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arXiv · 2303.12927

Study of the $f_{0}(980)$ and $f_{0}(500)$ Scalar Mesons through the Decay $D_{s}^{+} \to \pi^{+} \pi^{-} e^{+} \nu_{e}$

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. Berlowski·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·J. L. Fu·Y. W. Fu·H. Gao·Y. N. Gao·Yang Gao·S. Garbolino·I. Garzia·P. T. Ge·Z. W. Ge
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Abstract

Using $e^+e^-$ collision data corresponding to an integrated luminosity of 7.33~${\rm fb^{-1}}$ recorded by the BESIII detector at center-of-mass energies between 4.128 and 4.226~${\rm GeV}$, we present an analysis of the decay $D_{s}^{+} \to \pi^{+}\pi^{-} e^{+}\nu_{e}$, where the $D_s^+$ is produced via the process $e^+e^- \to D_{s}^{*\pm}D_{s}^{\mp}$. We observe the $f_{0}(980)$ in the $\pi^+\pi^-$ system and the branching fraction of the decay $D_{s}^{+} \to f_{0}(980)e^{+}\nu_{e}$ with $f_0(980)\to\pi^+\pi^-$ measured to be $(1.72 \pm 0.13_{\rm stat} \pm 0.10_{\rm syst}) \times10^{-3}$, where the uncertainties are statistical and systematic, respectively. The dynamics of the $D_{s}^{+} \to f_{0}(980)e^{+}\nu_{e}$ decay are studied with the simple pole parametrization of the hadronic form factor and the Flatt\'e formula describing the $f_0(980)$ in the differential decay rate, and the product of the form factor $f^{f_0}_{+}(0)$ and the $c\to s$ Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ is determined for the first time to be $f^{f_0}_+(0)|V_{cs}|=0.504\pm0.017_{\rm stat}\pm0.035_{\rm syst}$. Furthermore, the decay $D^+_s\to f_0(500) e^+\nu_e$ is searched for the first time but no signal is found. The upper limit on the branching fraction of $D^+_s\to f_0(500) e^+\nu_e,~f_0(500)\to\pi^+\pi^-$ decay is set to be $3.3 \times 10^{-4}$ at 90\% confidence level.

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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. Berlowski, 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, J. L. Fu, Y. W. Fu, H. Gao, Y. N. Gao, Yang Gao, S. Garbolino, I. Garzia, P. T. Ge, Z. W. Ge. 2023-03-22. Study of the $f_{0}(980)$ and $f_{0}(500)$ Scalar Mesons through the Decay $D_{s}^{+} \to \pi^{+} \pi^{-} e^{+} \nu_{e}$. https://doi.org/10.1103/physrevlett.132.141901

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