their respective experimental upper bounds if neutrinos are quasi-degenerate. (c) 2005 Elsevier B.V. All rights reserved.