In this paper, we construct the axialvector and tensor current operators to investigate the ground state tetraquark states and the first radially excited tetraquark states with the quantum numbers $J^{ PC}=1^{ +-}$ via the QCD sum rules systematically, and observe that there are one axialvector tetraquark candidate for the $Z_c(3900)$ and $Z_c(4430)$, two axialvector tetraquark candidates for the $Z_c(4020)$, three axialvector tetraquark candidates for the $Z_c(4600)$.
Categories: hep-ph