Light tetraquark states with the exotic quantum number $J^{PC}=3^{-+}$

Abstract

We apply the method of QCD sum rules to study the $sq\bar{s}\bar{q}$ tetraquark states with the exotic quantum number $J^{PC}=3^{-+}$, and extract mass of the lowest-lying state to be $2.33_{-0.16}^{+0.19}$ 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 $K^{\ast }(892){\bar{K}}_2^{\ast }(1430)$ channel but not into the $P$-wave $K^{\ast }(892){\bar{K}}^{\ast }(892)$ channel.

Comments: 9 pages, 4 figures, to be published in PRD