Theoretical study of the $\mathrm{\Sigma }N$ cusp in the $K^{-}d\to \pi \mathrm{\Lambda }N$ reaction

The $K^{-}d\to \pi \mathrm{\Lambda }N$ reaction is useful for exploring the hyperon-nucleon interaction through final state interactions. In particular, the cusp structure of the $\mathrm{\Lambda }N$ invariant mass spectrum at the $\mathrm{\Sigma }N$ threshold contains information about the s-wave interaction of 1/2-isospin hyperon-nucleon systems. The calculation of the spectrum is performed with the aim of extracting the scattering length of the $\mathrm{\Sigma }N(I=1\mathrm{/}2)$ channel that couples to the $\mathrm{\Lambda }N$ channel from this reaction, and the results are discussed in comparison with experimental data to highlight the factors that should be considered.