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Register a new userA discrete anatomy of the neutrino mass matrix
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We investigate the possibility of expressing the charged leptons and neutrino mass matrices as linear combinations of generators of a single finite group. Constraints imposed on the resulting mixing matrix by current data restrict the group types, but allow a non zero value for the theta_13 mixing angle
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Neutrino mass sum rules have recently gained again more attention as a powerful tool to discriminate and test various flavour models in the near future. A related question which was not yet discussed fully satisfactorily was the origin of these sum rules and if they are related to any residual or accidental symmetry. We will address this open issue here systematically and find previous statements confirmed. Namely, that the sum rules are not related to any enhanced symmetry of the Lagrangian after family symmetry breaking but that they are simply the result of a reduction of free parameters due to skillful model building.
We carry out diagonalization of a $3times3$ Hermitian matrix of which Real component and Imaginary part are commutative and apply it to Majorana neutrino mass matrix $M=M_ u M_ u^dagger$ which satisfies the same condition. It is shown in a model-independent way for the kind of matrix M of which Real component and Imaginary part are commutative that $delta = pmpi/2$ which implies the maximal strength of CP violation in neutrino oscillations. And we obtain the prediction $cos (2theta_{23})=0$ for this kind of M. It is shown that the kind of Hermitian Majorana neutrino mass matrix M has only five real parameters and furthermore, only one free real parameter (D or A) if using the measured values of three mixing angles and mass differences as input.
We analyze the different parametrizations of a general four-zero texture mass matrices for quarks and leptons, that are able to reproduce the CKM and PMNS mixing matrices. This study is done through a Chi-Square analysis. In quark sector, only four solutions are found to be compatible with CKM mixing matrix. In leptonic sector, using the last experimental results about the mixing angles in the neutrino sector, our Chi-Square analysis shows a preferred value for m_nu_3 to be around 0.05 eV independently of the parametrization of the four-zero texture mass matrices chosen for the charged leptons and neutrinos.
Using the residual symmetry approach, we propose a complex extension of the scaling ansatz on $M_ u$ which allows a nonzero mass for each of the three light neutrinos as well as a nonvanishing $theta_{13}$. Leptonic Dirac CP violation must be maximal while atmospheric neutrino mixing need not to be exactly maximal. Each of the two Majorana phases, to be probed by the search for $0 u betabeta$ decay, has to be zero or $pi$ and a normal neutrino mass hierarchy is allowed.
The recent enormous improvement of our knowledge of the neutrino oscillation parameters has motivated us to reinvestigate the allowed ranges of the elements of the neutrino mass matrix in the basis where the charged-lepton mass mass matrix is diagonal. Moreover, we have studied the correlations of the elements of the neutrino mass matrix. The result of this analysis is useful for finding textures in the neutrino mass matrix and, therefore, for model building in the lepton sector. As an example, we present two textures of the neutrino mass matrix which have only two parameters and fit very well all current experimental data on the neutrino parameters.
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