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Register a new userNon-Hermitian Perturbations to the Fritzsch Textures of Lepton and Quark Mass Matrices
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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 theta_{23} simeq 45^circ for the atmospheric neutrino mixing angle and predict theta_{13} simeq 3^circ to 6^circ 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 times 10^{-5}. In comparison, the strength of leptonic CP violation is possible to reach about 1.5 times 10^{-2} in neutrino oscillations.
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We propose a model that all quark and lepton mass matrices have the same zero texture. Namely their (1,1), (1,3) and (3,1) components are zeros. The mass matrices are classified into two types I and II. Type I is consistent with the experimental data in quark sector. For lepton sector, if seesaw mechanism is not used, Type II allows a large $ u_mu - u_tau$ mixing angle. However, severe compatibility with all neutrino oscillation experiments forces us to use the seesaw mechanism. If we adopt the seesaw mechanism, it turns out that Type I instead of II can be consistent with experimental data in the lepton sector too.
The hierarchical quark masses and small mixing angles are shown to lead to a simple triangular form for the U- and D-type quark mass matrices. In the basis where one of the matrices is diagonal, each matrix element of the other is, to a good approximation, the product of a quark mass and a CKM matrix element. The physical content of a general mass matrix can be easily deciphered in its triangular form. This parameterization could serve as a useful starting point for model building. Examples of mass textures are analyzed using this method.
Natural 4 zeros texture mass matrices recently proposed by Fritzsch and Xing have been investigated by including `non-leadingcorrections in the context of latest data regarding m_t^{pole} and V_{CKM} matrix elements. Apart from accommodating m_t^{pole} in the range 175pm15 GeV, |V_{cb}| and |V_{ub}/V_{cb}|=0.08pm0.02, the analysis with maximal CP-violation predicts |V_{td}| = .005-.013. Further, the CP-violating phase angle delta can be restricted to the ranges (i) 22^o -45^o and (ii) 95^o - 130^o, concretizing the ambiguity regarding phase of CKM matrix. Furthermore, we find that non-leading calculations are important when `Cabibbo triangle is to be linked to unitarity triangle.
It has been suggested that residual symmetries in the charged-lepton and neutrino mass matrices can possibly reveal the flavour symmetry group of the lepton sector. We review the basic ideas of this purely group-theoretical approach and discuss some of its results. Finally, we also list its shortcomings.
The quark-lepton complementarity (QLC) is very suggestive in understanding possible relations between quark and lepton mixing matrices. We explore the QLC relations in all the possible angle-phase parametrizations and point out that they can approximately hold in five parametrizations. Furthermore, the vanishing of the smallest mixing angles in the CKM and PMNS matrices can make sure that the QLC relations exactly hold in those five parametrizations. Finally, the sensitivity of the QLC relations to radiative corrections is also discussed.
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