\begin{document}$X(2239)$\end{document}, as well as \begin{document}$\eta(2225)$\end{document}, as a molecular state from the interaction of a baryon \begin{document}$\Lambda$\end{document} and an antibaryon \begin{document}$\bar{\Lambda}$\end{document}. With the help of effective Lagrangians, the \begin{document}$\Lambda\bar{\Lambda}$\end{document} interaction is described within the one-boson-exchange model with \begin{document}$\eta$\end{document}, \begin{document}$\eta'$\end{document}, \begin{document}$\omega$\end{document}, \begin{document}$\phi$\end{document}, and \begin{document}$\sigma$\end{document} exchanges considered. After inserting the potential kernel into the quasipotential Bethe-Salpeter equation, the bound states from the \begin{document}$\Lambda\bar{\Lambda}$\end{document} interaction can be studied by searching for the pole of the scattering amplitude. Two loosely bound states with spin parities \begin{document}$I^G(J^{PC})=0^+(0^{-+})$\end{document} and \begin{document}$0^-(1^{--})$\end{document} appear near the threshold with almost the same parameter. The \begin{document}$0^-(1^{--})$\end{document} state can be assigned to \begin{document}$X(2239)$\end{document} observed at BESIII, which is very close to the \begin{document}$\Lambda\bar{\Lambda}$\end{document} threshold. The scalar meson \begin{document}$\eta(2225)$\end{document} can be interpreted as a \begin{document}$0^+(0^{-+})$\end{document} state from the \begin{document}$\Lambda\bar{\Lambda}$\end{document} interaction. The annihilation effect is also discussed through a coupled-channel calculation plus a phenomenological optical potential. It provides large widths to two bound states produced from the \begin{document}$\Lambda\bar{\Lambda}$\end{document} interaction. The mass of the \begin{document}$1^-$\end{document} state is slightly larger than the mass of the \begin{document}$0^-$\end{document} state after including the annihilation effect, which is consistent with our assignment of these two states as \begin{document}$X(2239)$\end{document} and \begin{document}$\eta(2225)$\end{document}, respectively. The results suggest that further investigation is required to understand the structures near the \begin{document}$\Lambda\bar{\Lambda}$\end{document} threshold, such as \begin{document}$X(2239)$\end{document}, \begin{document}$\eta(2225)$\end{document}, and \begin{document}$X(2175)$\end{document}."> <inline-formula><tex-math id="M1">\begin{document}${{X(2239)}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/276bfe6e-f58d-4ead-96c0-c4819a3efc79/CPC-2020-0309_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/276bfe6e-f58d-4ead-96c0-c4819a3efc79/CPC-2020-0309_M1.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}${{\eta(2225)}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/276bfe6e-f58d-4ead-96c0-c4819a3efc79/CPC-2020-0309_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/276bfe6e-f58d-4ead-96c0-c4819a3efc79/CPC-2020-0309_M2.png"/></alternatives></inline-formula> as hidden-strange molecular states from <inline-formula><tex-math id="M3">\begin{document}${{\Lambda}}{\bar{\Lambda}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/276bfe6e-f58d-4ead-96c0-c4819a3efc79/CPC-2020-0309_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/276bfe6e-f58d-4ead-96c0-c4819a3efc79/CPC-2020-0309_M3.png"/></alternatives></inline-formula> interaction -
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