We study the tetraquark state with $I^G{J}^{PC}=0^{+}{1}^{-+}$ in the QCD sum rule. We exhaust all possible flavor structures by using a diquark-antidiquark construction and find that the flavor structure $(\overline{\mathbf{3}}\otimes \overline{\mathbf{6}})\oplus (\mathbf{6}\otimes \mathbf{3})$ is preferred. There are altogether four independent currents which have the quark contents $qs\overline{q}\overline{s}$. By using both the Shifman-Vainshtein-Zakharov sum rule and the finite energy sum rule, these currents lead to mass estimates around 1.8–2.1 GeV, where the uncertainty is due to the mixing of two single currents. Its possible decay modes are $S$-wave $b_1(1235)\eta$ and $b_1(1235){\eta }^{\prime }$, and $P$-wave $KK$, $\eta \eta$, $\eta {\eta }^{\prime }$, and ${\eta }^{\prime }{\eta }^{\prime }$, etc. The decay width is around 150 MeV through a rough estimation.

• Received 18 August 2008

DOI:https://doi.org/10.1103/PhysRevD.78.117502