Analysis of the Crystal Ball data on $K^-p\to\pi^0\Sigma^0$ reaction with center-of-mass energies of $1536\sim 1676$ MeV

TL;DR

This study uses an effective Lagrangian approach to analyze Crystal Ball data on the $K^-p\to\pi^0\Sigma^0$ reaction, revealing the necessity of the $\Lambda(1600)\frac{1}{2}^+$ resonance and evidence for a new $\Lambda(\frac{3}{2}^+)$ resonance around 1680 MeV.

Contribution

It introduces a detailed analysis of hyperon resonances in $K^-p$ reactions, identifying a previously less established resonance and proposing a new one based on experimental data.

Findings

Confirmation of the $\Lambda(1600)\frac{1}{2}^+$ resonance.

Evidence for a new $\Lambda(\frac{3}{2}^+)$ resonance around 1680 MeV.

Improved understanding of hyperon resonance spectrum.

Abstract

With an effective Lagrangian approach, we analyze the $K^-p\to \pi^0\Sigma^0$ reaction to study the $\Lambda$ hyperon resonances by fitting the Crystal Ball data on differential cross sections and $\Sigma^0$ polarization with the center-of-mass energies of $1536\sim 1676$ MeV. Besides well established PDG 4-star $\Lambda$ resonances around this energy range, the $\Lambda(1600){1\over 2}^+$ resonance, listed as a 3-star resonance in PDG, is found to be definitely needed. In addition, there is strong evidence for the existence of a new $\Lambda({3\over 2}^+)$ resonance around 1680 MeV.