Trace of $\Lambda (1405)$ resonance in low energy $K^{-}+{}^3\mathrm{He}\to ({\pi }^0{\Sigma }^0)+d$ reaction

Abstract

In present work, we investigated $K^{-}+{}^3\mathrm{He}$ reaction at low energies. The coupled-channel Faddeev AGS equations were solved for $\bar{K}Nd-\pi \Sigma d$ three-body system in momentum representation to extract the scattering amplitudes. To trace the signature of the $\Lambda$(1405) resonance in the $\pi \Sigma$ invariant mass, the deuteron energy spectrum for $K^{-}+{}^3\mathrm{He}\to \pi \Sigma d$ reaction was obtained. Different types of $\bar{K}N-\pi \Sigma$ potentials based on phenomenological and chiral SU(3) approaches were used. As a remarkable result of this investigation, it was found that the deuteron energy spectrum, reflecting the $\Lambda$(1405) mass distribution and width, depends quite sensitively on the $\bar{K}N-\pi \Sigma$ model of interaction. Hence accurate measurements of the $\pi \Sigma$ mass distribution have the potential to discriminate between possible mechanisms at work in the formation of the $\Lambda$(1405).

arXiv comment9 pages, 5 figures

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