Roles of $\Lambda$ resonances in the $K^- p \to \gamma \Sigma$ reaction

TL;DR

This study uses an effective Lagrangian model to analyze the $K^- p o \gamma \Sigma$ reaction, highlighting the importance of specific $\Lambda$ resonances in explaining experimental data and suggesting future measurements for clearer identification.

Contribution

It introduces a detailed isobar model including multiple resonance contributions to better understand the roles of $\Lambda$ resonances in the reaction.

Findings

$\Lambda(1600)$ is essential at lower energies

Inclusion of $\Lambda(1670)$ or $\Lambda(1690)$ improves high-energy data fit

Current data cannot distinguish between $\Lambda(1670)$ and $\Lambda(1690)$ roles

Abstract

We investigate the $K^- p \to \gamma \Sigma$ reaction using an effective Lagrangian approach within an isobar model framework. The model includes contributions from $s$-channel hyperon and hyperon resonance, $t$-channel $K$ and $K^*$, $u$-channel proton and $\Delta(1232)$ exchanges, and a phenomenological contact term. Our analysis focuses on the roles of various $\Lambda$ resonances. The results indicate that the $\Lambda(1600)$ resonance is crucial for describing the experimental data at lower energies. At higher energies, the inclusion of either the $\Lambda(1670)$ or the $\Lambda(1690)$ resonance significantly improves the agreement with data. However, the current data are insufficient to distinguish between these two scenarios. We suggest that future measurements at higher beam energies and the measurement of the $\Sigma$ polarization are needed to identify the roles of the $\Lambda(1670)$ and $\Lambda(1690)$ resonances.