The $\Sigma N$ threshold structure in the $K^-d\to\pi^-\Lambda p$ reaction

Abstract

The $\Lambda p$ invariant-mass spectrum near the two physical $\Sigma N$ thresholds in the $K^-d\to\pi^-\Lambda p$ reaction is studied as a probe of the low-energy $\Sigma N$ interaction. The reaction is formulated up to two-step processes, and the coupled $\Lambda p$, $\Sigma^+n$, and $\Sigma^0p$ channels are described within a constant-$K$-matrix model constrained by spin-triplet scattering lengths. The dependence of the $\Sigma N\to\Lambda p$ 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 $\Sigma N$ thresholds is found to be particularly sensitive to the complex spin-triplet $I=1/2$ $\Sigma N$ scattering length, indicating that measurements of this spectrum can provide useful constraints on the low-energy $\Sigma N$ interaction.