Non-diagonal charged lepton mass matrix and non-zero ${\theta }_{13}$

Abstract

Assuming that the neutrino mass matrix is diagonalized by the tribimaximal mixing matrix, we explore the textures for the charged lepton mass matrix that render an $U_{PMNS}$ lepton mixing matrix consistent with data. In particular we are interested in finding the textures with the maximum number of zeros. We explore the cases of real matrices with three and four zeros and find that only ten matrices with three zeros provide solutions in agreement with data. We present the successful Yukawa textures including the relative sizes of their non-zero entries as well as some new and interesting relations among the entries of these textures in terms of the charged lepton masses. We also show that these relations can be obtained directly from a parametrization of the charged lepton mixing matrix $U_l$.

16 pages, two figures. A parametrization of the mixing matrix $U_l$ was introduced to explain observed patterns in textures. References added

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• Charged lepton correction to tribimaximal lepton mixing and its implications to neutrino phenomenology
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• CP violating phase from charged-lepton mixing
• CP Violation in Predictive Neutrino Mass Structures
• The Dark Side of ${\theta }_{13}$, ${\delta }_{CP}$, Leptogenesis and Inflation in Type-I Seesaw
• On the ambiguities in the tri-bimaximal mixing matrix and corresponding charged lepton corrections