  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.
