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

TL;DR

This paper uses three-body calculations to analyze the $ar{K}NN-ar{K}N$ interactions and the $ ext{Lambda}(1405)$ resonance in $K^-d ightarrow ext{pi} ext{Sigma} n$ reactions, highlighting how different models affect observable spectra.

Contribution

It compares energy-dependent and energy-independent meson-baryon interaction models within a three-body framework to identify their signatures in reaction cross sections.

Findings

Characteristic patterns in invariant mass spectra distinguish models.

The reaction is a useful probe of subthreshold $ar{K}N$ interactions.

Different off-shell properties lead to observable differences in cross sections.

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.