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

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.