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

TL;DR

This study investigates the $ar{K}N-\pi\Sigma$ interactions in the low-energy $K^{-}+^3 ext{He}$ reaction to identify the $ ext{Lambda}(1405)$ resonance signature through the deuteron energy spectrum, highlighting its sensitivity to interaction models.

Contribution

It introduces a coupled-channel Faddeev AGS approach to analyze the $ ext{Lambda}(1405)$ in a three-body system, comparing phenomenological and chiral SU(3) potentials.

Findings

Deuteron energy spectrum is sensitive to the $ar{K}N-\pi\Sigma$ interaction model.

Accurate measurements can discriminate between different $ ext{Lambda}(1405)$ formation mechanisms.

The resonance signature depends on the chosen interaction potential model.

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 $K^{-}+\,^{3}\mathrm{He}\rightarrow\pi\Sigma{d}$ 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).