Determination of the πΣ scattering lengths from the weak decays of Λc

The scattering lengths of the πΣ systems are key quantities in understanding the structure of the Λ(1405) resonance and the subthreshold extrapolation of the KN interaction. We demonstrate that the πΣ scattering lengths can be extracted from the threshold cusp phenomena in the weak Λc→ππΣ decays, analogously with Cabibbo's method for determination of the ππ scattering length. We show that the substantial cusp effect should be observed in the spectrum, when the πΣ interaction in I=0 is strongly attractive to generate a near-threshold singularity, such as a bound state or a virtual state.