arXiv subjects

Ying-Ying Fan

Publications and source records attributed to Ying-Ying Fan.

At least 19 recordsLinked to original sources

arXiv2025

The $\phi p$ bound state in the unitary coupled-channel approximation

The attractive interaction of the $\phi$ meson and the proton is reported by the ALICE Collaboration, and the corresponding scattering length $f_0$ is given as $Re(f_0)=0.85\pm0.34(stat)\pm0.14(syst)$ fm and $Im(f_0)=0.16\pm0.10(stat)\pm0.09(syst)$ fm. The fact that the real part is significant in contrast to the imaginary part indicates a dominating role of the elastic scattering, whereas the inelastic process is less important. In this work, such scattering processes are inspected on the basis of a unitary coupled-channel approximation inspired by the Bethe-Salpeter equation. The $\phi p$ scattering length is calculated and it is found that the experimental value of the $\phi p$ scattering length can be obtained only if the attractive interaction of the $\phi$ meson and the proton is taken into account. A significant outcome of such an attractive interaction is a two-pole structure in the scattering amplitude. One of the poles, located at $1969-i283$ MeV, might be a resonance state of $\phi N$, while the other pole, located at $1949-i3$ MeV, should be a bound state of $\phi N$. Both of these states do not have counterparts in the data of the Particle Data Group(PDG).

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arXiv2025

Estimating of CP Violation in $B_{c}\rightarrow B K^{0}+B {\bar{K}}^0\rightarrow B \pi^{\pm} e^{\mp} \nu_{e}$ Decays

In this paper, we investigate the CP asymmetries ${\mathcal A}_{CP}^{pm}$ and ${\mathcal A}_{CP}^{mp}$ in $B_{c}^{\pm}\rightarrow B^{\pm} K^{0}+B^{\pm} {\bar{K}}^0\rightarrow B^{\pm} \pi^{\pm} e^{\mp} \nu_{e}$ and $B_{c}^{\pm}\rightarrow B^{\pm} K^{0}+B^{\pm} {\bar{K}}^0\rightarrow B^{\pm} \pi^{\mp} e^{\pm} \nu_{e}$ decays, both of them consist of three parts: the indirect CP violations in $K^0 -\bar{K}^0$ mixing $A_{CP,mix}^{pm}$ and $A_{CP,mix}^{mp}$, the direct CP violations in $B_{c}$ decay $A_{CP,dir}^{pm}$ and $A_{CP,dir}^{mp}$, the new CP violation effects $A_{CP,int}^{pm}$ and $A_{CP,int}^{mp}$, which originate from the interference between the amplitude of the $B_{c}^{-}\rightarrow B^{-} K^{0} ({\bar{K}}^0) \rightarrow B^{-} \pi^{-} e^{+} \nu_{e}(\pi^{+} e^{-} \bar{\nu}_{e})$ decay with the difference between the oscillating effect of $K^0\rightarrow {\bar{K}}^0$ and that of ${\bar{K}}^0\rightarrow K^0 $. The strong phase differences of the direct CP asymmetries $A_{CP,dir}^{pm}$ and $A_{CP,dir}^{mp}$ arising from $K^0-\bar{K}^0$ mixing parameters. ${\mathcal A}_{CP}^{pm}$ and ${\mathcal A}_{CP}^{mp}$ are of the order $\mathcal{O}(10^{-4})$ and $\mathcal{O}(10^{-3})$, respectively. The new CP violation effect ${\mathcal A}_{CP,int}^{pm}$ plays a dominant role in ${\mathcal A}_{CP}^{pm}$, the CP asymmetry ${\mathcal A}_{CP}^{mp}$ is dominated by the indirect CP violation ${\mathcal A}_{CP,mix}^{mp}$, so the CP asymmetry ${\mathcal A}_{CP}^{pm}$ provides an ideal place to study the new CP violation effect. We derive another two asymmetry observables ${\mathcal A}_{CP}^{pp}$ and ${\mathcal A}_{CP}^{mm}$, which are dominated by $K^0-\bar{K}^0$ mixing. The observables ${\mathcal A}_{CP}^{pm}$, ${\mathcal A}_{CP}^{mp}$, ${\mathcal A}_{CP}^{pp}$ and ${\mathcal A}_{CP}^{mm}$ are hopefully to be marginally observed at the LHC experiment and the HL-LHC experiment.

