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 $\Lambda\bar{\Lambda}(^3S_1)$ and $\Lambda\bar{\Lambda}(^1S_0)$ respectively. We consider the effective potential from the pseudoscalar $\eta$-exchange and $\eta^{'}$-exchange, the scalar $\sigma$-exchange, and the vector $\omega$-exchange and $\phi$-exchange. The $\eta$ and $\eta^{'}$ meson exchange potential is repulsive force for the state $^1S_0$ and attractive for $^3S_1$. The results depend very sensitively on the cutoff parameter of the $\omega$-exchange ($\Lambda_{\omega}$) and least sensitively on that of the $\phi$-exchange ($\Lambda_{\phi}$). Our result suggests the possible interpretation of Y(2175) and $\eta(2225)$ as the bound states of $\Lambda\bar{\Lambda}(^3S_1)$ and $\Lambda\bar{\Lambda}(^1S_0)$ respectively.