Charmonium states in a coupled-channel model

Zi-Long Man; Cheng-Rui Shu; Yan-Rui Liu; Hong Chen

doi:10.1140/epjc/s10052-024-13132-7

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 810
https://doi.org/10.1140/epjc/s10052-024-13132-7

Regular Article - Theoretical Physics

Charmonium states in a coupled-channel model

Zi-Long Man¹^a, Cheng-Rui Shu¹, Yan-Rui Liu¹ and Hong Chen²

¹ School of Physics, Shandong University, 250100, Jinan, Shandong, China
² School of Physical Science and Technology, Southwest University, 400715, Chongqing, China

^a manzilong@mail.sdu.edu.cn

Received: 17 April 2024
Accepted: 18 July 2024
Published online: 13 August 2024

Abstract

We systematically investigate the mass spectrum and two-body open-charm strong decays of charmonium states in a coupled-channel model where the $^{3} P_{0}$ $$^3P_0$$ quark-antiquark pair creation mechanism is employed. The results of masses, mass shifts, proportions of the $c \bar{c}$ $c\bar{c}$ component, and open-charm decay widths are provided. The S-D wave mixing angles and di-electric decay widths for vector mesons are also presented. Based on our results, we find that the $ψ (3770)$ $\psi (3770)$ , $ψ (4040)$ $\psi (4040)$ , $ψ (4160)$ $\psi (4160)$ , $ψ (4360)$ $\psi (4360)$ , and $ψ (4415)$ $\psi (4415)$ can be assigned as the $1^{3} D_{1}$ $$1^3D_1$$ -, $3^{3} S_{1}$ $$3^3S_1$$ -, $2^{3} D_{1}$ $$2^3D_1$$ -, $4^{3} S_{1}$ $$4^3S_1$$ -, and $3^{3} D_{1}$ $$3^3D_1$$ -dominated charmonium states, respectively. The $ψ_{3} (3842)$ $\psi _3(3842)$ is a good candidate of the $ψ_{3} (1 D)$ $\psi _3(1D)$ charmonium state. The calculated mass and strong decay width of $χ_{c 1} (2 P)$ $\chi _{c1}(2P)$ with significant continuum contribution ( $\sim$ $\sim$ 57%) favor the charmonium interpretation for the mysterious $χ_{c 1} (3872)$ $\chi _{c1}(3872)$ . When considering the large uncertainty in the observed decay width, the possibility to assign the $χ_{c 0} (3860)$ $\chi _{c0}(3860)$ as the $χ_{c 0} (2 P)$ $\chi _{c0}(2P)$ charmonium state cannot be ruled out. One may describe well the properties of $χ_{c 2} (3930)$ $\chi _{c2}(3930)$ with the $χ_{c 2} (2 P)$ $\chi _{c2}(2P)$ charmonium. The predictions on properties of other $c \bar{c}$ $c\bar{c}$ states can be tested by future experiments.

© The Author(s) 2024

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