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arXiv2023

The $ϕp$ bound state in the unitary coupled-channel approximation

The strong attractive interaction of the $ϕ$ meson and the proton is reported by ALICE collaboration recently. The corresponding scattering length $f_0$ is given as $Re(f_0)=0.85\pm0.34(stat)\pm0.14(syst)$fm and $Im(f_0)=0.16\pm0.10(stat)\pm0.09(syst)$fm. The fact that the real part is significant in contrast to the imaginary part indicates a dominate role of the elastic scattering, whereas the inelastic process is less important. In this work, such scattering processes are inspected based on a unitary coupled-channel approach inspired by Bethe-Salpeter equation. The $ϕp$ scattering length is calculated based on this approach, and it is found that the experimental value of the $ϕp$ scattering length can be obtained only if the attractive interaction of the $ϕ$ meson and the proton is taken into account. A significant outcome of such attractive interaction is a two-pole structure in the $ϕp$ scattering amplitude. One of the pole, locating at $(1969-i283)$~MeV might correspond to $N(1895)1/2^-$ or $N(1875)3/2^-$ listed in the review of the Particle Data Group(PDG). The other one, locating at ${1949-i3}$~MeV should be a $ϕN$ bound state, which has no counterpart in the PDG data.

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arXiv2020

Resonance contributions $ϕ(1020,1680)\to K\bar K$ for the three-body decays $B\to K\bar K h$

We study the contributions for the $K^+K^-$ and $K^0\bar K^0$ originated from the intermediate states $ϕ(1020)$ and $ϕ(1680)$ in the charmless three-body decays $B\to K\bar K h$, with $h=(π, K)$, in the perturbative QCD approach. The subprocesses $ϕ(1020,1680)\to K\bar K$ are introduced into the distribution amplitudes of $K\bar K$ system via the kaon electromagnetic form factors with the coefficients taken from the fitted results. The predictions of the branching fractions for the decays $B\toϕ(1680)h$ with the intermediate state $ϕ(1680)$ decays into $K^+K^-$ or $K^0\bar K^0$ are about $6\%$-$8\%$ of the corresponding results for the quasi-two-body decays $B\toϕ(1020)h \to K^+ K^- h$ in this work.

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arXiv2020

Studying Radiative Baryon Decays with the SU(3) Flavor Symmetry

The weak and electromagnetic radiative baryon decays of octet $T_{8}$, decuplet $T_{10}$, single charmed anti-triplet $T_{c3}$ and sextet $T_{c6}$, single heavy bottomed anti-triplet $T_{b3}$ and sextet $T_{b6}$ are investigated by using SU(3) flavor symmetry irreducible representation approach. We analyze the contributions from a single quark transition $q_1\to q_2γ$ and $W$ exchange transitions, and find that the amplitudes could be easily related by SU(3) flavor symmetry in the $T_{b3,b6}$ weak radiative decays, $T_{c3,c6}$ weak radiative decays, $T_{10}\to T_{8}γ$ weak decays, $T_{10}\to T'_{10}γ$ weak decays and $T_{10}\to T_{8}γ$ electromagnetic decays. Nevertheless, the amplitude relations are a little complex in the $T_{8}\to T'_{8}γ$ and $T_{8}\to T_{10}γ$ weak decays due to quark antisymmetry in $T_{8}$ and $W$ exchange contributions. Predictions for branching ratios of $Λ^{0}_b\to nγ$, $Ξ^{-}_b\to Ξ^-γ$, $Ξ^{-}_b\to Σ^-γ$, $Ξ^{0}_b\to Σ^0γ$, $Ξ^{0}_b\to Λ^0γ$, $Ξ^{0}_b\to Ξ^0γ$, $Ξ^{*}\to Ξγ$, $Σ^{*0}\to Σ^{0}γ$, $Δ^0\to nγ$ and $Δ^+\to pγ$ are given. The results in this work can be used to test SU(3) flavor symmetry approach in the radiative baryon decays by the future experiments at BESIII, LHCb and Belle-II.

