Precise determination of the $\eta \Lambda$ scattering length and effective range and relationship to the $\Lambda(1670)$ resonance

TL;DR

This study precisely determines the $ ext{eta} ext{Lambda}$ scattering length and effective range using Belle data, revealing their values and the $ ext{Lambda}(1670)$ resonance pole with high accuracy.

Contribution

The paper introduces a novel analysis that accurately extracts the $ ext{eta} ext{Lambda}$ scattering parameters and the $ ext{Lambda}(1670)$ pole position from experimental data.

Findings

Scattering length $a$ determined with high precision.

Effective range $r_0$ measured for the first time.

High-precision $ ext{Lambda}(1670)$ pole position obtained.

Abstract

We use the Belle data on the $K^- p$ mass distribution of the $\Lambda_c^+ \to p K^- \pi^+$ reaction near the $\eta \Lambda$ threshold to determine the $\eta \Lambda $ scattering length and effective range. We show that from these data alone we can determine the value of $a$ with better precision than so far determined, and the value of $r_0$ for the first time. The addition of the $K^- p \to \eta \Lambda$ data allows us to improve the precision of these magnitudes, with errors smaller than $15\%$. We also determine with high precision the pole position of the $\Lambda(1670)$.