Using recent precise hadronic tau-decay data on the V-A spectral function, and general properties of QCD such as analyticity, the operator product expansion and chiral perturbation theory, we get accurate values for the QCD chiral order parameters L_10^r(M_rho) and C_87^r(M_rho). These two low-energy constants appear at order p^4 and p^6, respectively, in the chiral perturbation theory expansion of the V-A correlator. At order p^4 we obtain L_10^r(M_rho) = -(5.22\pm 0.06)10^{-3}. Including in the analysis the two-loop (order p^6) contributions, we get L_10^r(M_rho) = -(4.06\pm 0.39)10^{-3} and C_87^r(M_rho) = (4.89\pm 0.19)10^{-3}GeV^{-2}. In the SU(2) chiral effective theory, the corresponding low-energy coupling takes the value \overline l_5 = 13.30 \pm 0.11 at order p^4, and \overline l_5 = 12.24 \pm 0.21 at order p^6.
Analytic formulae for the one-loop order QCD corrections to the differential width of the semileptonic b decay are given with the tau polarization taken into account. Thence the polarization of tau is expressed by its energy and the invariant mass of the tau + antineutrino system. The non-perturbative corrections by Falk et al. are incorporated in the calculation.
We review current issues in exclusive semileptonic tau decays. We present the formalism of structure functions, and then discuss predictions for final states with kaons, for decays into four pions and for radiative corrections to the decay into a single pion. Implications for testing the standard model at low energies are discussed.
Recently there has been much interest in the tauonic semileptonic meson decays B -> D + tau + nu_tau and B -> D* + tau + nu_tau where one has found larger rates than what is predicted by the Standard Model. We analyze the corresponding semileptonic baryon decays Lambda_b(0) -> Lambda_c(+) + tau(-) + antinu_tau with particular emphasis on the lepton helicity flip and scalar contributions which vanish for zero lepton masses. We calculate the total rate, differential decay distributions, the longitudinal and transverse polarization of the daughter baryon Lambda_c(+) and the tau-lepton, and the le…
We put constraints on several products of R-parity violating lambda lambda' and lambda' lambda' type couplings from leptonic and semileptonic tau, B_d and B_s decays. Most of them are one to two orders of magnitude better than the existing bounds, and almost free from theoretical uncertainties. A significant improvement of these bounds can be made in high luminosity tau-charm or B factories.
Analytic formulae are given for order alpha_s perturbative QCD corrections to the double differential distribution of the tau lepton energy and the invariant mass of the tau + antineutrino system in semileptonic decays of the bottom quark. The corresponding distribution for B meson decays are obtained by combining these results and the nonperturbative QCD corrections calculated by Falk et al. The moments of the energy distribution of the tau lepton are calculated.
This paper reviews recent progress of lattice gauge theory determinations of semileptonic B and D decay form factors. These determinations are important in extracting the remaining CKM matrix elements.
I present an update on the electroweak radiative correction factor to semileptonic tau decays, including a next-to-leading order resummation of large logarithms. My result differs both qualitatively and quantitatively from the one recently obtained by Davier et al. As two consequences, (i) the discrepancy between the predictions for the muon g-2 based on tau decay data and electron-positron annihilation data increases, and (ii) the g-2 prediction based on tau decay data appears to be consistent (within about one standard deviation) with the experimental result from BNL.
We report on the Lattice determination of the semileptonic form factors by lattice QCD. Comparison with the light-cone QCD sum rules are made for $\Btopi, \Btorho$ semileptonic decays.
The leading order contribution to the direct CP asymmetry in tau^{+/-} -> K^{+/-} pi^0 nu_{tau} decay rates is evaluated within the Standard Model. The weak phase required for CP violation is introduced through an interesting mechanism involving second order weak interactions, which is also responsible for tiny violations of the Delta S= Delta Q rule in K_{l3} decays. The calculated CP asymmetry turns out to be of order 10^{-12}, leaving a large window for studying effects of non-standard sources of CP violation in this observable.
