On the scattering length of the K^- d system

Multiple-scattering approximations to Faddeev calculations of the K ^- d scattering length are reviewed and compared with published K̄ N N - π Y N fully reactive Faddeev calculations. A new multiple-scattering approximation which goes beyond the 'fixed-center' assumption for the nucleons is proposed, aiming at accuracies of 5 - 10%. A precise value of the K^- d scattering length from the measurement of the K^- d 1s atomic level shift and width, planned by the DEAR/SIDDHARTA collaboration, plus a precise value for the K^- p scattering length by improving the K^- p atom measurements, are essential for extracting the K^- n scattering length, for resolving persistent puzzles in low-energy K̄ N phenomenology and for extrapolating into K̄-nuclear systems.