The hidden-charm strong decays of the Z_c states

Inspired by BESIII's measurement of the decay $Z_c(3900)^{\pm}\rightarrow \rho^{\pm}\eta_c$, 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 $R_{Z_c(3900)}=\frac{\mathcal{B}(Z_c(3900)^{\pm}\rightarrow \rho^{\pm}\eta_c)}{\mathcal{B}(Z_c(3900)^{\pm}\rightarrow \pi^{\pm}J/\psi)}$ is 1.3 and 1.6 in the molecular and tetraquark scenarios respectively, which is roughly consistent with the experimental data $R^{\mathrm{exp}}=2.2\pm0.9$. (ii) The ratios $\frac{\Gamma[Z_c(3900)\rightarrow \rho\eta_c]}{\Gamma[Z_c(4020)\rightarrow \rho\eta_c]}$ and $\frac{\Gamma[Z_c(3900)\rightarrow \pi J/\psi]}{\Gamma[Z_c(4020)\rightarrow \pi J/\psi]}$ 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 $D^{(*)}{\bar D}^{(*)}$ hadronic interactions.