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

Abstract

Recent high-precision $e^{+}{e}^{-}\to c\bar{c}$ data from the BESIII and Belle are highly useful to understand vector charmonium ($\psi$) pole structures and puzzling lineshapes due to the exotic hadron candidates $Y$. We thus perform a global coupled-channel analysis of most of the available data (10 two-body, 9 three-body, and 1 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 $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ cross sections are also predicted. Our model includes dozens of (quasi) two-body states that nonperturbatively couple with each other through bare $\psi$ excitations, particle-exchange, and short-range mechanisms; approximate three-body unitarity is considered. The amplitudes obtained from the fit are analytically continued to $\psi$ and $Z_c$ poles. We find $\psi$ states similar to those in the Particle Data Group listing and $Y(4320)$. Moreover, several $\psi$ 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 $D^{\ast }{\bar{D}}^{(\ast )}$ thresholds, being consistent with lattice QCD results. This work presents the first global analysis to determine $\psi$ and $Z_c$ poles, thereby paving the way to extracting detailed properties of the prominent exotic hadron candidates from data.

34 pages, 19 figures, 22 tables; (v3) more data included, short-range interactions between open-charm channels included, fits and pole values updated, detailed formalism and parameter values included; (v4) Regular-article format, inclusive cross section and ee->mumu cross section added, pole trajectories and pole compositeness added; (v5) published version, minor changes from v4

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Cited by in corpus (8)

• Two nearby states in the $X(3872)$ region: Resolving the radiative-decay ratio tension with ${\eta }_{c2}$
• The $B^{-}\to J/\psi {\eta }^{\prime }{K}^{-}$ reaction and the $Y(4710)$ and $K_0^{\ast }(1430)$ contributions
• Baryons and baryoniums in the perspective of QCD sum rules
• Cross section measurement of $e^{+}{e}^{-}\to {\pi }^0{\pi }^0\psi (3686)$ from $\sqrt{s}=$ 4.008 GeV to 4.951 GeV
• $D{\bar{D}}^{\ast }$-$\pi J/\psi$ scatterings of coupled channels for $Z_c(3900)$ channel
• Discovery of XYZ particles at the BESIII Experiment
• Unified coupled-channel description for the five near-threshold structures $\psi (3770)$, $G(3900)$, $R(3760)$, $R(3780)$ and $R(3810)$ from $e^{+}{e}^{-}$ annihilation
• Study of $e^{+}{e}^{-}\to h^{+}{h}^{-}J/\psi (h=\pi ,K,p)$ via initial-state radiation at Belle~II