Photoproduction of $\Lambda(1405)$ with the two-pole structure

TL;DR

This paper models the photoproduction of the $ ext{Lambda}(1405)$ resonance, explicitly considering its two-pole structure, and demonstrates that including this structure and nucleon resonances aligns well with experimental data.

Contribution

It introduces a two-pole structure model for $ ext{Lambda}(1405)$ photoproduction using an effective Lagrangian approach, supporting the two-pole hypothesis with qualitative data agreement.

Findings

The two-pole model reproduces experimental energy and angular distributions.

Nucleon resonance contributions are crucial near the threshold.

The model supports the two-pole structure of $ ext{Lambda}(1405)$.

Abstract

We investigate the $\Lambda(1405,1/2^-)\equiv\Lambda^*$ photoproduction off the proton target, i.e. $\gamma p\to K^+\Lambda^*$, considering explicitly its two-pole structure, the higher ($\Lambda^*_H:\,1430\,\mathrm{MeV}$) and lower ($\Lambda^*_L:\,1390\,\mathrm{MeV}$) mass-pole contributions, suggested by the chiral-unitary model (ChUM) approaches. For this purpose, we construct a two-body process model, which mimics the Dalitz process, $\gamma p\to K^+\pi\Sigma$, assuming that the mass of $\Lambda^*$ as the invariant mass of $\pi$ and $\Sigma$, i.e. $M_{\Lambda^*}\sim M_{\pi\Sigma}$. We employ the effective Lagrangian method with the tree-level Born approximation, using the gauge-invariant prescription for the phenomenological form factors. We provide the numerical results for the energy and angular dependences, $\pi$-$\Sigma$ invariant-mass distribution, and so on. It turns out that the model parameters determined from ChUM reproduce the experimental data qualitatively well, supporting the two-pole structure. Moreover, the nucleon resonance contribution near the threshold plays an important role to describe the data.