Is $Z_c(3900)$ a molecular state

TL;DR

This paper investigates whether the $Z_c(3900)$ particle is a molecular state by calculating its decay widths into various channels using the light front model, providing predictions to guide experimental verification.

Contribution

It presents the first detailed decay width calculations of $Z_c(3900)$ as a molecular state, including predictions for dominant decay modes and comparisons with alternative models.

Findings

$Z_c(3900) o J/a+pi$ is a dominant decay mode with width of a few MeV.

The decay rate to $c2s+pi$ can be larger than to $J/a+pi$.

If $Z_c(3900)$ is a molecular state, the partial width to $Dar D^*$ is small, but the $c2s+pi$ decay rate is significant.

Abstract

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 $Z_c(3900)\to J/\psi+\pi;\; \psi'+\pi;\; \eta_c+\rho$ and $D\bar D^*$ within the light front model (LFM). $Z_c(3900)\to J/\psi+\pi$ 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 $Z_c(3900)\to\psi(2s)\pi$ is even larger than $Z_c(3900)\to J/\psi\pi$. 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.