Meson-exchange model for theΛΛ¯interaction

Abstract

In the present work, we apply the one-boson-exchange potential model to investigate the possibility of $Y(2175)$ and $\ensuremath{\eta}(2225)$ as bound states of $\ensuremath{\Lambda}\overline{\ensuremath{\Lambda}}(^{3}S_{1})$ and $\ensuremath{\Lambda}\overline{\ensuremath{\Lambda}}(^{1}S_{0})$, respectively. We consider the effective potential from the pseudoscalar $\ensuremath{\eta}$ exchange and ${\ensuremath{\eta}}^{\ensuremath{'}}$ exchange, the scalar $\ensuremath{\sigma}$ exchange, and the vector $\ensuremath{\omega}$ exchange and $\ensuremath{\phi}$ exchange. The $\ensuremath{\eta}$- and ${\ensuremath{\eta}}^{\ensuremath{'}}$-meson-exchange potential is a 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 $\ensuremath{\omega}$ exchange (${\ensuremath{\Lambda}}_{\ensuremath{\omega}}$) and least sensitively on that of the $\ensuremath{\phi}$ exchange (${\ensuremath{\Lambda}}_{\ensuremath{\phi}}$). Our result suggests the possible interpretation of $Y(2175)$ and $\ensuremath{\eta}(2225)$ as the bound states of $\ensuremath{\Lambda}\overline{\ensuremath{\Lambda}}(^{3}S_{1})$ and $\ensuremath{\Lambda}\overline{\ensuremath{\Lambda}}(^{1}S_{0})$, respectively.