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

Abstract

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 $ss\bar{s}\bar{s}$ 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 $ss\bar{s}\bar{s}$ tetraquark states of $J^{PC}=0^{-+}$, and both the $\varphi (2170)$ and $X(2400)$ may be explained as the $P$-wave $ss\bar{s}\bar{s}$ tetraquark states of $J^{PC}=1^{--}$. The masses of the $ss\bar{s}\bar{s}$ tetraquark states with the exotic quantum number $J^{PC}=1^{-+}$ are extracted from two non-correlated currents to be $2.45_{-0.25}^{+0.20}$ GeV and $2.49_{-0.25}^{+0.21}$ GeV.

Comments: 20 pages, 6 figures, 2 tables, revised version to be published in PRD