η−dandK−−dzero-energy scattering: A Faddeev approach

Abstract

The $\ensuremath{\eta}\ensuremath{-}d$ scattering length ${A}_{\ensuremath{\eta}d}$ has been calculated using as input a variety of possible $\ensuremath{\eta}\ensuremath{-}N$ scattering length values that have been presented in the literature. The calculated ${A}_{\ensuremath{\eta}d}$ are in perfect agreement with the values obtained previously by summation of multiple-scattering series but we disagree with another Faddeev-type calculation. We show that the present $\ensuremath{\eta}\ensuremath{-}N$ data rule out the possibility of a quasibound $\ensuremath{\eta}\ensuremath{-}d$ state. The imaginary part of the ${K}^{\ensuremath{-}}\ensuremath{-}d$ scattering length calculated by using a single-channel absorptive ${K}^{\ensuremath{-}}$-nucleon interaction is found to be in good agreement with the value obtained from the full multichannel approach but the mismatch in the corresponding real parts is about 40%.