The hidden-charm strong decays of the $Z_c$ states

Abstract

Inspired by BESIII's measurement of the decay $Z_c(3900{)}^{\pm }\to {\rho }^{\pm }{\eta }_c$, we calculate the branching fraction ratio between the $\rho {\eta }_c$ and $\pi J/\psi$ decay modes for the charged states $Z_c(3900)$, $Z_c(4020)$ and $Z_c(4430)$ using a quark interchange model. Our results show that (i) the ratio $R_{Z_c(3900)}=\frac{\mathcal{B}(Z_c(3900{)}^{\pm }\to {\rho }^{\pm }{\eta }_c)}{\mathcal{B}(Z_c(3900{)}^{\pm }\to {\pi }^{\pm }J/\psi )}$ is 1.3 and 1.6 in the molecular and tetraquark scenarios respectively, which is roughly consistent with the experimental data $R^{\exp }=2.2\pm 0.9$. (ii) The ratios $\frac{\Gamma [Z_c(3900)\to \rho {\eta }_c]}{\Gamma [Z_c(4020)\to \rho {\eta }_c]}$ and $\frac{\Gamma [Z_c(3900)\to \pi J/\psi ]}{\Gamma [Z_c(4020)\to \pi J/\psi ]}$ are about 12.5 and 24.2, respectively in the molecular scenario. In contrast, these ratios are about 1.2 in the tetraquark scenario. The non-observation of the $Z_c(4020)$ signal in the $\pi J/\psi$ decay mode strongly indicates that $Z_c(3900)$ and $Z_c(4020)$ are molecule-like signals which arise from the $D^{(\ast )}{\bar{D}}^{(\ast )}$ hadronic interactions.

arXiv comment9 pages, 5 fogures

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• Decay behaviors of the fully-bottom and fully-charm tetraquark states
• hidden charm decays of $X(4014)$ in a $D^{\ast }{\bar{D}}^{\ast }$ molecule scenario
• Doubly charmed hexaquarks in the diquark picture
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• Light meson emissions of the selected charmonium-like states within compact tetraquark configurations
• Investigation of the $X(4020)$ peak in the $D^{\ast }{\bar{D}}^{\ast }$ and $\pi h_c$ channels
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