Testing chiral unitary models for the $\Lambda(1405)$ in $K^{+}\pi\Sigma$ photoproduction

TL;DR

This paper introduces a novel, parameter-free formalism for analyzing the $ ext{K}^+ ext{pi} ext{Sigma}$ photoproduction reaction, emphasizing the importance of meson-baryon rescattering and model sensitivity in understanding the $ ext{Lambda}(1405)$ resonance.

Contribution

It develops a new formalism that respects unitarity, gauge invariance, and chiral symmetry, providing insights into the $ ext{Lambda}(1405)$ without parameter adjustments.

Findings

Rescattering significantly affects the spectra.

Spectra are highly sensitive to coupled-channel model choices.

Method aligns well with experimental data.

Abstract

We adopt a novel formalism for the low-energy analysis of the $\gamma p \to K^{+}\pi\Sigma$ photoproduction reaction to calculate the $\pi\Sigma$ invariant mass distributions in the $\Lambda(1405)$ resonance region. The approach adheres to constraints arising from unitarity, gauge invariance and chiral perturbation theory, and is used without adjusting any model parameters. It is found that the meson-baryon rescattering in the final state has a major impact on the magnitude and structure of the generated spectra that are compared with the experimental data from the CLAS collaboration. We demonstrate a large sensitivity of the theoretical predictions to the choice of the coupled-channel $\pi\Sigma - \bar{K}N$ model amplitudes which should enable one to constrain the parameter space of these models.