$\mathcal R(3780)$ Resonance Interpreted as the $1^3D_1$-Wave Dominant State of Charmonium from Precise Measurements of the Cross Section of $e^+e^-\rightarrow$ Hadrons
Creators: name: Ablikim, M.
name: Achasov, M. N.
name: Adlarson, P.
name: Ai, X. C.
name: Aliberti, R.
name: Amoroso, A.
name: An, M. R.
name: An, Q.
name: Bai, Y.
name: Bakina, O.
name: Balossino, I.
name: Ban, Y.
name: Batozskaya, V.
name: Begzsuren, K.
name: Berger, N.
name: Berlowski, M.
name: Bertani, M.
name: Bettoni, D.
name: Bianchi, F.
name: Bianco, E.
name: Bloms, J.
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name: Cetin, S. A.
name: Chang, J. F.
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name: Chelkov, G.
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name: Chen, Chao
name: Chen, G.
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name: Fischer, K
name: Fritsch, M.
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name: Zhao, Lei
name: Zhao, Ling
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name: Zhao, Z. G.
name: Zhemchugov, A.
name: Zheng, B.
name: Zheng, J. P.
name: Zheng, W. J.
name: Zheng, Y. H.
name: Zhong, B.
name: Zhong, X.
name: Zhou, H.
name: Zhou, L. P.
name: Zhou, X.
name: Zhou, X. K.
name: Zhou, X. R.
name: Zhou, X. Y.
name: Zhu, W. J.
name: Zhu, Y. C.
name: Zhu, Z. A.
name: Zou, J. H.
name: Zu, J.
name: Collaboration, BESIII
Publisher: name: arXiv
Year: 2024
Subjects: subject: High Energy Physics - Experiment (hep-ex)
subject: FOS: Physical sciences
subject: FOS: Physical sciences

description: We report the precise measurements of the cross section of $e^+e^-\rightarrow$ hadrons at center-of-mass energies from 3.645 to 3.871 GeV. We thereby perform the most precise study of the cross sections and find a complex system composed of three resonances of $\mathcal R(3760)$, $\mathcal R(3780)$, and $\mathcal R(3810)$. For the first time, we measure the $\mathcal R(3810)$ electronic width to be $(19.4 \pm 7.4 \pm 12.1)$ eV. For the $\mathcal R(3760)$ resonance, we measure the mass to be $(3751.9\pm 3.8\pm 2.8)$ MeV/$c^2$, the total width to be $(32.8 \pm 5.8 \pm 8.7)$ MeV, and the electronic width to be $(184\pm 75\pm 86)$ eV. For the $\mathcal R(3780)$ resonance, we measure its mass to be $(3778.7\pm 0.5\pm 0.3)$ MeV/$c^2$, total width to be $(20.3 \pm 0.8 \pm 1.7)$ MeV, and electronic width to be $(265\pm 67\pm 83)$ eV. Forty-seven years ago, the $ψ(3770)$ resonance was discovered, and was subsequently interpreted as the $1^3D_1$-wave dominant state of charmonium. However, our analysis of the total-hadron cross sections indicates that the $ψ(3770)$ is not a single state, but a complex system composed of the $\mathcal R(3760)$, $\mathcal R(3780)$, and $\mathcal R(3810)$ resonances. Among these, we interpret the $\mathcal R(3780)$ is a resonance dominated by the $1^3D_1$ charmonium state.