Quantum numbers of heavy neutrinos, tri-bi-maximal mixing through double seesaw with permutation symmetry, and comment on
نویسنده
چکیده
Using the family symmetry, in the neutrino mass matrix we remove the Yukawa coupling (arising in the Dirac type mass between the heavy neutrinos and light lepton doublets) dependence in the double seesaw mechanism so that it is directly proportional to the mass matrix m of heavy Majorana neutrinos. Then, the neutrino mass matrix is given by the family symmetry at high energy scale. With the permutation symmetry S3, we note a variety of mass hierarchies arising distinctly in neutrinos, charged leptons, Qem = − 3 quarks, and Qem = 23 quarks. Distinguishing these hierarchies, we obtain a relation between the CKM angles and the MNS angles. Finally, we comment on the approximate relation θsol + θc ≃ π4 .
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