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

TL;DR

This paper predicts the existence of fully strange tetraquark resonant states with various quantum numbers using a constituent quark model, identifying potential states near 2.7 GeV that could be observed experimentally.

Contribution

It provides the first systematic calculation of fully strange tetraquark states with both normal and exotic quantum numbers using advanced four-body methods.

Findings

Resonant states found between 2.7 and 3.3 GeV with narrow widths

The $T_{4s,2^{++}}(2714)$ state is a promising candidate for experimental detection

Compact tetraquark states are indicated by small rms radii

Abstract

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