$N \Omega$ interaction: meson exchanges, inelastic channels, and quasibound state

Based on a baryon-baryon interaction model with meson exchanges, we investigate the origin of the strong attraction in the $N \Omega ( {}^{5}S_{2} )$ interaction, which was indicated by recent lattice QCD simulations. The long range part of the potential is constructed by the conventional mechanisms, the exchanges of the $\eta$ meson and of the correlated two mesons in the scalar-isoscalar channel, denoted by "$\sigma$" in the literature. The short range part is represented by the contact interaction. We find that the meson exchanges do not provide sufficient attraction. This means that most of the attraction is attributed to the short range contact interaction. We then evaluate the effect of the coupled channels to the $N \Omega ( {}^{5}S_{2} )$ interaction. We find that, while the $D$-wave mixing of the $N \Omega$ channel is negligible, the inelastic $\Lambda \Xi$, $\Sigma \Xi$, and $\Lambda \Xi (1530)$ channels via the $K$ meson exchange give the attraction of the $N \Omega ( {}^{5}S_{2} )$ interaction to the same level with the elastic meson exchanges. Although the elimination of these channels induces the energy dependence of the single-channel $N \Omega$ interaction, this effect is not significant. With the present model parameters fitted to reproduce the scattering length of the HAL QCD result of the nearly physical quark masses, we obtain the $N \Omega ( {}^{5}S_{2} )$ quasibound state with its eigenenergy $2611.3 - 0.7 i$ MeV, which corresponds to the binding energy $0.1$ MeV and width $1.5$ MeV for the decay to the $\Lambda \Xi$ and $\Sigma \Xi$ channels. From the analysis of the spatial structure and the compositeness, the quasibound state is shown to be the molecular state of $N\Omega$. We also construct an equivalent local potential for the $N \Omega ( {}^{5}S_{2} )$ system which is useful for various applications.
Comment: 22 pages, 17 eps figures