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.