The decay width of the $Z_c(3900)$ as an axialvector tetraquark state in solid quark-hadron duality

Abstract

In this article, we tentatively assign the $Z_c^{\pm }(3900)$ to be the diquark-antidiquark type axialvector tetraquark state, study the hadronic coupling constants $G_{Z_{c}J/\psi \pi }$, $G_{Z_c{\eta }_c\rho }$, $G_{Z_{c}D{\bar{D}}^{\ast }}$ with the QCD sum rules in details. We take into account both the connected and disconnected Feynman diagrams in carrying out the operator product expansion, as the connected Feynman diagrams alone cannot do the work. Special attentions are paid to matching the hadron side of the correlation functions with the QCD side of the correlation functions to obtain solid duality, the routine can be applied to study other hadronic couplings directly. We study the two-body strong decays $Z_c^{+}(3900)\to J/\psi {\pi }^{+}$, ${\eta }_c{\rho }^{+}$, $D^{+}{\bar{D}}^{\ast 0}$, ${\bar{D}}^0{D}^{\ast +}$ and obtain the total width of the $Z_c^{\pm }(3900)$. The numerical results support assigning the $Z_c^{\pm }(3900)$ to be the diquark-antidiquark type axialvector tetraquark state, and assigning the $Z_c^{\pm }(3885)$ to be the meson-meson type axialvector molecular state.

16 pages, 3 figures

References in corpus (3)

• Determination of spin and parity of the $Z_c(3900)$
• Analysis of the $Z(4430)$ as the first radial excitation of the $Z_c(3900)$
• Interpreting Z(3900)

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• The strange cousin of the $Z_c(4020/4025)$ as tetraquark state
• Triply-charmed hexaquark states with the QCD sum rules
• Analysis of the decay $Y(4500)\to D^{\ast }{\bar{D}}^{\ast }\pi$ with the light-cone QCD sum rules
• Analysis of the $D{\bar{D}}^{\ast }K$ system with QCD sum rules
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• Two-body strong decays of the hidden-charm tetraquark molecular states via the QCD sum rules
• Two-body strong decays of the pseudoscalar hidden-charm tetraquark states via the QCD sum rules