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M. Ablikim, М. Н. Ачасов, P. Adlarson, S. Ahmed, M. Albrecht, R. Aliberti, A. Amoroso, M. R. An, Q. An, X. H. Bai, Y. Bai, O. Bakina, R. Baldini Ferroli, I. Balossino, Y. Ban, K. Begzsuren, N. Berger, M. Bertani, D. Bettoni, F. Bianchi, J. Bloms, A. Bortone, I. Boyko, R. A. Briere, H. Cai, X. Cai, A. Calcaterra, G. F. Cao, N. Cao, S. A. Çetin, J. F. Chang, W. L. Chang, G. Chelkov, D. Y. Chen, G. Chen, H. S. Chen, M. L. Chen, S. J. Chen, X. R. Chen, Y. B. Chen, Z. J. Chen, W. S. Cheng, G. Cibinetto, F. Cossio, X. F. Cui, H. L. Dai, X. C. Dai, A. Dbeyssi, R. E. de Boer, D. Dedovich, Z. Y. Deng, A. Denig, I. Denysenko, M. Destefanis, F. De Mori, Y. Ding, C. Dong, J. Dong, L. Y. Dong, M. Y. Dong, X. Dong, S. X. Du, Y. L. Fan, J. Fang, S. S. Fang, Y. Fang, R. Farinelli, L. Fava, F. Feldbauer, G. Felici, C. Q. Feng, J. H. Feng, M. Fritsch, C. D. Fu, Y. Gao, Y. Gao, Y. Gao, Y. Gao, I. Garzia, P. T. Ge, C. Geng, E. Gersabeck, A. Gilman, K. Goetzen, L. Gong, W. X. Gong, W. Gradl, M. Greco, L. M. Gu, M. H. Gu, Shanqiang Gu, Y. T. Gu, C. Y. Guan, A. Q. Guo, L. B. Guo, R. P. Guo, Y. P. Guo, A. Guskov, T. T. Han, W. Y. Han
Abstract
By analyzing $6.32\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of ${e}^{+}{e}^{\ensuremath{-}}$ annihilation data collected at the center-of-mass energies between 4.178 and 4.226 GeV with the BESIII detector, we determine the branching fraction of the leptonic decay ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}{\ensuremath{\nu}}_{\ensuremath{\tau}}$, with ${\ensuremath{\tau}}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}{\overline{\ensuremath{\nu}}}_{\ensuremath{\tau}}$, to be ${\mathcal{B}}_{{D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}{\ensuremath{\nu}}_{\ensuremath{\tau}}}=(5.29\ifmmode\pm\else\textpm\fi{}{0.25}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{0.20}_{\mathrm{syst}})%$. We estimate the product of the Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{cs}|$ and the ${D}_{s}^{+}$ decay constant ${f}_{{D}_{s}^{+}}$ to be ${f}_{{D}_{s}^{+}}|{V}_{cs}|=(244.8\ifmmode\pm\else\textpm\fi{}{5.8}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{4.8}_{\mathrm{syst}})\text{ }\text{ }\mathrm{MeV}$, using the known values of the ${\ensuremath{\tau}}^{+}$ and ${D}_{s}^{+}$ masses as well as the ${D}_{s}^{+}$ lifetime, together with our branching fraction measurement. Combining the value of $|{V}_{cs}|$ obtained from a global fit in the standard model and ${f}_{{D}_{s}^{+}}$ from lattice quantum chromodynamics, we obtain ${f}_{{D}_{s}^{+}}=(251.6\ifmmode\pm\else\textpm\fi{}{5.9}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{4.9}_{\mathrm{syst}})\text{ }\text{ }\mathrm{MeV}$ and $|{V}_{cs}|=0.980\ifmmode\pm\else\textpm\fi{}{0.023}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{0.019}_{\mathrm{syst}}$. Using the branching fraction of ${\mathcal{B}}_{{D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}}=(5.35\ifmmode\pm\else\textpm\fi{}0.21)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, we obtain the ratio of the branching fractions ${\mathcal{B}}_{{D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}{\ensuremath{\nu}}_{\ensuremath{\tau}}}/{\mathcal{B}}_{{D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}}=9.89\ifmmode\pm\else\textpm\fi{}0.71$, which is consistent with the standard model prediction of lepton flavor universality.