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

Inspired by BESIII's measurement of the decay $Z_c(3900)^{\pm}\rightarrow ρ^{\pm}η_c$, we calculate the branching fraction ratio between the $ρη_c$ and $πJ/ψ$ 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 $R_{Z_c(3900)}=\frac{\mathcal{B}(Z_c(3900)^{\pm}\rightarrow ρ^{\pm}η_c)}{\mathcal{B}(Z_c(3900)^{\pm}\rightarrow π^{\pm}J/ψ)}$ 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 $\frac{Γ[Z_c(3900)\rightarrow ρη_c]}{Γ[Z_c(4020)\rightarrow ρη_c]}$ and $\frac{Γ[Z_c(3900)\rightarrow πJ/ψ]}{Γ[Z_c(4020)\rightarrow πJ/ψ]}$ 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 $πJ/ψ$ 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.