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In this article, we tentatively assign the $Z_c^\pm(3900)$ to be thediquark-antidiquark type axialvector tetraquark state, study the hadroniccoupling constants $G_{Z_cJ/\psi\pi}$, $G_{Z_c\eta_c\rho}$, $G_{Z_cD\bar{D}^{*}}$ with the QCD sum rules in details. We take into account both theconnected and disconnected Feynman diagrams in carrying out the operatorproduct expansion, as the connected Feynman diagrams alone cannot do the work.Special attentions are paid to matching the hadron side of the correlationfunctions with the QCD side of the correlation functions to obtain solidduality, the routine can be applied to study other hadronic couplings directly.We study the two-body strong decays $Z_c^+(3900)\to J/\psi\pi^+$,$\eta_c\rho^+$, $D^+ \bar{D}^{*0}$, $\bar{D}^0 D^{*+}$ and obtain the totalwidth of the $Z_c^\pm(3900)$. The numerical results support assigning the$Z_c^\pm(3900)$ to be the diquark-antidiquark type axialvector tetraquarkstate, and assigning the $Z_c^\pm(3885)$ to be the meson-meson type axialvectormolecular state.

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