Measurement of the absolute branching fractions for purely leptonic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>D</mml:mi><mml:mi>s</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:math> decays
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. 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, S. 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
We report new measurements of the branching fraction $\mathcal{B}({D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\ell}}^{+}\ensuremath{\nu})$, where ${\ensuremath{\ell}}^{+}$ is either ${\ensuremath{\mu}}^{+}$ or ${\ensuremath{\tau}}^{+}(\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\overline{\ensuremath{\nu}}}_{\ensuremath{\tau}})$, based on $6.32\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of electron-positron annihilation data collected by the BESIII experiment at six center-of-mass energy points between 4.178 and 4.226 GeV. Simultaneously floating the ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}$ and ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ components yields $\mathcal{B}({D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}{\ensuremath{\nu}}_{\ensuremath{\tau}})=(5.21\ifmmode\pm\else\textpm\fi{}0.25\ifmmode\pm\else\textpm\fi{}0.17)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$, $\mathcal{B}({D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}})=\phantom{\rule{0ex}{0ex}}(5.35\ifmmode\pm\else\textpm\fi{}0.13\ifmmode\pm\else\textpm\fi{}0.16)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, and the ratio of decay widths $R=\frac{\mathrm{\ensuremath{\Gamma}}({D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}{\ensuremath{\nu}}_{\ensuremath{\tau}})}{\mathrm{\ensuremath{\Gamma}}({D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}})}=9.7{3}_{\ensuremath{-}0.58}^{+0.61}\ifmmode\pm\else\textpm\fi{}0.36$, where the first uncertainties are statistical and the second systematic. No evidence of $CP$ asymmetry is observed in the decay rates ${D}_{s}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\nu}}_{\ensuremath{\mu}}$ and ${D}_{s}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\nu}}_{\ensuremath{\tau}}$: ${A}_{CP}({\ensuremath{\mu}}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\nu})=(\ensuremath{-}1.2\ifmmode\pm\else\textpm\fi{}2.5\ifmmode\pm\else\textpm\fi{}1.0)%$ and ${A}_{CP}({\ensuremath{\tau}}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\nu})=(+2.9\ifmmode\pm\else\textpm\fi{}\phantom{\rule{0ex}{0ex}}4.8\ifmmode\pm\else\textpm\fi{}1.0)%$. Constraining our measurement to the Standard Model expectation of lepton universality ($R=9.75$), we find the more precise results $\mathcal{B}({D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}{\ensuremath{\nu}}_{\ensuremath{\tau}})=(5.22\ifmmode\pm\else\textpm\fi{}0.10\ifmmode\pm\else\textpm\fi{}0.14)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ and ${A}_{CP}({\ensuremath{\tau}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\nu}}_{\ensuremath{\tau}})=(\ensuremath{-}0.1\ifmmode\pm\else\textpm\fi{}1.9\ifmmode\pm\else\textpm\fi{}1.0)%$. Combining our results with inputs external to our analysis, we determine the $c\ensuremath{\rightarrow}\overline{s}$ quark mixing matrix element, ${D}_{s}^{+}$ decay constant, and ratio of the decay constants to be $|{V}_{cs}|=0.973\ifmmode\pm\else\textpm\fi{}0.009\ifmmode\pm\else\textpm\fi{}0.014$, ${f}_{{D}_{s}^{+}}=249.9\ifmmode\pm\else\textpm\fi{}2.4\ifmmode\pm\else\textpm\fi{}3.5\text{ }\text{ }\mathrm{MeV}$, and ${f}_{{D}_{s}^{+}}/{f}_{{D}^{+}}=1.232\ifmmode\pm\else\textpm\fi{}0.035$, respectively.