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The only other contributions to the effective (Formula presented) and (Formula presented) vertices are from the SM (Formula presented) boson which we are ignoring since we expect the contributions from model III to be much bigger due to the presence of both neutral and charged scalars with large couplings to the top quark (see Fig. 11). Moreover, we expect model III to give bigger predictions, even with respect to model I and model II, due to the presence of the new FC couplings proportional to (Formula presented) and to the particular structure of the charged scalar couplings [see Eq. (9)]. See Ref. 15
-
The only other contributions to the effective (Formula presented) and (Formula presented) vertices are from the SM (Formula presented) boson which we are ignoring since we expect the contributions from model III to be much bigger due to the presence of both neutral and charged scalars with large couplings to the top quark (see Fig. 11). Moreover, we expect model III to give bigger predictions, even with respect to model I and model II, due to the presence of the new FC couplings proportional to (Formula presented) and to the particular structure of the charged scalar couplings [see Eq. (9)]. See Ref. 15 for the explicit calculation of (Formula presented) in the SM and in model I and model II 2HDM’s. Our expectations are also confirmed by the case of rare top decays, discussed in Sec. IV, in which the same form factors are used (see in particular Table I for a quantitative comparison of the SM and of the different types of 2HDM’s).
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We also observe that in Ref. 7 the form factors used in the analytical expressions for the rates [see their Eq. (10)] should include the factor (Formula presented), which is factored out in their Eq. (9), where the form factors are defined.
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Note that in Fig. 22 of Ref. 7 the authors factor out the FC coupling dependence: (Formula presented). For (Formula presented) GeV and (Formula presented) GeV, taking as we did (Formula presented), this amounts to multiplying their results by a factor (Formula presented). Also note that, unlike them, we have not multiplied the (Formula presented) by the (Formula presented).
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See Ref. 28.
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In fact, the SM predictions for the different (Formula presented) mixings reported in Table II include also QCD corrections.
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According to the results of Sec. VI, we neglect the mixing with the first family
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According to the results of Sec. VI, we neglect the mixing with the first family.
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passing, we should also mention that, we have also examined the decay (Formula presented) in model III. We found that due to the different couplings involved, this decay is never consistently enhanced with respect to the SM prediction
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In passing, we should also mention that, we have also examined the decay (Formula presented) in model III. We found that due to the different couplings involved, this decay is never consistently enhanced with respect to the SM prediction.
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our calculation all the quarks except the top quark are taken to be massless, keeping (Formula presented) only in the (Formula presented) couplings as in Eq. (10)
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In our calculation all the quarks except the top quark are taken to be massless, keeping (Formula presented) only in the (Formula presented) couplings as in Eq. (10).
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We assume that the changes for (Formula presented) and (Formula presented) in model III with suppressed FC couplings for the first family, i.e., in case 2 and case 3, are negligible.
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Even if the pole terms are not explicitly given in Ref. 7
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Even if the pole terms are not explicitly given in Ref. 7, they can be easily deduced from the corresponding logarithmic term (Formula presented) in each diagram.
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