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Structure of the $Λ(1405)$ and the $K^-d\rightarrowπΣn$ reaction

The $Λ(1405)$ 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 $\bar{K}NN-πYN$ amplitudes on the physical real energy axis and investigate how the signature of the $Λ(1405)$ appears in the cross sections of the $K^-d\rightarrow πΣn$ 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 $K^- d\rightarrow πΣn$ reactions. Characteristic patterns distinguishing between the two models are found in the invariant mass spectrum of the final $πΣ$ state. The $K^-d\rightarrow πΣn$ reaction, with different ($π^{\pm}Σ^{\mp}$ and $π^{0}Σ^{0}$) 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.