Determination of the π Σ scattering lengths from the weak decays of Λc

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