Is Zc(3900) a molecular state?

Assuming the newly observed Zc(3900) to be a molecular state of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$D\bar{D}^{*}(D^{*} \bar{D})$\end{document}, we calculate the partial widths of Zc(3900)→J/ψ+π; ψ′+π; ηc+ρ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$D\bar{D}^{*}$\end{document} within the light-front model (LFM). Zc(3900)→J/ψ+π is the channel by which Zc(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 Zb and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$Z_{b}'$\end{document}, Voloshin suggested that there should be a resonance \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$Z_{c}'$\end{document} at 4030 MeV, which can be a molecular state of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$D^{*}\bar{D}^{*}$\end{document}. Then we go on calculating its decay rates to all the aforementioned final states and the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$D^{*}\bar{D}^{*}$\end{document} as well. It is found that if Zc(3900) is a molecular state of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${1\over\sqrt{2}}(D\bar{D}^{*}+D^{*}\bar{D})$\end{document}, the partial width of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$Z_{c}(3900)\to D\bar{D}^{*}$\end{document} is rather small, but the rate of Zc(3900)→ψ(2s)π is even larger than Zc(3900)→J/ψπ. The implications are discussed and it is indicated that with the luminosity of BES and BELLE, the experiments may finally determine if Zc(3900) is a molecular state or a tetraquark.