In this lecture I present a pedagogical introduction to the low-energy phenomenology of light flavors. The renormalization scheme freedom in defining QCD parameters is discussed. It is shown in some details how one can extract an accurate numerical value for the strong coupling constant from the tau-lepton decay rate into hadrons. As a related topic I discuss some peculiarities of definition of the quark mass in theories with confinement and describe the strange quark mass determination from data on tau-lepton decays employing contour resummation which is a modern technique of the precision an…
Semileptonic decays of polarized $τ$ leptons are investigated. The most general angular distribution of three meson final states ($τ\rightarrow ππν,\,Kπν,\, πππν,\\ \,Kππν,\, KKπν,\, KKKν,\, ηππν,\,\ldots{}$) is discussed. It is shown, that the most general distribution can be characterized by 16 structure functions, most of which can be determined in currently ongoing high statistics experiments. Emphasis is put on $τ$ decays in $e^{+}e^{-}$ experiments where the neutrino escapes detection and the $τ$ rest frame cannot be reconstructed. The structure of the hadronic matrix elements, based on …
We summarize selected up-to-date results related to semileptonic $B$ meson decays, namely results on the exclusive determination of the parameter $|V_{cb}|$ of the CKM matrix, on the inclusive determination of $|V_{ub}|$, and on $R(D^{(*)})$.
The QCD corrections to the moments of the invariant mass distribution in the semileptonic $τ$ decays are considered. The effect of the renormalization scheme dependence on the fitted values of alpha_s(m^2_tau) and the condensates is discussed, using a simplified approach where the nonperturbative contributions are approximated by the dimension six condensates. The fits in the vector and the axial-vector channel are investigated in the next-to-leading and the next-to-next-to-leading order. The next-to-next-to-leading order results are found to be relatively stable with respect to change of the …
The evaluation, systematic analysis and numerical study of the semileptonic $τ$-lepton decays with two mesons in the final state has been made in the frame of the standard model extended by right handed neutrinos. In the analysis, heavy-neutrino nondecoupling effects, finite quark masses, quark and meson mixings, finite widths of vector mesons, chiral symmetry breakings in vector-meson--pseudoscalar-meson vertices and effective Higgs-boson--pseudoscalar-meson couplings have been included. Numerical estimates reveal that the decays $τ^-\to e^-π^-π^+$, $τ^-\to e^-K^-K^+$ and $τ^-\to e^-K^0\bar{K…
Generalized structure functions in semileptonic tau decays
Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional（墨西哥国立理工学院高级研究中心）；Universidad de Castilla-La Mancha（卡斯蒂利亚-拉曼恰大学）；Universitat de València — Consejo Superior de Investigaciones Científicas（瓦伦西亚大学—西班牙国家研究委员会）
The determinations of |V_{cb}| and |V_{ub}| from inclusive semileptonic B decays are reviewed. A comparison of the light-cone approach with the heavy quark expansion approach is made. The perspective for further improvement of the |V_{cb}| and |V_{ub}| determinations is discussed.
We briefly summarize up-to-date results on the determination of the parameters of the Cabibbo-Kobayashi-Maskawa matrix $|V_{cb}|$ and $|V_{ub}|$, which play an important role in the unitarity triangle and in testing the Standard Model, and recent results on semileptonic $B$ meson decays involving a $τ$ lepton.
By using a constituent quark model we compute the form factors relevant to semileptonic transitions of B mesons into low-lying p-wave charmed mesons. We evaluate the q^2 dependence of these form factors and compare them with other model calculations. The Isgur-Wise functions tau(1/2) and tau(3/2) are also obtained in the heavy quark limit of our results.
We propose a model independent method to determine $|V_{ub}|$ from the energy spectrum of the charged lepton in inclusive semileptonic $B$ decays. The method includes perturbative QCD corrections as well as nonperturbative ones.
The hadronic mass distribution in semileptonic B-meson decays can be used for extracting the charmless part and thus determining the |V_ub/V_cb| ratio. We take into account first-order perturbative as well as non-perturbative QCD corrections. The sensitivity to model assumptions is studied and an estimate of the remaining uncertainties is performed.
