Roles of $Λ$ resonances in the $K^- p \to γΣ$ reaction

TL;DR

The paper addresses identifying the roles of Lambda resonances in the radiative K- p reaction to map hyperon spectroscopy. It develops a gauge-invariant, effective Lagrangian isobar model that includes background terms and the resonances Lambda(1600), Lambda(1670), and Lambda(1690), and fits to Crystal Ball data in the 1.588–1.676 GeV region. The analysis finds that Lambda(1600) dominates at low energies, while either Lambda(1670) or Lambda(1690) is needed at higher energies, with two distinct interference solutions for each model; current data cannot distinguish between the two high-mass resonances, but polarization observables and higher-energy data could. Overall, the work constrains the hyperon resonance content in the strangeness sector and guides future experiments and modeling, including gauge-invariance restoration in radiative channels.

Abstract

We investigate the $K^- p \to γΣ$ 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 $Δ(1232)$ exchanges, and a phenomenological contact term. Our analysis focuses on the roles of various $Λ$ resonances. The results indicate that the $Λ(1600)$ resonance is crucial for describing the experimental data at lower energies. At higher energies, the inclusion of either the $Λ(1670)$ or the $Λ(1690)$ 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 $Σ$ polarization are needed to identify the roles of the $Λ(1670)$ and $Λ(1690)$ resonances.

Figures (6)

• Figure 1: Feynman diagrams for the $K^- p \rightarrow \gamma \Sigma$ reaction with $\Lambda^{*}$ denoting the $\Lambda(1600)$, $\Lambda(1670)$ or $\Lambda(1690)$.
• Figure 2: Fitted total cross sections for the $K^- p \rightarrow \gamma \Sigma$ reaction considering the background and one of the three $\Lambda$ resonances: $\Lambda(1600)$(solid line), $\Lambda(1670)$(dashed line) and $\Lambda(1690)$(dotted line). The individual contribution of background terms is shown by the dash-dotted line.
• Figure 3: Differential cross sections for the $K^- p \rightarrow \gamma \Sigma$ reaction as a function of $\cos\theta_\gamma$ in the center-of-mass frame in Model I. The solid, dashed, dotted, and dot-dashed lines represent the full, background, $\Lambda(1600)$, and $\Lambda(1670)$ contributions, respectively. The shaded bands correspond to the $1\sigma$ error regions of the fitting results.
• Figure 4: Differential cross sections for the $K^- p \rightarrow \gamma \Sigma$ reaction as a function of $\cos\theta_\gamma$ in the center-of-mass frame in Model II. The solid, dashed, dotted, and dot-dashed lines represent the full, background, $\Lambda(1600)$, and $\Lambda(1690)$ contributions, respectively. The shaded bands correspond to the $1\sigma$ error regions of the fitting results.
• Figure 5: Total cross sections for the $K^- +p \rightarrow \gamma +\Sigma$ reaction for Model I (Left) and Model II (Right). The shaded bands represent the $1\sigma$ error regions of the fitting results, reflecting uncertainties due to $1\sigma$ parameter variations. The solid, dotted, and dashed lines denote the contributions of the full model, the $\Lambda(1600)$, and the background terms, respectively. The dash-dotted line shows the contribution of either $\Lambda(1670)$ (in Model I) or $\Lambda(1690)$ (in Model II). The dash-dot-dotted line illustrates the corresponding sum of the resonance contributions.