Open Access

Global coupled-channel analysis of $e^{+} e^{-} \to c \bar{c}$ processes in $\sqrt{s} = 3.75 to 4.7 GeV$

S. X. Nakamura ^1,2,3,*, X.-H. Li ^2,3, H.-P. Peng^2,3, Z.-T. Sun ¹, and X.-R. Zhou^2,3

¹Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, China
²University of Science and Technology of China, Hefei 230026, China
³State Key Laboratory of Particle Detection and Electronics, Beijing 100049, Hefei 230026, China

^*Contact author: satoshi@sdu.edu.cn

Phys. Rev. D 112, 054027 – Published 15 September, 2025

DOI: https://doi.org/10.1103/fch8-xwb8

Abstract

Recent high-precision $e^{+} e^{-} \to c \bar{c}$ data from BESIII and Belle are highly useful to understand vector charmonium ( $ψ$ ) pole structures and puzzling line shapes due to the exotic hadron candidates $Y$ . We, thus, perform a global coupled-channel analysis of most of the available data (ten two-body, nine three-body, and one four-body final states) in $\sqrt{s} = 3.75 - 4.7 GeV$ . Not only cross sections, but also invariant-mass distributions of subsystems are fitted. The $e^{+} e^{-} \to μ^{+} μ^{-}$ cross sections are also predicted. Our model includes dozens of (quasi-)two-body states that nonperturbatively couple with each other through bare $ψ$ excitations, particle-exchange, and short-range mechanisms; approximate three-body unitarity is considered. The amplitudes obtained from the fit are analytically continued to $ψ$ and $Z_{c}$ poles. We find $ψ$ states similar to those in the Particle Data Group listing and $Y (4320)$ . Moreover, several $ψ$ states, including new ones, are found close to open-charm thresholds. Trajectories and compositeness of the near-threshold poles suggest dominant hadron-molecule contents in their internal structures. Two $Z_{c}$ poles are found as virtual states $\sim 40 MeV$ below the $D^{*} {\bar{D}}^{(*)}$ thresholds, consistent with lattice QCD results. This work presents the first global analysis to determine $ψ$ and $Z_{c}$ poles, thereby paving the way to extracting detailed properties of the prominent exotic hadron candidates from data.

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Phys. Rev. D 112, 054027– Published 15 September, 2025

Vol. 112, Iss. 5 — 1 September 2025

Received 8 February 2024
Accepted 12 August 2025

DOI: https://doi.org/10.1103/fch8-xwb8

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Global coupled-channel analysis of $e^{+} e^{-} \to c \bar{c}$ processes in $\sqrt{s} = 3.75 to 4.7 GeV$

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Global coupled-channel analysis of e+e−→cc¯ processes in s=3.75 to 4.7 GeV

Abstract

Physics Subject Headings (PhySH)

Article Text

References (118)

Global coupled-channel analysis of $e^{+} e^{-} \to c \bar{c}$ processes in $\sqrt{s} = 3.75 to 4.7 GeV$