Λ−ΣConversion and the Hypertriton

Abstract

The binding energy of $_{\ensuremath{\Lambda}}\mathrm{H}^{3}$ is calculated using a Faddeev-type multiple-scattering formalism. The effects of virtual $\ensuremath{\Lambda}\ensuremath{-}\ensuremath{\Sigma}$ conversion via $\ensuremath{\Lambda}N\ensuremath{\leftrightarrow}\ensuremath{\Sigma}N$ 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 $\ensuremath{\Lambda}N$ scattering parameters and two different symmetry models for the $\mathrm{YN}$ potential. The introduction of $\ensuremath{\Lambda}\ensuremath{-}\ensuremath{\Sigma}$ conversion in the $\mathrm{YN}$ spin-triplet channel increases the binding energy. The binding is decreased by the use of $\ensuremath{\Lambda}\ensuremath{-}\ensuremath{\Sigma}$ conversion in the $\mathrm{YN}$ spin-singlet channel. When incorporated into both $\mathrm{YN}$ spin channels, the effect of $\ensuremath{\Lambda}\ensuremath{-}\ensuremath{\Sigma}$ conversion is to reduce the $_{\ensuremath{\Lambda}}\mathrm{H}^{3}$ binding energy.