Determination of the pi Sigma scattering lengths from the weak decays of Lambda_c

TL;DR

This paper proposes a novel method to determine pi Sigma scattering lengths by analyzing threshold cusp effects in weak Lambda_c decays, providing insights into the Lambda(1405) resonance structure.

Contribution

It introduces a new approach to extract pi Sigma scattering lengths from weak decay spectra, analogous to Cabibbo's method for pi pi scattering.

Findings

Cusp effects are significant when pi Sigma interaction is strongly attractive.

The method can reveal near-threshold singularities like bound or virtual states.

Potential to improve understanding of Lambda(1405) resonance structure.

Abstract

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 barK 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.