The meson-exchange model for the $\mathrm{\Lambda }\bar{\mathrm{\Lambda }}$ interaction

In the present work, we apply the one-boson-exchange potential (OBEP) model to investigate the possibility of Y(2175) and $\eta (2225)$ as bound states of $\mathrm{\Lambda }\bar{\mathrm{\Lambda }}{(}^3{S}_1)$ and $\mathrm{\Lambda }\bar{\mathrm{\Lambda }}{(}^1{S}_0)$ respectively. We consider the effective potential from the pseudoscalar $\eta$-exchange and ${\eta }^{{}^{\mathrm{\prime }}}$-exchange, the scalar $\sigma$-exchange, and the vector $\omega$-exchange and $\varphi$-exchange. The $\eta$ and ${\eta }^{{}^{\mathrm{\prime }}}$ meson exchange potential is repulsive force for the state ${}^1{S}_0$ and attractive for ${}^3{S}_1$. The results depend very sensitively on the cutoff parameter of the $\omega$-exchange (${\mathrm{\Lambda }}_{\omega }$) and least sensitively on that of the $\varphi$-exchange (${\mathrm{\Lambda }}_{\varphi }$). Our result suggests the possible interpretation of Y(2175) and $\eta (2225)$ as the bound states of $\mathrm{\Lambda }\bar{\mathrm{\Lambda }}{(}^3{S}_1)$ and $\mathrm{\Lambda }\bar{\mathrm{\Lambda }}{(}^1{S}_0)$ respectively.