Based on $10.64~\mathrm{ fb}^{ -1}$ of $e^+e^-$ collision data taken at center-of-mass energies between 4.237 and 4.699 GeV with the BESIII detector, we study the leptonic $D^+_s$ decays using the $e^+e^-\to D^{ *+}_{ s} D^{ *-}_{ s}$ process. The branching fractions of $D_s^+\to\ell^+\nu_{ \ell}\,(\ell=\mu,\tau)$ are measured to be $\mathcal{ B}(D_s^+\to\mu^+\nu_\mu)=(0.547\pm0.026_{ \rm stat}\pm0.016_{ \rm syst})\%$ and $\mathcal{ B}(D_s^+\to\tau^+\nu_\tau)=(5.60\pm0.16_{ \rm stat}\pm0.20_{ \rm syst})\%$, respectively. The product of the decay constant and Cabibbo-Kobayashi-Maskawa matrix element $|V_{ cs}|$ is determined to be $f_{ D_s^+}|V_{ cs}|=(246.5\pm5.9_{ \rm stat}\pm3.6_{ \rm syst}\pm0.5_{ \rm input})_{ \mu\nu}~\mathrm{ MeV}$ and $f_{ D_s^+}|V_{ cs}|=(252.7\pm3.6_{ \rm stat}\pm4.5_{ \rm syst}\pm0.6_{ \rm input}))_{ \tau \nu}~\mathrm{ MeV}$, respectively. Taking the value of $|V_{ cs}|$ from a global fit in the Standard Model, we obtain ${ f_{ D^+_s}}=(252.8\pm6.0_{ \rm stat}\pm3.7_{ \rm syst}\pm0.6_{ \rm input})_{ \mu\nu}$ MeV and ${ f_{ D^+_s}}=(259.2\pm3.6_{ \rm stat}\pm4.5_{ \rm syst}\pm0.6_{ \rm input})_{ \tau \nu}$ MeV, respectively. Conversely, taking the value for $f_{ D_s^+}$ from the latest lattice quantum chromodynamics calculation, we obtain $|V_{ cs}| =(0.986\pm0.023_{ \rm stat}\pm0.014_{ \rm syst}\pm0.003_{ \rm input})_{ \mu\nu}$ and $|V_{ cs}| = (1.011\pm0.014_{ \rm stat}\pm0.018_{ \rm syst}\pm0.003_{ \rm input})_{ \tau \nu}$, respectively.
Categories: hep-ex hep-ph