Fine Structure and Decays of Hidden-Strangeness Tetraquarks in the Dynamical Diquark Model

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We analyze the fine structure and ``fall-apart'' decay patterns of hidden-strangeness tetraquarks within the dynamical diquark model. Several well-established negative-parity resonances listed by the Particle Data Group (PDG) [$ϕ(2170)$, $η(2225)$, $η(2370)$] are examined as potential $q\bar q s\bar s$ tetraquark candidates using a Hamiltonian that incorporates (iso)spin-dependent, spin--orbit, and tensor interactions. We further show that the isovector resonances $ρ(2150)$ and $ρ_3(2250)$ observed by BESIII in $ψ(2S)\rightarrow K^{+}K^{-}η$ are compatible with a tetraquark assignment. Predictions for 28 states, including those with exotic quantum numbers, are also presented. Comparison of the model spectrum with the PDG's unverified ``Further States'' highlights additional promising candidates worth future experimental investigation. The predicted fall-apart decay channels are easily reconstructed by experiment and may stimulate ongoing searches for hidden-strangeness tetraquarks at GlueX and BESIII. While current data does not yet provide an unambiguous interpretation for any state in this range, the observation of the fall-apart modes, in addition to the distinct multiplet structure for tetraquark states from that of hybrids or glueballs, provides the most incisive test for discriminating state content.

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