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Diverse mass and mixing patterns between the quarks and leptons makes it challenging to construct a simple grand unified theory of flavor.
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For an example of a scenario where type II dominates for SO(10), see H. S. Goh et al, ref. [ 8 ] . In this case threshold corrections due to large representations are also controllable
Cited in the paper.
A 3 × 3 3\times 3 unitary matrix U U can be expressed as U = P 1 U ¯ P 2 U=P_{1}\bar{U}P_{2} where P 1 P_{1} and P 2 P_{2} are diagonal phase matrices and U ¯ \bar{U} is a standard form of the unitary matrix which includes one phase and three mixings. The usual expression of the CKM matrix is parameterized in the U ¯ \bar{U} part since P 1 P_{1} and P 2 P_{2} are unphysical. The phase matrix diag ( 1 , e i α , e i β ) {\rm diag}(1,e^{i\alpha},e^{i\beta}) corresponds to the P 2 P_{2} part of V ~ e \tilde{V}_{e} which is physical in the PMNS matrix. Actually, one can find that the phase α \alpha corresponds to the PMNS phase (which appears in the long baseline neutrino oscillation) approximately up to a quadrant
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G. L. Fogli, E. Lisi, A. Marrone, A. Palazzo and A. M. Rotunno, arXiv:0809.2936 [hep-ph]
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MINOS Collaboration, arXiv:0909.4996 [hep-ex]
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G. L. Fogli, E. Lisi, A. Marrone, A. Palazzo and A. M. Rotunno, arXiv:0905.3549 [hep-ph]
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