Study on decays of $Z_c(4020)$ and $Z_c(3900)$ into $h_c+\pi$

At the invariant mass spectrum of $h_c\pi^\pm$ a new resonance $Z_c(4020)$ has been observed, however the previously confirmed $Z_c(3900)$ does not show up at this channel. In this paper we assume that $Z_c(3900)$ and $Z_c(4020)$ are molecular states of $D\bar D^*(D^{*} \bar D)$ and $D^*\bar D^*$ respectively, then we calculate the transition rates of $Z_c(3900)\to h_c+\pi$ and $Z_c(4020)\to h_c+\pi$ in the light front model. Our results show that the partial width of $Z_c(3900)\to h_c+\pi$ is only three times smaller than that of $Z_c(4020)\to h_c+\pi$. $Z_c(4020)$ seems to be a molecular state, so if $Z_c(3900)$ is also a molecular state it should be observed in the portal $e^+e^-\to h_c\pi^\pm$ as long as the database is sufficiently large, by contrary if the future more precise measurements still cannot find $Z_c(3900)$ at $h_c\pi^\pm$ channel, the molecular assignment to $Z_c(3900)$ should be ruled out.