Dynamical study of \(T_{ss}\) systems at a chiral quark model

Since the discovery of \(T_{cc}\) by LHCb, there has been considerable interest in \(T_{cc}\) and its heavy-flavor partners. However, the study of its strange partner \(T_{ss}\) has been largely overlooked. Within the framework of the chiral quark model, we conducted a systematic study of the bound states of \(T_{ss}\) utilizing the Gaussian Expansion Method. Considering all physical channels with \(01^{+}\), including molecular and diquark structures. Our calculations revealed that upon considering the coupling between diquarks and molecular states, we identified a deep bound state with a bounding energy of 60 MeV, primarily composed of \(K K^{*}\). Using the \(^3P_0\) model, we calculated the decay width of \(K^{*}\) within the \(KK^{*}\) bound state, which is approximated as the decay width of the bound state in the \(T_{ss}\) system. The results indicate that due to the effect of binding energy, the decay width of \(K^{*}\) in \(KK^{*}\) is approximately \(3\) MeV smaller than that of \(K^{*}\) in vacuum. Additionally, resonance state calculations were performed. Utilizing the real-scaling method, we searched for possible resonance states in the \(T_{ss}\) sysytem. Due to the strong attraction in the \([K^{*}]_8[K^{*}]_8\) configuration, four resonance states were found in the vicinity of \(2.2\)-\(2.8\) GeV, predominantly featuring hidden-color structures, and their decay widths are all less than \(10\) MeV. We strongly recommend experimental efforts to search for the resonance states in the \(T_{ss}\) system predicted by our calculations.