Λ−ΣConversion and the Hypertriton

The binding energy of ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}$ is calculated using a Faddeev-type multiple-scattering formalism. The effects of virtual $\Lambda -\Sigma$ conversion via $\Lambda N\leftrightarrow \Sigma N$ are included in a full two-channel representation of the $\mathrm{YN}$ interaction. Nonlocal separable, $S$-wave, spin-dependent potentials are used for each two-body interaction. Calculations are performed for two sets of low-energy $\Lambda N$ scattering parameters and two different symmetry models for the $\mathrm{YN}$ potential. The introduction of $\Lambda -\Sigma$ conversion in the $\mathrm{YN}$ spin-triplet channel increases the binding energy. The binding is decreased by the use of $\Lambda -\Sigma$ conversion in the $\mathrm{YN}$ spin-singlet channel. When incorporated into both $\mathrm{YN}$ spin channels, the effect of $\Lambda -\Sigma$ conversion is to reduce the ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}$ binding energy.