Measurement of the branching fraction of $D_s^+\to \tau^+ \nu_{\tau}$
via $\tau^+ \to \mu^+ \nu_{\mu}\bar{\nu_{\tau}}$
BESIII Collaboration,M. Ablikim,M. N. Achasov,P. Adlarson,R. Aliberti,A. Amoroso,M. R. An,Q. An,Y. Bai,O. Bakina,I. Balossino,Y. Ban,V. Batozskaya,K. Begzsuren,N. Berger,M. Bertani,D. Bettoni,F. Bianchi,E. Bianco,J. Bloms,A. Bortone,I. Boyko,R. A. Briere,A. Brueggemann,H. Cai,X. Cai,A. Calcaterra,G. F. Cao,N. Cao,S. A. Cetin,J. F. Chang,T. T. Chang,W. L. Chang,G. R. Che,G. Chelkov,C. Chen,Chao Chen,G. Chen,H. S. Chen,M. L. Chen,S. J. Chen,S. M. Chen,T. Chen,X. R. Chen,X. T. Chen,Y. B. Chen,Y. Q. Chen,Z. J. Chen,W. S. Cheng,S. K. Choi,X. Chu,G. Cibinetto,S. C. Coen,F. Cossio,J. J. Cui,H. L. Dai,J. P. Dai,A. Dbeyssi,R. E. de Boer,D. Dedovich,Z. Y. Deng,A. Denig,I. Denysenko,M. Destefanis,F. De Mori,B. Ding,X. X. Ding,Y. Ding,J. Dong,L. Y. Dong,M. Y. Dong,X. Dong,S. X. Du,Z. H. Duan,P. Egorov,Y. L. Fan,J. Fang,S. S. Fang,W. X. Fang,Y. Fang,R. Farinelli,L. Fava,F. Feldbauer,G. Felici,C. Q. Feng,J. H. Feng,K Fischer,M. Fritsch,C. Fritzsch,C. D. Fu,Y. W. Fu,H. Gao,Y. N. Gao,Yang Gao,S. Garbolino,I. Garzia,P. T. Ge,Z. W. Ge,C. Geng,E. M. Gersabeck,A Gilman,K. Goetzen,L. Gong,W. X. Gong,W. Gradl,S. Gramigna,M. Greco,M. H. Gu,Y. T. Gu,C. Y Guan,Z. L. Guan,A. Q. Guo,L. B. Guo,R. P. Guo,Y. P. Guo,A. Guskov,X. T. H.,W. Y. Han,X. Q. Hao,F. A. Harris,K. K. He,K. L. He,F. H. Heinsius,C. H. Heinz,Y. K. Heng,C. Herold,T. Holtmann,P. C. Hong,G. Y. Hou,Y. R. Hou,Z. L. Hou,H. M. Hu,J. F. Hu,T. Hu,Y. Hu,G. S. Huang,K. X. Huang,L. Q. Huang,X. T. Huang,Y. P. Huang,T. Hussain,N Hüsken,W. Imoehl,M. Irshad,J. Jackson,S. Jaeger,S. Janchiv,J. H. Jeong,Q. Ji,Q. P. Ji,X. B. Ji,X. L. Ji,Y. Y. Ji,Z. K. Jia,P. C. Jiang,S. S. Jiang,T. J. Jiang,X. S. Jiang,Y. Jiang,J. B. Jiao,Z. Jiao,S. Jin,Y. Jin,M. Q. Jing,T. Johansson,X. K.,S. Kabana,N. Kalantar-Nayestanaki,X. L. Kang,X. S. Kang,R. Kappert,M. Kavatsyuk,B. C. Ke,A. Khoukaz,R. Kiuchi,R. Kliemt,L. Koch,O. B. Kolcu,B. Kopf,M. Kuessner,A. Kupsc,W. Kühn,J. J. Lane,J. S. Lange,P. Larin,A. Lavania,L. Lavezzi,T. T. Lei,Z. H. Lei,H. Leithoff,M. Lellmann,T. Lenz,C. Li,C. H. Li,Cheng Li,D. M. Li,F. Li,G. Li,H. Li,H. B. Li,H. J. Li,H. N. Li,Hui Li,J. R. Li,J. S. Li,J. W. Li,Ke Li,L. J Li,L. K. Li,Lei Li,M. H. Li,P. R. Li,S. X. Li,T. Li,W. D. Li,W. G. Li,X. H. Li,X. L. Li,Xiaoyu