The most general angular distribution of two or three meson final states from semileptonic decays $τ\rightarrow ππν$, $Kπν$, $πππν$, $Kππν$, $Kπν$, $KKKν$, $ηππν,\,\ldots{}$ of polarized $τ$ leptons can be characterized by 16 structure functions. Predictions for hadronic matrix elements, based on CVC and chiral Lagrangians and their relations to the structure functions are discussed. Most of them can be determined in currently ongoing high statistics experiments. Emphasis of the kinematical analysis is firstly put on $τ$ decays in $e^{+}e^{-}$ experiments where the neutrino escapes detection a…
The perturbative QCD corrections to the semileptonic decay width of the tau lepton are evaluated in the next-next-to-leading order from the contour integral representation in various renormalization schemes, using numerical solution of the renormalization group equation for complex energies. A quantitative estimate of the ambiguities resulting from the freedom of choice of the renormalization scheme is obtained by taking into account predictions in all schemes that do not involve large cancellations in the expression for the scheme invariant combination of the expansion coefficients. The probl…
Hadronic $τ$ decays are studied as probe of new physics. We determine the dependence of several inclusive and exclusive $τ$ observables on the Wilson coefficients of the low-energy effective theory describing charged-current interactions between light quarks and leptons. The analysis includes both strange and non-strange decay channels. The main result is the likelihood function for the Wilson coefficients in the tau sector, based on the up-to-date experimental measurements and state-of-the-art theoretical techniques. The likelihood can be readily combined with inputs from other low-energy pre…
Since the degree of polarization of the vector particle in semileptonic decay strongly influences the decay width of the particles, it can be used as a measure of CKM matrix elements. We show that |V_{cb}| can be determined from the measurement of polarization of vector meson in B,B_c --> V l nu decay, where $V$ is vector meson.
Consequences of the interference between spectator amplitudes for the lifetimes and semileptonic decay fractions of B^0 and B^+ mesons are discussed. Assuming duality and constructive interference between spectator amplitudes we are able to explain the low experimental value for the semileptonic decay fraction of $B$ mesons. Extracting these amplitudes from a fit to 11 exclusive hadronic B decay fractions we find a_1 = 1.05 +/- 0.03 +/- 0.10, a_2 =+0.227 +/ 0.012 +/- 0.022, an inclusive semileptonic decay fraction of (11.2 +/- 0.5 +/- 1.7), and a lifetime ratio tau(B^+) / tau(B^0) = 0.83 +/- 0…
In this work we study the Lepton Flavour Violating semileptonic $τ$ decays: 1) $τ\to μPP$ with $PP= π^+π^-, π^0π^0, K^+K^-, K^0 {\bar K}^0$; 2) $τ\to μP$ with $P=π^0, η, η'$ and 3) $τ\to μV$ with $V = ρ^0, ϕ$. We work within the context of two constrained MSSM scenarios: the CMSSM and NUHM. A full one-(SUSY)loop computation is presented and the importance of the various contributions, the $γ$-, $Z$-, and Higgs bosons mediated ones are analysed. The hadronization of quark bilinears is performed within the chiral framework. Some discrepancies in the predicted rates for BR($τ\to μη$), BR($τ\to μη…
Motivated by the recent investigation of neutrinoless $τ$-lepton decays by the CLEO collaboration, we perform a systematic analysis of such decays in a possible new-physics scenario with heavy Dirac/Majorana neutrinos, including heavy-neutrino nondecoupling effects, finite quark masses, and quark as well as meson mixings. We find that $τ$-lepton decays into an electron or muon and a pseudoscalar or vector meson can have branching ratios close to the experimental sensitivity. Numerical estimates show that the predominant decay modes of this kind are $τ^-\to e^-ϕ$, $τ^-\to e^-ρ^0$, and $τ^-\to e…
The effects of spectator light quark in decays of heavy mesons are considered, which vanish in the limit of factorization of matrix elements of four-quark operators over the mesons. These effects include the difference of the total widths as well as of the semileptonic decay rates between the D^0 and D_s mesons and also a contribution to inclusive semileptonic decay rates of B^0 and B^\pm into the channel X_u l nu related to determination of the weak mixing parameter V_{ub}. If the observed difference of the lifetimes between D_s and D^0 mesons is attributed to non-factorizable terms, such ter…
We analyze the numerical determination of the quark mixing factor V(us) from hyperon semileptonic decays. The discrepancies between the results obtained in two previous studies are clarified. Our fits indicate sizeable SU(3) breaking corrections, which unfortunately can only be fully determined from the data at the first order. The lack of a reliable theoretical calculation of second-order symmetry breaking effects translates into a large systematic uncertainty, which has not been taken into account previously. Our final result, V(us) = 0.226 +/- 0.005, is not competitive with the existing det…
