Resonances in $\Lambda d$ Scattering and the $\Sigma$-hypertriton

Using separable $NN$ and $\Lambda N$-$\Sigma N$ potentials in the Faddeev equations, we have demonstrated that the predicted enhancement in the $\Lambda d$ cross section near the $\Sigma d$ threshold is associated with resonance poles in the scattering amplitude. The positions of these poles, on the second Riemann sheet of the complex energy plane, are determined by examining the eigenvalues of the kernel of the Faddeev equations. This suggests that for a certain class of $\Lambda N$-$\Sigma N$ potentials we can form a $\Sigma$-hypertriton with a width of about 8 MeV.