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For other modifications, see C. H. Albright, Phys. Lett. B 246, 451 (1990);
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Albright, C.H.1
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This procedure has a long history going back at least to L. Wolfenstein, Phys. Rev. Lett. 51, 1945 (1983); see also
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Wolfenstein, L.1
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Schmaltz, M.1
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34
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85038306001
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Notice that the first two constraints can lead to an apparent solution which has both the two lower eigenvalues (Formula presented) and (Formula presented) generated just from the mixing with the third family. This actually gives a vanishing determinant for the mass matrix. For instance, in Eq. (6) the case with (Formula presented) and (Formula presented) as the leading contributions to (Formula presented) and (Formula presented), respectively. This admits a solution of the form (Formula presented)which has zero determinant. This “solution” of course has to be discarded
-
Notice that the first two constraints can lead to an apparent solution which has both the two lower eigenvalues (Formula presented) and (Formula presented) generated just from the mixing with the third family. This actually gives a vanishing determinant for the mass matrix. For instance, in Eq. (6) the case with (Formula presented) and (Formula presented) as the leading contributions to (Formula presented) and (Formula presented), respectively. This admits a solution of the form (Formula presented)which has zero determinant. This “solution” of course has to be discarded.
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35
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85038336560
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During the preparation of the manuscript, the authors came across Ref. 24
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During the preparation of the manuscript, the authors came across Ref. 24 which analyzes general texture patterns at low energy, and their RG evolution to GUT scale. Their “natural mass matrix” philosophy is similar to that of our approach. The actual analysis and solutions are not the same. Among other things, our texture patterns, with some entries given as inequalities, give more general “natural” patterns.
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-
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38
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0004361318
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W.-S. Hou and G.-G. Wong, 52, 5269 (1995).
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X.-G. He and W.-S. Hou, Phys. Rev. D 41, 1517 (1990);
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Phys. Rev. D 45, 4192 (1992);
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85038309536
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46, R4793 (1992);
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45
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P. Nath, 76, 2218 (1996).
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Nath, P.1
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46
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85038288993
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We neglect in our analysis FCNC constraints from (Formula presented); assuming proportionality to the Yukawa couplings, such contraints can be easily satisfied
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We neglect in our analysis FCNC constraints from (Formula presented); assuming proportionality to the Yukawa couplings, such contraints can be easily satisfied.
-
-
-
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47
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85038292945
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Assuming a (Formula presented) structure, the squarks of the first two families can be represented by a horizontal doublet (Formula presented). A (Formula presented) term is invariant, allowing the leading order (Formula presented) terms. Further contributions to the terms can come from operators of the form (Formula presented)suppressed by powers of some mass scale. The product of the (Formula presented) scalars must be an invariant. In order to contribute to the diagonal terms in the mass matrix, the nonzero horizontal symmetry-breaking vacuum expectation values therefore must come from states that also form an invariant product. This naturally gives identical contributions to (Formula presented) and (Formula presented) other possibilities have to base on a more contrived mechanism. We hence stick to the case in our analysis
-
Assuming a (Formula presented) structure, the squarks of the first two families can be represented by a horizontal doublet (Formula presented). A (Formula presented) term is invariant, allowing the leading order (Formula presented) terms. Further contributions to the terms can come from operators of the form (Formula presented)suppressed by powers of some mass scale. The product of the (Formula presented) scalars must be an invariant. In order to contribute to the diagonal terms in the mass matrix, the nonzero horizontal symmetry-breaking vacuum expectation values therefore must come from states that also form an invariant product. This naturally gives identical contributions to (Formula presented) and (Formula presented) other possibilities have to base on a more contrived mechanism. We hence stick to the case in our analysis.
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49
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30244526989
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C.A. Savoy, Invited Talk at HEP95 Euroconference, Brussels, 1995 (unpublished), and references therein
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E. Gabrielli, A. Masiero, and L. Silvestrini, Phys. Lett. B 374, 80 (1996); C.A. Savoy, Invited Talk at HEP95 Euroconference, Brussels, 1995 (unpublished), and references therein.
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Phys. Lett. B
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Gabrielli, E.1
Masiero, A.2
Silvestrini, L.3
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