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Abstract In this article, we tentatively assign the $$Z_c^\pm (3900)$$ Zc±(3900) to be the diquark–antidiquark type axialvector tetraquark state, study the hadronic coupling constants $$G_{Z_cJ/\psi \pi }, G_{Z_c\eta _c\rho }, G_{Z_cD \bar{D}^{*}}$$ GZcJ/ψπ,GZcηcρ,GZcDD¯∗ 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 $$Z_c^+(3900)\rightarrow J/\psi \pi ^+, \eta _c\rho ^+, D^+ \bar{D}^{*0}, \bar{D}^0 D^{*+}$$ Zc+(3900)→J/ψπ+,ηcρ+,D+D¯∗0,D¯0D∗+ and obtain the total width of the $$Z_c^\pm (3900)$$ Zc±(3900) . The numerical results support assigning the $$Z_c^\pm (3900)$$ Zc±(3900) to be the diquark–antidiquark type axialvector tetraquark state, and assigning the $$Z_c^\pm (3885)$$ Zc±(3885) to be the meson–meson type axialvector molecular state.