Is $Z_c(3900)$ a molecular state

Assuming the newly observed $Z_c(3900)$ to be a molecular state of $D\bar D^*(D^{*} \bar D)$, we calculate the partial widths of $Z_c(3900)\to J/ψ+π;\; ψ'+π;\; η_c+ρ$ and $D\bar D^*$ within the light front model (LFM). $Z_c(3900)\to J/ψ+π$ is the channel by which $Z_c(3900)$ was observed, our calculation indicates that it is indeed one of the dominant modes whose width can be in the range of a few MeV depending on the model parameters. Similar to $Z_b$ and $Z_b'$, Voloshin suggested that there should be a resonance $Z_c'$ at 4030 MeV which can be a molecular state of $D^*\bar D^*$. Then we go on calculating its decay rates to all the aforementioned final states and as well the $D^*\bar D^*$. It is found that if $Z_c(3900)$ is a molecular state of ${1\over\sqrt 2}(D\bar D^*+D^*\bar D)$, the partial width of $Z_c(3900)\to D\bar D^*$ is rather small, but the rate of $Z_c(3900)\toψ(2s)π$ is even larger than $Z_c(3900)\to J/ψπ$. The implications are discussed and it is indicated that with the luminosity of BES and BELLE, the experiments may finally determine if $Z_c(3900)$ is a molecular state or a tetraquark.

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