Five Texture Zeros for Dirac Neutrino Mass Matrices

Abstract

In this work we propose new five textures zeros for the mass matrices in the lepton sector in order to predict values for the neutrino masses. In our approach we go beyond the Standard Model by assuming Dirac masses for the neutrinos, feature which allows us to make a theoretical prediction for the lightest neutrino mass in the normal ordering. The textures analyzed have enough free parameters to adjust the VPMNS mixing matrix including the CP-violating phase, the neutrino mass squared differences δm 2 21 , δm 2 31 , and the three charged lepton masses. In order to have reliable results two different approaches are used: the first one is based on a least-squares analysis to fit the lepton masses and the mixing parameters to their corresponding experimental values, for this case the best fit for the lightest neutrino mass is (3.9± 0.6 0.8 ) × 10 −3 eV.; the second approach is just algebraic, based on the weak basis transformation method, in this case the lightest neutrino mass consistent with the experimental values and the restrictions coming from the five texture zeros of the mass matrices is equal to (3.5 ± 0.9) × 10 −3 eV.

Flavored axions and the flavor problem

“…For future work, it is necessary to extend the PQ symmetry to leptons. Although it is true that in the literature there are textures that can adjust the parameters of the lepton sector [43,[57][58][59][60][61], these textures are different from those used with quarks [9] and therefore require additional Higgs doublets. The analysis is not trivial since each additional Higgs doublet generates 7 inequalities involving the SM PQ charges.…”

“…For the time being we only consider the quark sector but a similar analysis can be done in the lepton sector [43]. We can obtain texture-zeros by imposing the conditions:…”