The $X(2239)$ and $\eta(2225)$ as hidden-strange molecular states from $\Lambda\bar{\Lambda}$ interaction

In this work, we propose a possibility to assign the newly observed $X(2239)$, as well as the $\eta(2225)$, as a molecular state from the interaction of a baryon $\Lambda$ and antibaryon $\bar{\Lambda}$. With the help of the effective Lagrangians, the $\Lambda\bar{\Lambda}$ interaction is described within the one-boson-exchange model with $\eta$, $\eta'$, $\omega$, $\phi$, and $\sigma$ exchanges considered. After inserting the interaction potential kernel into the quasipotential Bethe-Salpeter equation, the bound states from the $\Lambda\bar{\Lambda}$ interaction can be found by searching for the pole of scattering amplitude. Two loosely bound states appears near the threshold with spin parities $J^P=0^-$ and $1^-$ with almost the same parameter. The $1^-$ state can be assigned into the $X(2239)$ observed at BESIII, which is very close to the $\Lambda\bar{\Lambda}$ threshold. The scalar meson $\eta(2225)$ can be interpreted as a $0^-$ state from the $\Lambda\bar{\Lambda}$ interaction. The results suggest further investigation is needed to understand the internal structure of $X(2239)$, $\eta(2225)$, and $X(2175)$.