We apply the method of QCD sum rules to study the $sq\overline{s}\overline{q}$ tetraquark states with the exotic quantum number $J^{PC}=3^{-+}$, and extract mass of the lowest-lying state to be ${2.33}_{-0.16}^{+0.19}\mathrm{GeV}$. To construct the relevant tetraquark currents we need to explicitly add the covariant derivative operator. Our systematical analysis on their relevant interpolating currents indicates that (a) this state well decays into the $P$-wave $\rho \varphi /\omega \varphi$ channel but not into the $\rho f_2(1525)/\omega f_2(1525)/\varphi f_2(1270)$ channels, and (b) it well decays into the $K^{*}(892){\overline{K}}_2^{*}(1430)$ channel but not into the $P$-wave $K^{*}(892){\overline{K}}^{*}(892)$ channel.

• Received 22 November 2020
• Accepted 15 February 2021

DOI:https://doi.org/10.1103/PhysRevD.103.054006

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Published by the American Physical Society