Tetraquark state candidates: $Y(4260)$, $Y(4360)$, $Y(4660)$ and $Z_c(4020\mathrm{/}4025)$

In this article, we construct the axialvector-diquark-axialvector-antidiquark type tensor current to interpolate both the vector and axialvector tetraquark states, then calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion, and obtain the QCD sum rules for both the vector and axialvector tetraquark states. The numerical results support assigning the $Z_c(4020\mathrm{/}4025)$ to be the $J^{PC}=1^{+-}$ diquark-antidiquark type tetraquark state, and assigning the $Y(4660)$ to be the $J^{PC}=1^{--}$ diquark-antidiquark type tetraquark state. Furthermore, we take the $Y(4260)$ and $Y(4360)$ as the mixed charmonium-tetraquark states, and construct the two-quark-tetraquark type tensor currents to study the masses and pole residues. The numerical results support assigning the $Y(4260)$ and $Y(4360)$ to be the mixed charmonium-tetraquark states.