The scalar and pseudoscalar hidden-charm tetraquark states with QCD sum rules

Based on the diquark configuration, we construct the diquark-antidiquark interpolating tetraquark currents with $J^{PC}=1^{-\pm }$ and $1^{+\pm }$, which can couple to the scalar and pseudoscalar tetraquark states respectively, since they are not conserved currents. Then we investigate their two-point correlation functions including the contributions of the vacuum condensates up to dimension-10 and extract the masses and pole residues of the tetraquark states with $J^{PC}=0^{+\pm }$ and $0^{-\pm }$ through the QCD sum rule approach. The predicted masses can be confronted with the experimental data in the future. Moreover, we briefly discuss the possible decay patterns of the tetraquark states.