Li,Y. G. Li,Z. J. Li,Z. X. Li,Z. Y. Li,C. Liang,H. Liang,Y. F. Liang,Y. T. Liang,G. R. Liao,L. Z. Liao,J. Libby,A. Limphirat,D. X. Lin,T. Lin,B. J. Liu,B. X. Liu,C. Liu,C. X. Liu,D. Liu,F. H. Liu,Fang Liu,Feng Liu,G. M. Liu,H. Liu,H. B. Liu,H. M. Liu,Huanhuan Liu,Huihui Liu,J. B. Liu,J. L. Liu,J. Y. Liu,K. Liu,K. Y. Liu,Ke Liu,L. Liu,L. C. Liu,Lu Liu,M. H. Liu,P. L. Liu,Q. Liu,S. B. Liu,T. Liu,W. K. Liu,W. M. Liu,X. Liu,Y. Liu,Y. B. Liu,Z. A. Liu,Z. Q. Liu,X. C. Lou,F. X. Lu,H. J. Lu,J. G. Lu,X. L. Lu,Y. Lu,Y. P. Lu,Z. H. Lu,C. L. Luo,M. X. Luo,T. Luo,X. L. Luo,X. R. Lyu,Y. F. Lyu,F. C. Ma,H. L. Ma,J. L. Ma,L. L. Ma,M. M. Ma,Q. M. Ma,R. Q. Ma,R. T. Ma,X. Y. Ma,Y. Ma,F. E. Maas,M. Maggiora,S. Maldaner,S. Malde,A. Mangoni,Y. J. Mao,Z. P. Mao,S. Marcello,Z. X. Meng,J. G. Messchendorp,G. Mezzadri,H. Miao,T. J. Min,R. E. Mitchell,X. H. Mo,N. Yu. Muchnoi,Y. Nefedov,F. Nerling,I. B. Nikolaev,Z. Ning,S. Nisar,Y. Niu,S. L. Olsen,Q. Ouyang,S. Pacetti,X. Pan,Y. Pan,A. Pathak,Y. P. Pei,M. Pelizaeus,H. P. Peng,K. Peters,J. L. Ping,R. G. Ping,S. Plura,S. Pogodin,V. Prasad,F. Z. Qi,H. Qi,H. R. Qi,M. Qi,T. Y. Qi,S. Qian,W. B. Qian,C. F. Qiao,J. J. Qin,L. Q. Qin,X. P. Qin,X. S. Qin,Z. H. Qin,J. F. Qiu,S. Q. Qu,C. F. Redmer,K. J. Ren,A. Rivetti,V. Rodin,M. Rolo,G. Rong,Ch. Rosner,S. N. Ruan,N. Salone,A. Sarantsev,Y. Schelhaas,K. Schoenning,M. Scodeggio,K. Y. Shan,W. Shan,X. Y. Shan,J. F. Shangguan,L. G. Shao,M. Shao,C. P. Shen,H. F. Shen,W. H. Shen,X. Y. Shen,B. A. Shi,H. C. Shi,J. Y. Shi,Q. Q. Shi,R. S. Shi,X. Shi,J. J. Song,T. Z. Song,W. M. Song,Y. X. Song,S. Sosio,S. Spataro,F. Stieler,Y. J. Su,G. B. Sun,G. X. Sun,H. Sun,H. K. Sun,J. F. Sun,K. Sun,L. Sun,S. S. Sun,T. Sun,W. Y. Sun,Y. Sun,Y. J. Sun,Y. Z. Sun,Z. T. Sun,Y. X. Tan,C. J. Tang,G. Y. Tang,J. Tang,Y. A. Tang,L. Y Tao,Q. T. Tao,M. Tat,J. X. Teng,V. Thoren,W. H. Tian,Y. Tian,Z. F. Tian,I. Uman,B. Wang,B. L. Wang,Bo Wang,C. W. Wang,D. Y. Wang,F. Wang,H. J. Wang,H. P. Wang,K. Wang,L. L. Wang,M. Wang,Meng Wang,S. Wang,T. Wang,T. J. Wang,W. Wang,W. H. Wang,W. P. Wang,X. Wang,X. F. Wang,X. J. Wang,X. L. Wang,Y. Wang,Y. D. Wang,Y. F. Wang,Y. H. Wang,Y. N. Wang,Y. Q. Wang,Yaqian Wang,Yi Wang,Z. Wang,Z. L. Wang,Z. Y. Wang,Ziyi Wang,D. Wei,D. H. Wei,F. Weidner,S. P. Wen,C. W. Wenzel,U. Wiedner,G. Wilkinson,M. Wolke,L. Wollenberg,C. Wu,J. F. Wu,L. H. Wu,L. J. Wu,X. Wu,X. H. Wu,Y. Wu,Y. J