Reanalysis of the $Z_c(4020)$, $Z_c(4025)$, $Z(4050)$ and $Z(4250)$ as tetraquark states with QCD sum rules

Abstract: In this article, we calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion, and study the $C\gamma_\mu-C\gamma_\nu$ type scalar, axial-vector and tensor tetraquark states in details with the QCD sum rules. In calculations, we use the formula $\mu=\sqrt{M^2_{X/Y/Z}-(2{\mathbb{M}}_c)^2}$ to determine the energy scales of the QCD spectral densities. The predictions $M_{J=2} =\left(4.02^{+0.09}_{-0.09}\right)\,\rm{GeV}$, $M_{J=1} =\left(4.02^{+0.07}_{-0.08}\right)\,\rm{GeV}$ favor assigning the $Z_c(4020)$ and $Z_c(4025)$ as the $J^{PC}=1^{+-}$ or $2^{++}$ diquark-antidiquark type tetraquark states, while the prediction $M_{J=0}=\left(3.85^{+0.15}_{-0.09}\right)\,\rm{GeV}$ disfavors assigning the $Z(4050)$ and $Z(4250)$ as the $J^{PC}=0^{++}$ diquark-antidiquark type tetraquark states. Furthermore, we discuss the strong decays of the $0^{++}$, $1^{+-}$, $2^{++}$ diquark-antidiquark type tetraquark states in details.