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arXiv2019

Quasi-two-body decays $B_{(s)} \to P D_0^*(2400) \to P D π$ in the perturbative QCD approach

We study the quasi-two-body decays $B\to P D^{\ast}_0(2400) \to P Dπ$ with $P=(π, K, η, η^{\prime})$ in the perturbative QCD factorization approach. The predicted branching fractions for the considered decays are in the range of $10^{-9}$-$10^{-4}$. The strong Cabibbo-Kobayashi-Maskawa (CKM) suppression factor $R_{CKM}\approx λ^4 (\barρ^2 + \barη^2) \approx 3\times 10^{-4}$ results in the great difference of the branching ratios for the decays with $D_0^*$ and $\bar{D}_0^*$ as the intermediate states. The ratio $R_{\bar{D}_0^{*0}}$ between the decays $B^0 \to \bar{D}_0^{*0} K^0\to D^-π^+K^0$ and $B^0 \to \bar{D}_0^{*0}π^0 \to D^-π^+π^0$ is about $0.091^{+0.003}_{-0.005}$, consistent with the flavour-$SU$(3) symmetry result. The ratio for the branching fractions is found to be $1.10^{+0.05}_{-0.02}$ between $\mathcal{B}(B_s^0\to D_0^{*+}K^-\to D^0π^+K^-)$ and $\mathcal{B}(B^0\to D_0^{*+} π^-\to D^0π^+ π^-)$ and to be $1.03^{+0.06}_{-0.07}$ between $\mathcal{B}(B_s^0\to\bar{D}_0^{*0} \bar{K}^0\to D^-π^+ \bar{K}^0)$ and $2\mathcal{B}(B^0\to \bar{D}_0^{*0}π^0\to D^-π^+π^0)$. The predictions in this work can be tested by the future experiments.

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arXiv2016

Probing the R-parity violating supersymmetric effects in the exclusive b\to c\ell^-\barν_\ell decays

Motivated by recent results from the LHCb, BABAR and Belle collaborations on B\to D^{(*)}\ell^-\barν_\ell decays, which significantly deviate from the Standard Model and hint the possible new physics beyond the Standard Model, we probe the R-parity violating supersymmetric effects in B^-_c\to \ell^-\barν_\ell and B\to D^{(*)}\ell^-\barν_\ell decays. We find that (i) \mathcal{B}(B^-_c\to e^- \barν_e) and \mathcal{B}(B^-_c\toμ^-\barν_μ) are sensitive to the constrained slepton exchange couplings; (ii) the normalized forward-backward asymmetries of B\to De^-\barν_{e} decays have been greatly affected by the constrained slepton exchange couplings, and their signs could be changed; (iii) all relevant observables in the exclusive b\to cτ^-\barν_τdecays and the ratios \mathcal{R}(D^{(*)}) are sensitive to the slepton exchange coupling, \mathcal{R}(D^*) could be enhanced by the constrained slepton exchange coupling to reach each 95\% confidence level experimental range from BABAR, Belle and LHCb, but it could not reach the lower limit of the 95\% confidence level experimental average. Our results in this work could be used to probe R-parity violating effects, and will correlate with searches for direct supersymmetric signals at the running LHCb and the forthcoming Belle-II.

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arXiv2015

The $B\to D^{(*)} lν_l$ decays in the pQCD approach with the Lattice QCD input

In this paper, we studied the semileptonic decays $B \to D^{(*)} l^- \barν_l$ by using the "pQCD+Lattice QCD" method. We made the extrapolation for the six relevant form factors by using the input values obtained from the pQCD factorization approach in the low $q^2$ region of $0\leq q^2 \leq m_τ^2$, and the Lattice QCD input at the end-point $q^2=q^2_{\rm max}$. We then calculated the ratios $R(D)$ and $R(D^*)$ of the branching ratios ${\cal B}(B \to D^{(*)} l^- \barν_l)$, and found numerically that (1) the "pQCD+Lattice QCD" predictions for the branching ratios ${\cal B}(B \to D^{(*)} l^-\barν_l)$ agree well with the measured values within one standard deviation, and (2) the "pQCD+Lattice QCD" predictions for the ratios $R(D^{(*)})$ are $ R(D)=0.337^{+0.038}_{-0.037}$ and $ R(D^*)=0.269^{+0.021}_{-0.020}$, they agree with the data within $2σ$ deviation, in other words, one can explain the "$R(D^{(*)})$-puzzle" in the framework of the standard model.

