The $ΣN$ threshold structure in the $K^-d\toπ^-Λp$ reaction

Abstract

The $Λp$ invariant-mass spectrum near the two physical $ΣN$ thresholds in the $K^-d\toπ^-Λp$ reaction is studied as a probe of the low-energy $ΣN$ interaction. The reaction is formulated up to two-step processes, and the coupled $Λp$, $Σ^+n$, and $Σ^0p$ channels are described within a constant-$K$-matrix model constrained by spin-triplet scattering lengths. The dependence of the $ΣN\toΛp$ conversion amplitude on these scattering lengths is examined, and the relation between its line shape and nearby pole positions is investigated. The resulting invariant-mass spectra are studied at different incident kaon momenta and compared qualitatively with existing experimental data. The effects of the spin-singlet $YN$ amplitude and the deuteron wave function are also examined. The line shape near the $ΣN$ thresholds is found to be particularly sensitive to the complex spin-triplet $I=1/2$ $ΣN$ scattering length, indicating that measurements of this spectrum can provide useful constraints on the low-energy $ΣN$ interaction.