Contributions of box diagrams and $\Delta(1940)$ resonance to $K^0\Sigma^+$ photoproduction

TL;DR

This paper investigates the roles of box diagrams and the $ ext{Δ}(1940)$ resonance in $K^0 ext{Σ}^+$ photoproduction, aiming to explain experimental cross-section anomalies by combining theoretical models with experimental data.

Contribution

It introduces a combined theoretical approach including box diagrams and the $ ext{Δ}(1940)$ resonance to accurately describe $K^0 ext{Σ}^+$ photoproduction cross sections.

Findings

Box diagrams alone do not explain the cross-section drop.

Including the $ ext{Δ}(1940)$ resonance improves the model fit.

The combined model aligns well with CBELSA/TAPS data.

Abstract

We study first the box-diagram contribution to the $\gamma p\,\rightarrow \,K^0\Sigma^+$ process to understand the anomaly of the kaon photoproduction cross section from CBELSA/TAPS experiment at Electron Stretcher Accelerator (ELSA), where the imaginary part of the scattering amplitude from the box-diagrams is calculated by using Cutkosky's rules in the on-shell approximation while the real part of the amplitude is derived by dispersion relation calculations. Together with the results of the K-MAID model, the contribution of the box-diagrams fails to provide the sudden drop of the differential cross-section between the $K^*\,\Lambda$ and $K^*\,\Sigma$ thresholds. In addition, we include the $\Delta(1940)$ resonance in the process to complete the description of the differential cross-section. Combining the contributions from the K-MAID model, the box-diagrams and the $\Delta(1940)$ resonance, we have obtained the theoretical differential cross-section the $\gamma p\,\rightarrow \,K^0\Sigma^+$ process, which is compatible with the CBELSA/TAPS experimental data.