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arXiv2014

Decays $D^+_{(s)}\to π(K)^{+}\ell^+\ell^-$ and $D^0\to \ell^+\ell^-$ in the MSSM with and without R-parity

We study the rare decays $D^+\to π^{+}\ell^+\ell^-$, $D^+_s\to K^{+}\ell^+\ell^-$ and $D^0\to \ell^+\ell^-(\ell=e,μ)$ in the minimal supersymmetic standard model with and without R-parity. Using the strong constraints on relevant supersymmetric parameters from $D^0-\bar{D}^0$ mixing and $K^+\to π^+ν\barν$ decay, we examine constrained supersymmetry contributions to relevant branching ratios, direct CP violations and ratios of $D^+_{(s)}\to π(K)^{+}μ^+μ^-$ and $D^+_{(s)}\to π(K)^{+}e^+e^-$ decay rates. We find that both R-parity conserving LR as well as RL mass insertions and R-parity violating squark exchange couplings have huge effects on the direct CP violations of $D^+_{(s)}\to π(K)^{+}\ell^+\ell^-$, moreover, the constrained LR and RL mass insertions still have obvious effects on the ratios of $D^+_{(s)}\to π(K)^{+}μ^+μ^-$ and $D^+_{(s)}\to π(K)^{+}e^+e^-$ decay rates. The direct CP asymmetries and the ratios of $D^+_{(s)}\to π(K)^{+}μ^+μ^-$ and $D^+_{(s)}\to π(K)^{+}e^+e^-$ decay rates are very sensitive to both moduli and phases of relevant supersymmetric parameters. In addition, the differential direct CP asymmetries of $D^+_{(s)}\to π(K)^{+}\ell^+\ell^-$ are studied in detail.

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arXiv2014

$\bar{B}^0_s \to (π^0 η^{()}, η^{()}η^{(*)})$ decays and the effects of next-to-leading order contributions in the perturbative QCD approach

In this paper, we calculate the branching ratios and CP violating asymmetries of the five $\bar{B}^0_s \to (π^0η^{(*)},η^{(*)}η^{(*)})$ decays, by employing the perturbative QCD (pQCD) factorization approach and with the inclusion of all currently known next-to-leading order (NLO) contributions. We find that (a) the NLO contributions can provide about 100% enhancements to the LO pQCD predictions for the decay rates of $\bar{B}_s^0 \to ηη^\prime$ and $η^\prime η^\prime$ decays, but result in small changes to $Br(\bar{B}_s \to π^0 η^{(*)})$ and $Br(\bar{B}_s \to ηη)$; (b) the newly known NLO twist-2 and twist-3 contributions to the relevant form factors can provide about 10% enhancements to the decay rates of the considered decays; (c) for $\bar{B}_s \to π^0 η^{(*)}$ decays, their direct CP-violating asymmetries $\cala_f^{dir}$ could be enhanced significantly by the inclusion of the NLO contributions; and (d) the pQCD predictions for $Br(\bar{B}_s \to ηη^{(*)})$ and $Br(\bar{B}_s \to η^\prime η^\prime)$ can be as large as $4\times 10^{-5}$, which may be measurable at LHCb or the forthcoming super-B experiments.

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arXiv2014

The semileptonic decays of $B/B_s$ meson in the perturbative QCD approach: A short review

In this short review, we present the current status about the theoretical and experimental studies for some important semileptonic decays of $B/B_s$ mesons. We firstly gave a brief introduction for the experimental measurements for $B/B_s \to P (l^+l^-, l^-\barν_l, ν\barν)$ decays, the BaBar's $R(D)$ and $R(D^*)$ anomaly, the $P_5^\prime$ deviation for $B^0 \to K^{*0} μ^+ μ^-$ decay. We then made a careful discussion about the evaluations for the relevant form factors in the light-cone QCD sum rule (LCSRs), the heavy quark effective theory, and the perturbative QCD factorization approach. By using the form factors calculated in the perturbative (pQCD) approach, we then calculate and show the pQCD predictions for the decay rates of many semileptonic decays of $B/B_s$ mesons. We also made careful phenomenological analysis for these pQCD predictions and found, in general, the following points: (a) For all the considered $B/B_s$ semileptonic decays, the next-to-leading order (NLO) pQCD predictions for their decay rates agree well with the data and those from other different theoretical methods; (b) For $R(D)$ and $R(D^*)$, the pQCD predictions agree very well with the data, the BaBar's anomaly of $R(D^{(*)})$ are therefore explained successfully in the standard model by employing the pQCD approach; and (c) We defined several new ratios $R_D^{l,τ}$ and $R_{D_s}^{l,τ}$, they may be more sensitive to the QCD dynamics which controls the $B/B_s \to (D^{(*)},D_s^{(*)})$ transitions than the old ratios, we therefore strongly suggest LHCb and the forthcoming Super-B experiments to measure these new ratios.

