Fully strange tetraquark ss(s)over-bar(s)over-bar 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 (s) over bar(s) over bar 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 (s) over bar(s) over bar )0++ (2218) and T(ss (s) over bar(s) over bar )2++ (2378), respectively, and the newly observed X(2500) at BESIII may be a candidate of the lowest mass 1P-wave 0(-+) state T(ss (s) over bar(s) over bar )0-+ (2481). Signals for the other 0(++) ground state T(ss (s) over bar(s) over bar )0++ (2440) may also have been observed in the phi phi invariant mass spectrum in J/psi -> gamma phi phi at BESIII. The masses of the J(PC) = 1(--) T-ss (s) over bar(s) over bar states are predicted to be in the range of similar to 2A4-2.99 GeV, which indicates that the phi(2170) resonance may not be a good candidate of the T-ss (s) over bar(s) over bar state. This study may provide a useful guidance for searching for the T-ss (s) over bar(s) over bar all states in experiments.