Fully strange tetraquark resonant states as the cousins of X (6900)

We conduct systematic calculations of the S-wave fully strange systems with ``normal" (J^P C=0^++, 1^+-, 2^++) and ``exotic" (J^P C=0^+-, 1^++, 2^+-) C-parities, which are the strange analogue of the fully charmed tetraquark state X (6900). Within a constituent quark potential model, we employ the Gaussian expansion method to solve the four-body Schr\"odinger equation and the complex scaling method to identify resonant states. We obtain a series of resonant states and zero-width states in the mass range of 2. 7 to 3. 3 GeV, with their widths ranging from less than 1 MeV to about 50 MeV. Their rms radii strongly indicate that they are compact tetraquark states. Among these states, the T₄ₒ, ₂^++ (2714) may be the most likely one to be observed experimentally. We urge the experimental exploration of the 2^++ s s s s state around 2. 7 GeV in the channel. Since the lowest S-wave s s s s state is around 2. 7 GeV, the compact P-wave s s s s states are expected to be heavier. Hence, (2170) and X (2370) are unlikely to be compact tetraquark states.