$S$- and $P$-wave fully-strange tetraquark states from QCD sum rules

We apply the QCD sum rule method to systematically study the $S$- and $P$-wave fully-strange tetraquark states within the diquark-antidiquark picture. We systematically construct their interpolating currents by explicitly adding the covariant derivative operator. Our results suggest that the $f_0(2100)$, $X(2063)$, and $f_2(2010)$ may be explained as the $S$-wave $s s \bar s \bar s$ tetraquark states with the quantum numbers $J^{PC} = 0^{++}$, $1^{+-}$, and $2^{++}$, respectively. Our results also suggest that both the $X(2370)$ and $X(2500)$ may be explained as the $P$-wave $s s \bar s \bar s$ tetraquark states of $J^{PC} = 0^{-+}$, and both the $\phi(2170)$ and $X(2400)$ may be explained as the $P$-wave $s s \bar s \bar s$ tetraquark states of $J^{PC} = 1^{--}$. The masses of the $s s \bar s \bar s$ tetraquark states with the exotic quantum number $J^{PC} = 1^{-+}$ are extracted from two non-correlated currents to be $2.45^{+0.20}_{-0.25}$ GeV and $2.49^{+0.21}_{-0.25}$ GeV.