Abstract
We compute the effect of nondiagonal neutrino mass inli→ljγin Supersymmetry (SUSY) theories with nontrivial quark-lepton complementarity and a flavor symmetry. The correlation matrixVM=UCKMUPMNSis such that its (1,3) entry, as preferred by the present experimental data, is zero. We do not assume thatVMis bimaximal. Quark-lepton complementarity and the flavor symmetry strongly constrain the theory and we obtain a clear prediction for the contribution toμ→eγand theτdecaysτ→eγandτ→μγ. If the Dirac neutrino Yukawa couplings are degenerate but the low-energy neutrino masses are not degenerate, then the lepton decays are related among them by theVMentries. On the other hand, if the Dirac neutrino Yukawa couplings are hierarchical or the low-energy neutrino masses are degenerate, then the prediction for the lepton decays comes from theUCKMhierarchy.
Highlights
The present experimental situation is such that we are very close to obtain a theory of flavor that is able to explain in a clear way all the standard model masses and mixing
The disparity that nature indicates between quark and lepton mixing angles has been viewed in terms of a “quark-lepton complementarity” QLC 1, 2 which can be expressed in Advances in High Energy Physics the relations θP12MNS θC12KM 45◦; θP23MNS θC23KM 45◦
If the Yukawa matrices are diagonalized by a similar matrix on the left and on the right, for example, in minimal renormalizable SO 10 with only small contributions from the antisymmetric representations such as 120 or more important in models where the diagonalization is strongly constrained by the flavor symmetry, the previous relationship translates into a relation between UPMNS, UCKM, and VM
Summary
The present experimental situation is such that we are very close to obtain a theory of flavor that is able to explain in a clear way all the standard model masses and mixing. The clear nontrivial structure of VM and the strong indication of gauge coupling unification allow us to obtain in a straightforward way constraints on the high-energy spectrum too Within this framework we get information about flavor physics from the correlation matrix VM too. In this work we compute the effect of nondiagonal neutrino mass in li→ljγ in SUSY theories with nontrivial quark-lepton complementarity and flavor symmetry. By using the nontrivial quark-lepton complementarity, flavor symmetry, and the see-saw mechanism we will compute the explicit spectrum of the heavy neutrinos This will allow us to investigate the relevance of the form of VM in li→ljγ.
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