Structure of the \(\Lambda(1405)\) and the \(K^-d\rightarrow\pi\Sigma n\) reaction

Abstract

The \(\Lambda(1405)\) resonance production reaction is investigated within the framework of the coupled-channels Alt-Grassberger-Sandhas (AGS) equations. We perform full three-body calculations for the \(\bar{K}NN-\pi YN\) amplitudes on the physical real energy axis and investigate how the signature of the \(\Lambda(1405)\) appears in the cross sections of the \(K^-d\rightarrow \pi\Sigma n\) reactions, also in view of the planned E31 experiment at J-PARC. Two types of meson-baryon interaction models are considered: an energy-dependent interaction based on chiral \(SU(3)\) effective field theory, and an energy-independent version that has been used repeatedly in phenomenological approaches. These two models have different off-shell properties that imply correspondingly different behavior in the three-body system. We investigate how these features show up in differential cross sections of \(K^- d\rightarrow \pi\Sigma n\) reactions. Characteristic patterns distinguishing between the two models are found in the invariant mass spectrum of the final \(\pi\Sigma\) state. The \(K^-d\rightarrow \pi\Sigma n\) reaction, with different (\(\pi^{\pm}\Sigma^{\mp}\) and \(\pi^{0}\Sigma^{0}\)) charge combinations in the final state, is thus demonstrated to be a useful tool for investigating the subthreshold behavior of the \(\bar{K}N\) interaction.