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arXiv2014

$B\to ππ$ decays and effects of the next-to-leading order contributions

In this paper we perform a systematic study for the three $B \to (π^+π^-,π^+π^0,π^0π^0)$ decays in the perturbative QCD (pQCD) factorization approach with the inclusion of all currently known next-to-leading order (NLO) contributions from various sources. We found that (a) for the CP-averaged decay rates $Br(B^0\to π^+π^-)$ and $Br(B^+\to π^+π^0)$, the NLO pQCD predictions agree with the data within one standard dviation; (b) for $Br(B^0\to π^0π^0)$, however, although the NLO contributions can provide a $\sim 100\%$ enhancement to the leading order (LO) result, it is still not large enough to interpret the data; (c) for the CP-violating asymmetries of $B^0\to π^+π^-$ decay, the central values of the NLO PQCD predictions agree with the data; and (d) we also examined the relative strength of the LO and NLO contributions from different sources.

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arXiv2014

RPV SUSY effects in $τ^- \to e^-(μ^-) K\bar{K}$ Decays

In this paper, we investigate $τ^- \to e^-(μ^-) K\bar{K}(K\bar{K}=K ^+K^-,K^0\bar{K}^0)$ decays in the framework of the RPV SUSY model. We discuss the tree level contribution of the sparticles $\tildeν$ and $\tilde{u}$ to these decay branching ratios. In the two channels, the $\tildeν$-mediated channel is more sensitive to the parameter product $|λ^{'*}_{i22}λ_{i31(2)}|$ than the $\tilde{u}$-mediated channel to $|λ^{'*}_{1(2)j2}λ'_{3j2}|$. And the parameter product $|λ^{'*}_{i22}λ_{i31(2)}|$ is severely constrained to the order of ${\cal O}(10^{-5})$ by the experiment data with $m_{\tildeν}=100 GeV$, which is one order of magnitude more stringent than before. In the calculation of hadronic matrix elements, the resonant effects are large than those of non-resonant terms. Especially, the resonant contribution of scalar meson $f_{(980)}$ plays a dominate role in $\tildeν$-mediated channel.

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arXiv2014

The NLO twist-3 contributions to $B \to π$ form factors in $k_{T}$ factorization

In this paper, we calculate the next-to-leading-order (NLO) twist-3 contribution to the form factors of $B \to π$ transitions by employing the $k_{T}$ factorization theorem. All the infrared divergences regulated by the logarithms $\ln(k_{iT}^{2})$ cancel between those from the quark diagrams and from the effective diagrams for the initial $B$ meson wave function and the final pion meson wave function. An infrared finite NLO hard kernel is therefore obtained, which confirms the application of the $k_{T}$ factorization theorem to $B$ meson semileptonic decays at twist-3 level. From our analytical and numerical evaluations, we find that the NLO twist-3 contributions to the form factors $f^{+,0}(q^2)$ of $B \to π$ transition are similar in size, but have an opposite sign with the NLO twist-2 contribution, which leads to a large cancelation between these two NLO parts. For the case of $f^+(0)$, for example, the $24\%$ NLO twist-2 enhancement to the full LO prediction is largely canceled by the negative ( about $-17\%$ ) NLO twist-3 contribution, leaving a small and stable $7\%$ enhancement to the full LO prediction in the whole range of $0\leq q^2\leq 12$ GeV$^2$. At the full NLO level, the perturbative QCD prediction is $F^{B \to π}(0)=0.269^{+0.054}_{-0.050}$. We also studied the possible effects on the pQCD predictions when different sets of the B meson and pion distribution amplitudes are used in the numerical evaluation.

