Fully-strange tetraquark $ss\bar{s}\bar{s}$ spectrum and possible experimental evidence

In this work, we construct 36 tetraquark configurations for the $1S$-, $1P$-, and $2S$-wave states, and make a prediction of the mass spectrum for the tetraquark $ss\overline{s}\overline{s}$ system in the framework of a nonrelativistic potential quark model without the diquark-antidiquark approximation. The model parameters are well determined by our previous study of the strangeonium spectrum. We find that the resonances ${f}_{0}(2200)$ and ${f}_{2}(2340)$ may favor the assignments of ground states ${T}_{(ss\overline{s}\overline{s}){0}^{++}}(2218)$ and ${T}_{(ss\overline{s}\overline{s}){2}^{++}}(2378)$, respectively, and the newly observed $X(2500)$ at BESIII may be a candidate of the lowest mass $1P$-wave ${0}^{\ensuremath{-}+}$ state ${T}_{(ss\overline{s}\overline{s}){0}^{\ensuremath{-}+}}(2481)$. Signals for the other ${0}^{++}$ ground state ${T}_{(ss\overline{s}\overline{s}){0}^{++}}(2440)$ may also have been observed in the $\ensuremath{\phi}\ensuremath{\phi}$ invariant mass spectrum in $J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\phi}\ensuremath{\phi}$ at BESIII. The masses of the ${J}^{PC}={1}^{\ensuremath{-}\ensuremath{-}}$ ${T}_{ss\overline{s}\overline{s}}$ states are predicted to be in the range of $\ensuremath{\sim}2.44--2.99\text{ }\text{ }\mathrm{GeV}$, which indicates that the $\ensuremath{\phi}(2170)$ resonance may not be a good candidate of the ${T}_{ss\overline{s}\overline{s}}$ state. This study may provide a useful guidance for searching for the ${T}_{ss\overline{s}\overline{s}}$ states in experiments.