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

Abstract

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 $\Lambda \bar{\Lambda }{(}^3{S}_1)$ and $\Lambda \bar{\Lambda }{(}^1{S}_0)$ respectively. We consider the effective potential from the pseudoscalar $\eta$-exchange and ${\eta }^{{}^{\prime }}$-exchange, the scalar $\sigma$-exchange, and the vector $\omega$-exchange and $\varphi$-exchange. The $\eta$ and ${\eta }^{{}^{\prime }}$ 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 (${\Lambda }_{\omega }$) and least sensitively on that of the $\varphi$-exchange (${\Lambda }_{\varphi }$). Our result suggests the possible interpretation of Y(2175) and $\eta (2225)$ as the bound states of $\Lambda \bar{\Lambda }{(}^3{S}_1)$ and $\Lambda \bar{\Lambda }{(}^1{S}_0)$ respectively.