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

We use the Belle data on the K(-)p mass distribution of the Lambda(+)(c)-> pK(-)pi(+) reaction near the eta Lambda threshold to determine the eta Lambda 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 r(0) for the first time. The addition of the K(-)p ->eta Lambda 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 Lambda(1670).