Determination of the Sigma-Pi scattering lengths in the weak Lambda c decay using Belle data

Abstract

This thesis deals with the analysis of the weak decays of Lambda_c -> Sigma pion pion using Belle data with the ultimate purpose of extracting scattering lengths of Sigma and pion. The Sigma-pion scattering length is one of the important missing experimental inputs to understand the Lambda(1405) state, an exotic resonance which can be considered as a quasi-bound state of proton and kaon. A determination of a scattering length of short lived particle is diifficult since a direct scattering experiment is not possible. In the case of the Sigma-pion system, due to the final state interaction, isospin violation and interference, threshold cusps will appear in the Sigma-pion spectra. The strength of the cusp effect reflects the Sigma-pion scattering lengths. The scope of this thesis is limited to the Monte Carlo studies that precede the measurement of real data. The reconstruction of Lambda_c in Sigma +pi +pi -, Sigma +pi 0pi 0 and Sigma 0pi +pi 0 decay modes as well as the determination of branching ratios of those decay modes relative to the reference channel pKpi is presented. Finally the MC Sigma-pi spectrum is compared with theoretical predictions.