Theoretical study of the $\Sigma N$ cusp in the $K^-d\rightarrow\pi\Lambda N$ reaction

TL;DR

This paper provides a theoretical analysis of the $ ext{K}^-d ightarrow ext{pi}\Lambda N$ reaction, focusing on the $ ext{Lambda}N$ cusp at the $ ext{Sigma}N$ threshold to extract hyperon-nucleon interaction parameters.

Contribution

It offers a theoretical calculation of the $ ext{Lambda}N$ invariant mass spectrum to determine the $ ext{Sigma}N$ scattering length, aiding understanding of hyperon-nucleon interactions.

Findings

The cusp structure reveals information about the s-wave hyperon-nucleon interaction.

The calculated spectrum helps in extracting the $ ext{Sigma}N$ scattering length.

Comparison with experimental data highlights key factors affecting the spectrum.

Abstract

The $K^-d\rightarrow\pi\Lambda N$ reaction is useful for exploring the hyperon-nucleon interaction through final state interactions. In particular, the cusp structure of the $\Lambda N$ invariant mass spectrum at the $\Sigma N$ 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 $\Sigma N(I=1/2)$ channel that couples to the $\Lambda N$ channel from this reaction, and the results are discussed in comparison with experimental data to highlight the factors that should be considered.