The recoil corrections, correlation functions and possible double-strange hadronic molecules

In this work, we perform a systematic investigation of ${K}^{(*)}{K}^{(*)}$ interactions within a one-boson-exchange model.The framework incorporates both $S-D$ wave mixing and coupled-channel effects, with effective potentials retained up to order $\mathcal{O}(1/M^2)$. By solving the coupled channel Schr\"{o}dinger equations, we can predict two double-strange molecular candidates: a $KK^*$ molecule with $I(J^P)=0(1^+)$ and a $K^*K^*$ molecule with $0(1^+)$. Our results also show that the recoil corrections play a crucial role in the formation of these two molecular candidates. Furthermore, the $S-D$ wave mixing effects contribute positively to the formation process. As a byproduct of this analysis, we extend our study to $K^{(*)}\bar{K}^{(*)}$ interactions with the same model. Our findings suggest that the $K\bar{K}^{*}$ states with $0(1^{+-}, 1^{++})$ and $K^{*}\bar{K}^{*}$ states with $0(0^{++}, 1^{+-}, 2^{++})$ can be promising molecular candidates. Additionally, we analyze the correlations between the constituent mesons, the resulting correlation functions provide additional support for our predictions of both double-strange and strangonium-like molecular states.