Measurement of the Absolute Branching Fraction of <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:mo stretchy="false">→</mml:mo><mml:msup><mml:mi>τ</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msub><mml:mi>ν</mml:mi><mml:mi>τ</mml:mi></mml:msub></mml:math> via <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>τ</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msub><mml:mi>ν</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:msub><mml:mover accent="true"><mml:mi>ν</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mi>τ</mml:mi></mml:msub></mml:math>
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. 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
Using a dataset of $6.32\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of ${e}^{+}{e}^{\ensuremath{-}}$ annihilation data collected with the BESIII detector at center-of-mass energies between 4178 and 4226 MeV, we have measured the absolute branching fraction of the leptonic decay ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ via ${\ensuremath{\tau}}^{+}\ensuremath{\rightarrow}{e}^{+}{\ensuremath{\nu}}_{e}{\overline{\ensuremath{\nu}}}_{\ensuremath{\tau}}$, and find ${\mathcal{B}}_{{D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}{\ensuremath{\nu}}_{\ensuremath{\tau}}}=(5.27\ifmmode\pm\else\textpm\fi{}0.10\ifmmode\pm\else\textpm\fi{}0.12)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$, where the first uncertainty is statistical and the second is systematic. The precision is improved by a factor of 2 compared to the previous best measurement. Combining with ${f}_{{D}_{s}^{+}}$ from lattice quantum chromodynamics calculations or the $|{V}_{cs}|$ from the CKMfitter group, we extract $|{V}_{cs}|=0.978\ifmmode\pm\else\textpm\fi{}0.009\ifmmode\pm\else\textpm\fi{}0.012$ and ${f}_{{D}_{s}^{+}}=(251.1\ifmmode\pm\else\textpm\fi{}2.4\ifmmode\pm\else\textpm\fi{}3.0)\text{ }\text{ }\mathrm{MeV}$, respectively. Combining our result with the world averages of ${\mathcal{B}}_{{D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}{\ensuremath{\nu}}_{\ensuremath{\tau}}}$ and ${\mathcal{B}}_{{D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}}$, we obtain the ratio of the branching fractions ${\mathcal{B}}_{{D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}{\ensuremath{\nu}}_{\ensuremath{\tau}}}/{\mathcal{B}}_{{D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}}=9.72\ifmmode\pm\else\textpm\fi{}0.37$, which is consistent with the standard model prediction of lepton flavor universality.