A supersymmetric D 4 model for μ-τ Symmetry

Abstract

We construct a supersymmeterized version of the model presented by Grimus and Lavoura (GL) in [1] which predicts θ 23 maximal and θ 13 = 0 in the lepton sector. For this purpose, we extend the flavor group, which is D 4 × Z 2(aux) in the original model, to D 4 × Z 5. An additional difference is the absence of right-handed neutrinos. Despite these changes the model is the same as the GL model, since θ 23 maximal and θ 13 = 0 arise through the same mismatch of D 4 subgroups, D 2 in the charged lepton and Z 2 in the neutrino sector. In our setup D 4 is solely broken by gauge singlets, the flavons. We show that their vacuum structure, which leads to the prediction of θ 13 and θ 23, is a natural result of the scalar potential. We find that the neutrino mass matrix only allows for inverted hierarchy, if we assume a certain form of spontaneous CP violation. The quantity |m ee|, measured in neutrinoless double beta decay, is nearly equal to the lightest neutrino mass m 3. The Majorana phases φ 1 and φ 2 are restricted to a certain range for m 30.06 eV. We discuss the next-to-leading order corrections which give rise to shifts in the vacuum expectation values of the flavons. These induce deviations from maximal atmospheric mixing and vanishing θ 13. It turns out that these deviations are smaller for θ 23 than for θ 13. © 2009 SISSA.