Precise determination of the ηΛ scattering length and effective range and relationship to the Λ(1670) resonance

Abstract

We use the Belle data on the K−p mass distribution of the Λc+→pK−π+ reaction near the ηΛ threshold to determine the ηΛ scattering length and effective range. We show that from these data alone we can determine the value of a with better precision than so far determined, and the value of r0 for the first time. The addition of the K−p→ηΛ data allows us to improve the precision of these magnitudes, with errors smaller than 15%. We also determine with high precision the pole position of the Λ(1670).