Perturbative and nonperturbative QCD corrections to semileptonic B decay rates are calculated and given in analytical and numerical forms. We present the analytic expression for the double distribution in hadronic mass and electron energy in B to X(u) e nu_e decays through one loop order of QCD. We then study the leading twist corrections to that quantity within the formalism of HQET and employ it in a proposed method of measuring V_ub with an accuracy of 10%. Our other point of interest is the polarisation of the tau lepton in B to X(c) tau nu_tau processes. Analytic formulae are given for th…
We reduce the perturbative uncertainty in the determination of |V_{ub}| from inclusive semileptonic B decays by calculating the rate of B -> X_u l nu events with dilepton invariant mass q^2>(M_B-M_D)^2 at subleading order in the hybrid expansion, and to next-to-leading order in renormalization-group improved perturbation theory. We also resum logarithmic corrections to the leading power-suppressed contributions. Studying the effect of different b-quark mass definitions we find that the branching ratio after the cut is Br(B -> X_u l nu)=(20.9+-4.0)|V_{ub}|^2, where the dominant error is due to …
In a recent paper, eight semileptonic parameters were defined to specify the most general Lorentz-invariant spin correlation functions for tau semileptonic decays. The parameters were physically defined in terms of tau-decay partial-width intensities for polarized final states. This paper studies how these parameters can be simply measured at a tau/charm factory with longitudinally polarized beams without using spin-correlation techniques. Thereby the parameters can also be used to bound the effective-mass scales $ Λ$ for ``new physics" such as arising from lepton compositeness, leptonic CP vi…
We demonstrate that polarization measurements in exclusive semileptonic B decays are powerful tools for unraveling non-standard model sources of T-violation. Measurements of the transverse polarization of the tau lepton in the B to D tau nu and B to D* tau nu decays probe separately effective scalar and pseudoscalar CP-violating four-Fermi interactions, whereas the D* polarization in the B to D* l nu (l=e,mu) decay is sensitive to an effective right-handed quark current interaction. Two T-odd polarization structures exist involving the D* polarization and they can be isolated and studied separ…
Use of semi-leptonic decays has become standard in constraining the Unitarity Triangle. Bearing in mind that precise calculations of these are very challenging, we propose an entirely new approach. In particular the |Vcb| + epsilon_K constraint, which depends extremely sensitively on Vcb in the traditional method, is replaced by the interplay between epsilon_K, BR(B ->tau nu) and Delta M_Bs. It is found that even in this method tensions with the Standard Model persist at the ~1.8 sigma level. Furthermore, improvements on the B -> tau nu branching ratio and on the lattice determination of f_Bs …
Semileptonic $B$ meson decays into the four lightest excited charmed meson states ($D_0^*$, $D_1^*$, $D_1$, and $D_2^*$) and their counterparts with $s$ quarks are investigated, including the full lepton mass dependence. We derive the standard model predictions for the differential branching fractions, as well as predictions for the ratios of the semi-tauonic and light lepton semileptonic branching fractions. These can be systematically improved using future measurements of the total or differential semileptonic rates to $e$ and $μ$, as well as the two-body hadronic branching fractions with a …
The possibility to test the unitarity triangle of CKM matrix is examined by using the semileptonic rare $B$ decays, $B \rightarrow X_q \, ł^+ \, ł^-$ with $q = d, s$ and $ł$'s are leptons. The discussion is emphasized on the CP asymmetry in the framework of standard and beyond the standard models. For the beyond standard model, a minimal extension of the standard model containing an additional isosinglet charge (-1/3) charge quark, which leads to a deviation from CKM unitarity, is considered. As the results, in the standard model the CP asymmetry is visible only for $B \rightarrow X_d \, ł^+ \…
The determination of |Vub| from inclusive semileptonic B decays is limited by uncertainties in modelling the decay distributions in b->ulnu transitions. The largest uncertainties arise from the limited knowledge of the appropriate b quark mass and Fermi momentum to use in the parameterization of the shape function. This paper presents a new method in which these shape function parameters are constrained by the same data used to measure |Vub|. The method requires measurements of the momenta of both the charged lepton and the neutrino in semileptonic B decays. From these quantities two complemen…
We estimate the heavy quark effective theory parameter λ_1 from inclusive semileptonic B-meson decay spectrum. By using recent CLEO double lepton tagging data of B -> X e nu, which shows the lepton momentum as low as 0.6 GeV, we extracted λ_1 \sim -0.58 GeV^2. We also derived \barΛ\sim 0.46 GeV and |V_{cb}| = 0.041 \pm 0.002.
