Fermion Masses and Origin of Family

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(1) Anomalous U (1) and Family Structure: If one uses the Grand Unified theory with family symmetry U (1), all the breaking scales determined from the Higgs sector can be fixed only from the U (1) charges of the fields in the system. This means that once the U (1) charges of the relevant fields are fixed, the effective low energy theory including the particles of standard theory is uniquely determined. Using full U (1) scheme, we examine E6 Model and found that it reproduces the present experiments very successfully(2) The so called "triplet-doublet splitting" problem : It is recognized that the grand unified theory can be consistent with the experimental gap of quarks and leptons. Thus it has become very important to solve the fundamental problems which we are now facing with. One of the serious problems is the big difference between the of masses of triplet and doublet Higgs fields. One of the ideas to solve such triplet-doublet splitting is to identify the low energy light Higgs fie … More lds to the Numbu Gold stone fields appearing due to the spontaneous symmetry breaking. Such possibility was considered by some authors but recent neutrino oscillation experiments indicates the family twisting structure for quarks and leptons. So this dictates larger GUT groups than SU(5) or SO(10). The most provable candidate is E6. Gauge group. So we examine whether E6 model can solve the triplet doublet problem and reproduce the Humbu Goldstone particles as we expect. I with Kugo showed that this can be possible if we choose the correct representations for the fermions with the proper breaking chain(3) Neutrino Mass matrix in terms of up-quark masses: I started a new subject with Obara. We examine the possibility that the neutrino mass matrix can be reproduced from the Pati-Salam symmetry relation. We have found that this is possible only when we adopt the "zero texture" with some special Higgs representation. Unlike the Froggatt-Nielsen mechanism case, even the coefficients of the lepton mass parameters can be uniquely determined from the up^type quark mass matrix. Here we note that the "zero texture" is essential to reproduce bi-large missing matrix. Now I and Obara are investigating the detailed calculation(4) Genera structure of neutrino bi-large mixing: After KamLAND, the neutrino bi-large mixing is established as well as mass differences, Now the question is what is the indication of this after all. ! With Kugo, are making general conditions for reproducing those data This will give the hints to answer the quwstion on the origin of family Less