Abstract
We show that non-Hermitian and nearest-neighbor-interacting perturbations to the Fritzsch textures of lepton and quark mass matrices can make both of them fit current experimental data very well. In particular, we obtain θ23≃45° for the atmospheric neutrino mixing angle and predict θ13≃3° to 6° for the smallest neutrino mixing angle when the perturbations in the lepton sector are at the 20% level. The same level of perturbations is required in the quark sector, where the Jarlskog invariant of CP violation is about 3.7×10−5. In comparison, the strength of leptonic CP violation is possible to reach about 1.5×10−2 in neutrino oscillations.
Highlights
The flavor sector in the standard model (SM) of electroweak interactions has been puzzling because it involves most of the free parameters of the model itself
We have introduced non-Hermitian and nearest-neighbor-interacting perturbations to the Fritzsch textures of lepton and quark mass matrices such that both of them can fit current experimental data very well
We find that it is possible to obtain θ23 ≃ 45◦ for the atmospheric neutrino mixing angle and predict θ13 ≃ 3◦ to 6◦ for the smallest neutrino mixing angle when the dimensionless perturbation parameters in the lepton sector are at the 20% level
Summary
The flavor sector in the standard model (SM) of electroweak interactions has been puzzling because it involves most of the free parameters of the model itself. We shall introduce non-Hermitian perturbations to both Ml(F) and Mν(F) so that the resultant chargedlepton and neutrino mass matrices can agree with current neutrino oscillation data to a better degree of accuracy 2 Such a parallel study of lepton and quark mass matrices of approximate Fritzsch textures is useful to reveal the similarities and differences between the lepton and quark sectors, and it should be helpful for building a unified flavor model of leptons and quarks. (2) The analytical approximations made in our perturbative calculation are valid to a better degree of accuracy and allow one to see the difference between the contribution of fermion mass ratios and that of perturbation parameters (which signify a departure of the NNI texture from Hermiticity) to the flavor mixing matrix elements in a clearer way.
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