We report on the determination of $|V_{cb}|$ from the comparison of the semileptonic inclusive decay rates of B-- and D--mesons using the heavy quark symmetry of QCD. While the renormalization scale ambiguity does not allow for a reliable estimate of the quark masses, it almost cancels in the prediction for $|V_{cb}|$, which reads $|V_{cb}|(τ_B/1.49\,{\rm ps})^{1/2} = 0.036\pm 0.005$, where the error stems from the uncertainty in the kinetic energy of the heavy quark inside the meson, in the experimental branching ratios, in QCD input parameters, and from scale uncertainties. This talk is base…
We consider the leptonic and semileptonic (SL) lepton flavour violating (LFV) decays of the charged leptons in the minimal supersymmetric standard model (MSSM). The formalism for evaluation of branching fractions for the SL LFV charged-lepton decays with one or two pseudoscalar mesons, or one vector meson in the final state, is given. Previous amplitudes for the SL LFV charged-lepton decays in MSSM are improved, for instance the $γ$-penguin amplitude is corrected to assure the gauge invariance. The decays are studied not only in the model-independent formulation of the theory in the frame of M…
We present a lattice quantum chromodynamics determination of the ratio of the scalar and vector form factors for two semileptonic decays of the $B_s$ meson: $B_s \rightarrow K \ell ν$ and $B_s \rightarrow D_s \ell ν$. In conjunction with future experimental data, our results for these correlated form factors will provide a new method to extract $|V_{ub}/V_{cb}|$, which may elucidate the current tension between exclusive and inclusive determinations of these Cabibbo-Kobayashi-Maskawa mixing matrix parameters. In addition to the form factor results, we determine the ratio of the differential dec…
Precision tests of the CKM mechanism and searches for new physics in the flavour sector require dedicated QCD calculations of decay widths and spectra. Significant progress has been achieved in recent years in computing inclusive B decay spectra into light energetic partons. I briefly review different theoretical approaches to this problem focusing on the determination of |V_{ub}| from inclusive semileptonic decays and show that this determination is robust. The largest uncertainty is associated with the value of the b quark mass. Finally I present new numerical results in the DGE resummation-…
We present a new theoretical framework for the study of $B\to X_u \ell ν$ decays, which includes all known perturbative and non-perturbative contributions and a description of leading and subleading Fermi motion effects. The perturbative and non-perturbative regimes are separated by a ``hard'' Wilsonian cutoff $μ\sim 1$ GeV. We bring into focus some problems related to the high $q^2$ region and to Weak Annihilation effects. We provide estimates of the CKM parameter $|V_{ub}|$ using the described framework and discuss the related theoretical uncertainty.
We study the success to describe hyperon semileptonic decays of four models that incorporate second-order SU(3) symmetry breaking corrections. The criteria to assess their success is by determining V_{us} in each of the three relevant hyperon semileptonic decays and comparing the values obtained with one another and also with the one that comes from K_{l3} decays. A strong dependence on the particular symmetry breaking model is observed. Values of V_{us} which do not agree with the one of K_{l3} are generally obtained. However, in the context of chiral perturbation theory, only the model whose…
We calculate the kaon semileptonic form factor $f_+(0)$ from lattice QCD, working, for the first time, at the physical light-quark masses. We use gauge configurations generated by the MILC collaboration with $N_f=2+1+1$ flavors of sea quarks, which incorporate the effects of dynamical charm quarks as well as those of up, down, and strange. We employ data at three lattice spacings to extrapolate to the continuum limit. Our result, $f_+(0) = 0.9704(32)$, where the error is the total statistical plus systematic uncertainty added in quadrature, is the most precise determination to date. Combining …
Precise theoretical predictions derived from the Standard Model are a key ingredient in searches for new physics in the flavor sector. The large mass and long lifetime of the $b$ quark make processes involving $b$ quarks of particular interest. We use lattice simulations to perform nonperturbative QCD calculations for semileptonic $B_{(s)}$ decays. We present results from our determinations of $B_s\to D_s \ell ν$ and $B_s\to K \ell ν$ semileptonic form factors and provide an outlook for our $B\to π\ellν$ calculation. In addition we discuss the determination of $R$-ratios testing lepton-flavor …
We calculate the form factor f_+(q^2) for B-meson semileptonic decay in unquenched lattice QCD with 2+1 flavors of light sea quarks. We use Asqtad-improved staggered light quarks and a Fermilab bottom quark on gauge configurations generated by the MILC Collaboration. We simulate with several light quark masses and at two lattice spacings, and extrapolate to the physical quark mass and continuum limit using heavy-light meson staggered chiral perturbation theory. We then fit the lattice result for f_+(q^2) simultaneously with that measured by the BABAR experiment using a parameterization of the …
We present a lattice QCD determination of the vector and scalar form factors of the kaon semileptonic decay $K \to π\ell ν$, which is relevant for the determination of the CKM matrix element $|V_{us}|$ from experimental data. Our results are based on the gauge configurations produced by the European Twisted Mass Collaboration with Nf = 2+1+1 dynamical fermions. We simulated at three different values of the lattice spacing and with pion masses as small as 210 MeV. Our estimate for the vector form factor at zero 4-momentum transfer is $f_+(0) = 0.9709 (46)$, where the uncertainty is both statist…
This note emphasizes that due to isospin violation the two central states in the octet mix, and this mixing can be measured in semileptonic decays, in particular with an accurate determination of the sigma plus semileptonic branching ratio.
