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In this article, we take the $Z_c(3900)$ and $Z(4430)$ as the ground stateand the first radial excited state of the axial-vector tetraquark states with$J^{PC}=1^{+-}$, respectively, and study their masses and pole residues withthe QCD sum rules by calculating the contributions of the vacuum condensates upto dimension-10 in a consistent way in the operator product expansion. Thenumerical result favors assigning the $Z_c(3900)$ and $Z(4430)$ as the groundstate and first radial excited state of the axial-vector tetraquark states,respectively.

Analysis of the $Z(4430)$ as the first radial excitation of the $Z_c(3900)$