Wu,Z. Wu,L. Xia,X. M. Xian,T. Xiang,D. Xiao,G. Y. Xiao,H. Xiao,S. Y. Xiao,Y. L. Xiao,Z. J. Xiao,C. Xie,X. H. Xie,Y. Xie,Y. G. Xie,Y. H. Xie,Z. P. Xie,T. Y. Xing,C. F. Xu,C. J. Xu,G. F. Xu,H. Y. Xu,Q. J. Xu,W. L. Xu,X. P. Xu,Y. C. Xu,Z. P. Xu,F. Yan,L. Yan,W. B. Yan,W. C. Yan,X. Q Yan,H. J. Yang,H. L. Yang,H. X. Yang,Tao Yang,Y. Yang,Y. F. Yang,Y. X. Yang,Yifan Yang,M. Ye,M. H. Ye,J. H. Yin,Z. Y. You,B. X. Yu,C. X. Yu,G. Yu,T. Yu,X. D. Yu,C. Z. Yuan,L. Yuan,S. C. Yuan,X. Q. Yuan,Y. Yuan,Z. Y. Yuan,C. X. Yue,A. A. Zafar,F. R. Zeng,X. Zeng,Y. Zeng,Y. J. Zeng,X. Y. Zhai,Y. H. Zhan,A. Q. Zhang,B. L. Zhang,B. X. Zhang,D. H. Zhang,G. Y. Zhang,H. Zhang,H. H. Zhang,H. Q. Zhang,H. Y. Zhang,J. J. Zhang,J. L. Zhang,J. Q. Zhang,J. W. Zhang,J. X. Zhang,J. Y. Zhang,J. Z. Zhang,Jiawei Zhang,L. M. Zhang,L. Q. Zhang,Lei Zhang,P. Zhang,Q. Y. Zhang,Shuihan Zhang,Shulei Zhang,X. D. Zhang,X. M. Zhang,X. Y. Zhang,Y. Zhang,Y. T. Zhang,Y. H. Zhang,Yan Zhang,Yao Zhang,Z. H. Zhang,Z. L. Zhang,Z. Y. Zhang,G. Zhao,J. Zhao,J. Y. Zhao,J. Z. Zhao,Lei Zhao,Ling Zhao,M. G. Zhao,S. J. Zhao,Y. B. Zhao,Y. X. Zhao,Z. G. Zhao,A. Zhemchugov,B. Zheng,J. P. Zheng,W. J. Zheng,Y. H. Zheng,B. Zhong,X. Zhong,H. Zhou,L. P. Zhou,X. Zhou,X. K. Zhou,X. R. Zhou,X. Y. Zhou,Y. Z. Zhou,J. Zhu,K. Zhu,K. J. Zhu,L. Zhu,L. X. Zhu,S. H. Zhu,S. Q. Zhu,T. J. Zhu,W. J. Zhu,Y. C. Zhu,Z. A. Zhu,J. H. Zou,J. Zu
arxiv（2023）
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摘要
Utilizing $7.33~\mathrm{fb}^{-1}$ of $e^+e^-$ collision data taken at the center-of-mass energies of 4.128, 4.157, 4.178, 4.189, 4.199, 4.209, 4.219, and 4.226 GeV with the BESIII detector, the branching fraction of the leptonic decay $D_s^+\to\tau^+\nu_\tau$ via $\tau^+\to\mu^+\nu_\mu\bar \nu_\tau$ is measured to be $\mathcal{B}_{D_s^+\to\tau^+\nu_\tau}=(5.34\pm0.16_{\rm stat}\pm0.10_{\rm syst})\%$. Combining this branching fraction with the world averages of the measurements of the masses of $\tau^+$ and $D_s^+$ as well as the lifetime of $D_s^+$, we extract the product of the decay constant of $D_s^+$ and the $c\to s$ Cabibbo-Kobayashi-Maskawa matrix element to be $f_{D_s^+}|V_{cs}|=(246.2\pm3.7_{\rm stat}\pm2.5_{\rm syst})~\mathrm{MeV}$. Taking $|V_{cs}|$ from a global fit in the standard model we obtain $f_{D_s^+}=(252.7\pm3.8_{\rm stat}\pm2.6_{\rm syst})$ MeV. Conversely, taking $f_{D_s^+}$ from lattice quantum chromodynamics calculations, we obtain $|V_{cs}| = 0.984\pm0.015_{\rm stat}\pm0.010_{\rm syst}$.
