Signature of the $\Lambda(1405)$ resonance in neutron spectra from the $K^-+d$ reaction

Abstract

Neutron spectra from the reaction $K^-+d\rightarrow \pi+\Sigma+n$ were calculated in the energy range $E^{cm}_{K^-}= 0-50\ MeV$ using coupled channel Faddeev equations for the description of the $\bar KNN-\pi\Sigma N$ three-body system. The aim was to trace the signature of the $\Lambda(1405)$ resonance in the spectra. We found, that while in the direct spectra kinematic effects mask completely the peak corresponding to the resonance, the deviation spectrum method [1] is able to eliminate kinematics and differentiate between different models of $\Lambda(1405)$. Four different phenomenological $\bar{K}N-\pi\Sigma$ interactions were used in order to study the effect of their pole positions on the neutron spectra.