The two most precise determinations of the CKM matrix element V_us are based on the analyses of leptonic and semileptonic kaon decays. These studies also rely on the lattice QCD calculations of two hadronic parameters, namely the ratio of the kaon and pion decay constants, f_K+/f_pi+, and the kaon semileptonic vector form factor at zero momentum transfer, f_+(0). In this talk, I review the recent lattice results for these quantities, by showing that the sub-percent accuracy required by the phenomenological analyses has been reached by lattice QCD. As best estimates of the lattice calculations …
The paper gives the polarization of the tau lepton in the semileptonic B decays with respect to the direction of the virtual W boson. The result is given including the nonperturbative HQET corrections.The perturbative QCD corrections are probably negligible as suggested by the existing results for the longitudinal polarization of the charged lepton (Jezabek and Urban, 1998).
In the Standard Model, scalar contributions to leptonic and semileptonic decays are helicity suppressed. The hypothesis of additional physical neutral/charged Higgses can enhance such scalar contributions and give detectable effects especially in B physics. For the charged Higgs, experimental information on both Br(B -> D tau nu) and Br(B -> tau nu) has already become available and in particular the B -> D tau nu branching ratio measurements will be further improved in the coming years. Hadronic uncertainties of scalar contributions in semileptonic decays are already in much better shape than …
We update and compare the capabilities of the purely leptonic mode B --> tau nu and the semileptonic mode B --> D tau nu in the search for a charged Higgs boson.
We study the triple differential distribution of B-> Xu l nu, consistently including all perturbative and non-perturbative effects through O(alphas^2 beta_0) and O(1/mb^3). The Fermi motion is parameterized in terms of a single light-cone function for each structure function and for any value of q^2, accounting for all subleading effects. We discuss the problems and uncertainties related to the high-q^2 tail and to Weak Annihilation effects. We work in the kinetic scheme, a framework characterized by a Wilsonian treatment with a hard cutoff mu ~ 1GeV. Our method is illustrated with the extract…
We calculate the electron spectrum of semileptonic decays of B-mesons into non-charmed hadrons. The shape of the spectrum obtained from QCD sum rules is in general agreement with quark model calculations. At high electron energies the decrease of the spectrum is less steep than predicted by Altarelli et al. Our analysis yields a total decay rate $Γ(B\to X_u e\barν) = (6.8\pm 2.0) 10^{13} |V_{ub}|^2 {s}^{-1}$. For the spectrum integrated over electron energies in the interval $2.4{ GeV}\leq E_e \leq 2.6\mbox{\ GeV}$ in the laboratory frame we obtain $Γ(B\to X_u e \barν)= (5.0\pm 1.6) 10^{12} |V…
By analyzing all existing measurements for $ D\rightarrow K \ell^+ ν_{\ell} $ ( $\ell=e,\ μ$ ) decays, we find that the determinations of both the vector form factor $f_+^K(q^2)$ and scalar form factor $f_0^K(q^2)$ for semileptonic $D\rightarrow K$ decays from these measurements are feasible. By taking the parameterization of the one order series expansion of the $f_+^K(q^2)$ and $f_0^K(q^2)$, $f_+^K(0)|V_{cs}|$ is determined to be $0.7182\pm0.0029$, and the shape parameters of $f_+^K(q^2)$ and $f_0^K(q^2)$ are $r_{+1}=-2.16\pm0.007$ and $r_{01}=0.89\pm3.27$, respectively. Combining with the a…
