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Recently, a curious neutrino mass matrix has been proposed: it is related to up-quark masses, and it can excellently give a nearly tribimaximal mixing. It is pointed out that, in order to obtain such successful results, three phenomenological relations among masses and Cabibbo-Kobayashi-Maskawa parameters must be simultaneously satisfied. This suggests that there must be a specific flavor basis in which down-quark and charged lepton mass matrices are simultaneously diagonalized.
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Yoshio Koide (2008) studied this question.
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