Abstract
The \( {D}_s^{+}\to {K}^{+}{K}^{-}{\mu}^{+}{\nu}_{\mu } \) decay is studied based on 7.33 fb−1 of e+e− collision data collected with the BESIII detector at center-of-mass energies in the range from 4.128 to 4.226 GeV. The absolute branching fraction is measured as \( \mathcal{B}\left({D}_s^{+}\to \phi {\mu}^{+}{\nu}_{\mu}\right)=\left(2.25\pm 0.09\pm 0.07\right)\times {10}^{-2} \), the most precise measurement to date. Combining with the world average of \( \mathcal{B}\left({D}_s^{+}\to \phi {e}^{+}{\nu}_e\right) \), the ratio of the branching fractions obtained is \( \frac{\mathcal{B}\left({D}_s^{+}\to \phi {\mu}^{+}{\nu}_{\mu}\right)}{\mathcal{B}\left({D}_s^{+}\to \phi {e}^{+}{\nu}_e\right)}=0.94\pm 0.08 \), in agreement with lepton universality. By performing a partial wave analysis, the hadronic form factor ratios at q2 = 0 are extracted, finding \( {r}_V=\frac{V(0)}{A_1(0)}=1.58\pm 0.17\pm 0.02 \) and \( {r}_2=\frac{A_2(0)}{A_1(0)}=0.71\pm 0.14\pm 0.02 \), where the first uncertainties are statistical and the second are systematic. No significant S-wave contribution from f0(980) → K+K− is found. The upper limit \( \mathcal{B}\left({D}_s^{+}\to {f}_0(980){\mu}^{+}{\nu}_{\mu}\right)\cdot \mathcal{B}\left({f}_0(980)\to {K}^{+}{K}^{-}\right)<5.45\times {10}^{-4} \) is set at 90% credibility level.
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Acknowledgments
The BESIII collaboration thanks the staff of BEPCII and the IHEP computing center for their strong support. The authors thank Prof. Yao Yu for helpful discussions. This work is supported in part by National Key R&D Program of China under Contracts Nos. 2020YFA0406400, 2020YFA0406300; National Natural Science Foundation of China (NSFC) under Contracts Nos. 11805037, 11635010, 11735014, 11835012, 11935015, 11935016, 11935018, 11961141012, 12022510, 12025502, 12035009, 12035013, 12061131003, 12192260, 12192261, 12192262, 12192263, 12192264, 12192265, 12221005, 12225509, 12235017; Guangdong Basic and Applied Basic Research Foundation under Grant No. 2023A1515010121; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; Joint Large-Scale Scientific Facility Funds of the NSFC and CAS under Contracts No. U2032104; the CAS Center for Excellence in Particle Physics (CCEPP); CAS Key Research Program of Frontier Sciences under Contracts Nos. QYZDJ-SSW-SLH003, QYZDJ-SSW-SLH040; 100 Talents Program of CAS; The Institute of Nuclear and Particle Physics (INPAC) and Shanghai Key Laboratory for Particle Physics and Cosmology; ERC under Contract No. 758462; European Union’s Horizon 2020 research and innovation programme under Marie Sklodowska-Curie grant agreement under Contract No. 894790; German Research Foundation DFG under Contracts Nos. 443159800, 455635585, Collaborative Research Center CRC 1044, FOR5327, GRK 2149; Istituto Nazionale di Fisica Nucleare, Italy; Ministry of Development of Turkey under Contract No. DPT2006K-120470; National Research Foundation of Korea under Contract No. NRF-2022R1A2C1092335; National Science and Technology fund of Mongolia; National Science Research and Innovation Fund (NSRF) via the Program Management Unit for Human Resources & Institutional Development, Research and Innovation of Thailand under Contract No. B16F640076; Polish National Science Centre under Contract No. 2019/35/O/ST2/02907; The Swedish Research Council; U.S. Department of Energy under Contract No. DE-FG02-05ER41374.
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The BESIII collaboration., Ablikim, M., Achasov, M.N. et al. Studies of the decay \( {\textrm{D}}_{\textrm{s}}^{+}\to {\textrm{K}}^{+}{\textrm{K}}^{-}{\mu}^{+}{\nu}_{\mu } \). J. High Energ. Phys. 2023, 72 (2023). https://doi.org/10.1007/JHEP12(2023)072
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DOI: https://doi.org/10.1007/JHEP12(2023)072