Eur. Phys. J. A (2021) 57: 120
https://doi.org/10.1140/epja/s10050-021-00379-x

Regular Article – Theoretical Physics

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

¹ Department of Physics, Faculty of Basic Sciences, Shahrekord University, 115, Shahrekord, Iran
² Department of Physics, Isfahan University of Technology, 84156-83111, Isfahan, Iran
³ Department of Physics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran

^a This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 4 July 2020
Accepted: 1 February 2021
Published online: 8 April 2021

Abstract

In present work, we investigated $K^{-}+{}^3\mathrm{He}$ reaction at low energies. The coupled-channel Faddeev AGS equations were solved for $\overline{K}Nd-\pi \Sigma d$ 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 $\overline{K}N-\pi \Sigma$ 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 $\overline{K}N-\pi \Sigma$ 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).