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arXiv2014

The NLO twist-3 contribution to the pion electromagnetic form factors in $k_{T}$ factorization

In this paper, by employing the $k_{T}$ factorization theorem, we calculate firstly the next-to-leading-order (NLO) twist-3 contributions to the pion electromagnetic form factors in the $πγ^* \to π$ process. From the analytical and numerical calculations we find the following points: (a) For the leading order (LO) twist-2, twist-3 and the NLO twist-2 contributions, our results agree very well with those obtained in previous works; (b) We extract out two factors $F^{(1)}_{\rm T3}(x_i,t,Q^2)$ and $\ov{F}^{(1)}_{\rm T3}(x_i,t,Q^2)$, which describe directly the NLO twist-3 contributions to the pion electromagnetic form factors $F^+(Q^2)$; (c) The NLO twist-3 contribution is negative in sign and cancel partially with the NLO twist-2 part, the total NLO contribution can therefore provide a roughly $\pm 20\%$ corrections to the total LO contribution in the considered ranges of $Q^2$; and (d) The theoretical predictions for $Q^2 F^+(Q^2)$ in the low-$Q^2$ region agree well with currently available data, this agreement can be improved by the inclusion of the NLO contributions.

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arXiv2014

Semileptonic decays $B \to D^{(*)} lν$ in the perturbative QCD factorization approach

In this paper, we study the $B \to D^{(*)} l^- \barν_{\rm l}$ semileptonic decays and calculate the branching ratios ${\cal B}(B \to D^{(*)} l^- \barν_{\rm l})$ and the ratios $R(D^{(*)})$ and $R_{\rm D}^{\rm l,τ}$ by employing the perturbative QCD (pQCD) factorization approach. We find that (a) for $R(D)$ and $R(D^*)$ ratios, the pQCD predictions are $R(D)=0.430^{+0.021}_{-0.026}$, $R(D^*)=0.301 \pm 0.013$ and agree well with BaBar's measurements of $R(D^{(*)})$; (b) for the newly defined $R_{\rm D}^{\rm l}$ and $R_{\rm D}^{\rm τ}$ ratios, the pQCD predictions are $R_{\rm D}^{\rm l} = 0.450^{+0.064}_{-0.051}$ and $R_{\rm D}^{\rm τ} =0.642^{+0.081}_{-0.070}$, which may be more sensitive to the QCD dynamics of the considered semileptonic decays than $R(D^{(*)})$ and should be tested by experimental measurements.

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arXiv2013

$B \to K \etap$ decays in the SM with fourth generation fermions

By employing the perturbative QCD (pQCD) factorization approach, we calculate the new physics contributions to the four $B \to K \etap$ decays in the Standard Model (SM) with a fourth generation of fermions (SM4), induced by the loop diagrams involving $\tp$ quark. Within the considered parameter space of the SM4 we find that (a) the next-to-leading order (NLO) pQCD predictions for the branching ratios and CP-violating asymmetries in both the SM and SM4 generally agree with the data within one standard deviation; (b) for $Br(B \to K η)$, the inclusion of the fourth generation contributions can improve the agreement between the theoretical predictions and the data effectively; (c) for $Br(B \to K \etar)$, however, the decrease due to $\tp$ loops is disfavored by the data; and (d) the new physics corrections to the CP-violating asymmetries of the considered decays are about 10% only.

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arXiv2013

Study of $\bar{B}_s^0 \to (D_s^+,D_s^{*+}) l^-\barν_l$ decays in the pQCD factorization approach

The $\bar{B}_s^0 \to D_s^{(*)+} l^- \barν_l$ semileptonic decays were calculated in the framework of the standard model (SM) by employing the perturbative QCD (pQCD) factorization approach. We defined four ratios of the branching ratios of the considered decays $R(D_s^{(*)})$ and $R_{D_s}^{l,τ}$. From the numerical results and phenomenological analysis we found that: (a) The pQCD predictions for the branching ratios $Br(\bar{B}_s^0 \to D_s^{(*)+} l^-\barν_l)$ generally agree well with the previous theoretical predictions; (b) For the four ratios, the pQCD predictions are $R(D_s)= 0.392 \pm 0.022$, $R(D_s^{*})= 0.302\pm 0.011$, $R_{D_{s}}^l=0.448^{+0.058}_{-0.041}$ and $R_{D_{s}}^τ=0.582^{+0.071}_{-0.045}$, which show a very good $SU(3)_F$ flavor symmetry with the corresponding ratios for $B\to D^{(*)} l^- \barν_l$ decays; and (c) we strongly suggest the measurements of the new ratios $R(D_s^{(*)})$ and $R_{D_{s}}^{l,τ}$ in the forthcoming Super-B experiments.

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