Study of the $\Lambda p$ Interaction Close to the $\Sigma^+n$ and $\Sigma^0p$ Thresholds

TL;DR

This paper analyzes the $ ext{Lambda} p$ interaction near the $ ext{Sigma} N$ threshold, identifying a cusp structure indicative of an inelastic virtual state and discussing experimental peak positions and their implications.

Contribution

It provides a detailed analysis of the $ ext{Lambda} p$ interaction near the $ ext{Sigma} N$ threshold, interpreting experimental structures as evidence of virtual states in coupled-channel models.

Findings

Identification of a cusp structure at 2128.7 MeV consistent with the $ ext{Sigma}^+ n$ threshold.

Evidence supporting the virtual state interpretation in the $ ext{Sigma} N$ system.

Observation of a second, less well-defined peak above the threshold.

Abstract

The $\Lambda p$ interaction close to the $\Sigma N$ threshold is considered. Specifically, the pronounced structure seen in production reactions like $K^-d \to \pi^- \Lambda p$ and $pp\to K^+ \Lambda p$ around the $\Sigma N$ threshold is analyzed. Modern interaction models of the coupled $\Lambda N - \Sigma N$ systems generate such a structure either due to the presence of a (deuteron-like) unstable bound state or of an inelastic virtual state. % A determination of the position of the prominent peak as observed in various experiments for the two aforementioned reactions leads to values that agree quite well with each other. Furthermore, the deduced mean value of $2128.7\pm 0.3$ MeV for the peak position coincides practically with the threshold energy of the $\Sigma^+ n$ channel. This supports the interpretation of the structure as a genuine cusp, signaling an inelastic virtual state in the $^3S_1-^3D_1$ partial wave of the $\Sigma N$ isospin 1/2 channel. % There is also evidence for a second peak (or shoulder) in the data sets considered which appears at roughly 10-15 MeV above the $\Sigma N$ threshold. However, its concrete position varies significantly from data set to data set and, thus, a theoretical interpretation is difficult.