Faddeev calculation of ${}_{\Lambda \Lambda }{}^6\mathrm{He}$ using ${\mathrm{SU}}_6$ quark-model baryon-baryon interactions

Quark-model hyperon-nucleon and hyperon-hyperon interactions by the Kyoto-Niigata group are applied to the two-$\Lambda$ plus $\alpha$ system in a three-cluster Faddeev formalism using two-cluster resonating-group method kernels. The model fss2 gives a reasonable two-$\Lambda$ separation energy $\Delta B_{\Lambda \Lambda }=1.41\mathrm{MeV}$, which is consistent with the recent empirical value, $\Delta B_{\Lambda \Lambda }^{\exp }=1.01\pm 0.20\mathrm{MeV}$, deduced from the Nagara event. Some important effects that are not taken into account in the present calculation are discussed.

Figure 1

${}^{1}S_0$ phase shifts, predicted by fss2, in the $\Lambda \Lambda \text{−}\Xi N\text{−}\Sigma \Sigma$ coupled-channel system with the isospin $I=0$. The single-channel phase shift of the $\Lambda \Lambda$ scattering, predicted by the SB potential, is also shown in circles.