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4
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84927891639
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We are ignoring the possible fields from incomplete multiplets. Our arguments will not be affected by their inclusion.
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13
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84927891637
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We shall consider only real symmetric Yukawa coupling matrices; hence only orthogonal matrices OL= OR=O for diagonalizing M prime.
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16
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84927891635
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We are ignoring the distinction between weak and mass eigenstates of the Higgs fields. This introduces an arbitrary mixing angle app 1 into each term, which will not affect our arguments. See also Eq. (13) with respect to the related matter of ``characteristic Higgs-boson mass'' mH.
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18
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84927891633
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For reference one may note that this result agrees well with that obtained with the method of inserting vacuum state in all possible ways: L langleK¯| (s¯γ5d) (s¯γ5d)|K > vac mark = - case 1 over case 6 langleK¯|s¯γλγ5d | 0 > < 0 |s¯γλγ5d |K > lineup + case 11 over case 6 langleK¯|s¯γ5d | 0 > < 0 |s¯γ5d|K > lineup = {fK mK2 over2} {12 mK}left ( - 1 + {11 mK over2} {(ms+ md)2}right ) because langleK¯|s¯d|0 > and langleK¯|s¯γλd|0 > vanish due to parity, and langleK¯|s¯σ μλ d|0 > =0 as we cannot construct an antisymmetric tensor out of the kaon momentum. We then have langleK¯| (s¯γ5d)(s¯γ5d)|K > markvac apeq 11 over 12 {fk mk2 over2} {ms 2} lineup apeq 8.7 times 10-2~ GeV3~.
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19
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40249089086
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Througout this paper we shall for definiteness use the quark mass values (at 1 GeV) estimated by, : mbapeq 5.3 GeV, mcapeq 1.35 GeV, msapeq 175 MeV, mdapeq 8.9 MeV, and muapeq 5.1 MeV.
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(1982)
Phys. Rep.
, vol.87
, pp. 77
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Gasser, H.1
Leutwyler, H.2
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20
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84927891631
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O. Shanker in Ref. 9 has also estimated this mH lower bound from μ e conversion in nucleus, yielding mH> 11 TeV; K -> μ e and K -> ee, 7 TeV; K -> μ mu, 4.7 TeV; K -> π μ e, 0.7 TeV; μ -> 3e, 0.4 TeV; μ -> e gamma, 0.2 TeV.
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26
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84927891628
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If the coupling is given by Δjk mjmk, then this should be multiplied by Δsd/ Δcu, which is expected to be app 1.
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28
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84927891627
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T. P. Cheng and L. F. Li (Ref. 7). Also, in this paper all KM angles are worked out with ``maximal CP clzquo phases. However, the essential results for the magnitudes Vus, Vcb, and Vub are the same as stated here with all mass matrix elements taken to be real.
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30
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84927891623
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We take the viaposs to be all comparable. In many supersymmetric E6 models is assumed that only one vi is nonzero. This can only occur if there is no mixing between the Higgs fields. Although this might occur for topological reasons, in general mixings will exist and the viaposs are expected to be comparable.
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31
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84927891621
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To extend this argument further, as noted in the previous footnote the Higgs-boson mass eigenstates Hi are some linear combinations of the weak eigenstates, Hi= sumlUilHlsprime; the couplings λijksprime in Eq. (1) are linear combinations of the Yukawa couplings λijk2sprime defined with respect to the fermion and the Higgs weak eigenstates: λijksprime= sumlUilλljk2sprime. Thus the mass matrix of Eq. (23) results from a double sum Mjksprime= sum sumilviUilλljk2sprime/ sqrt 2. If there are any zeros, they result most likely from some discrete symmetry and/or topological restrictions acting on weak eigenstates and first appear in λijk2sprime. In order for such zeros to survive all the way down to the mass matrix M prime, the most natural way is for them to have fixed locations throughout.
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32
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84927891619
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If the vi form a hierarchy, say v1>> v2>> v3 then is easy to show that the lower bound on the mass H1 is decreased by O(v2/v1).
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35
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84927891617
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Given the previous remarks about the relative size of Yukawa couplings in an orbifold compactification, can be realized only if v1 is correspondingly small.
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36
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84927891614
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The more familiar CP-violation mechanisms due to Higgs-boson exchanges is of the milliweak type since a value of mHapeq 10 – 50 GeV is taken with flavor-changing effects suppressed by specific coupling arrangements;
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