Determination of the pi Sigma scattering lengths from the weak decays of Lambda_c
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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.
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Isospin-breaking effects on the threshold cusp structures in $\Lambda N$-$\Sigma N$ scattering
Isospin breaking splits threshold cusps in ΛN-ΣN scattering into constrained structures whose relative sharpness or type can change, as shown via K-matrix classification and N²LO chiral EFT calculations.
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