Fully-strange tetraquarks: fall-apart decays and experimental candidates

We presents a systematic analysis of the fall-apart decays for the $1S$, $1P$, and $2S$-wave fully-strange tetraquark states. It shows that most of the fully-strange tetraquark states have a relatively narrow fall-apart decay width of $\mathcal{O}(10)$ MeV. The newly observed axial-vector state $X(2300)$ at BESIII may favor the low-lying $1S$-wave $1^{+-}$ state $T_{(4s)1^{+-}}(2323)$, while the $X(2500)$ resonance observed in the earlier BESIII experiment may favor the low-lying $1P$-wave $0^{-+}$ state $T_{(4s)0^{-+}}(2481)$. Some fully-strange tetraquark states predicted in theory can be searched for in their dominant fall-apart decay channels in experiment, such as $\phi\phi$, $\phi\phi(1680)$, $\eta^{(\prime)}\phi$, $\eta^{(\prime)}h_1(1415)$, and $\phi f_2^{\prime}(1525)$, to which they have relatively large couplings.