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

Abstract

We conduct systematic calculations of the S-wave fully strange systems with ``normal" $\left(J^{PC}=0^{++},1^{+-},2^{++}\right)$ and ``exotic" $\left(J^{PC}=0^{+-},1^{++},2^{+-}\right)$ 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 Schrödinger 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 $T_{4s,2^{++}}(2714)$ may be the most likely one to be observed experimentally. We urge the experimental exploration of the $2^{++}$ $ss\bar{s}\bar{s}$ state around 2.7 GeV in the $\varphi \varphi$ channel. Since the lowest S-wave $ss\bar{s}\bar{s}$ state is around 2.7 GeV, the compact P-wave $ss\bar{s}\bar{s}$ states are expected to be heavier. Hence, $\varphi (2170)$ and $X(2370)$ are unlikely to be compact tetraquark states.

9 pages, 2 figures. Comments are welcomed

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