# Studies on photo- and electro-productions of $\Lambda(1405)$ via $\gamma^{(*)} p\to K^{*+}\pi^0\Sigma^0$

## TL;DR

This study investigates the photo- and electro-production mechanisms of the $ ext{Lambda}(1405)$ resonance via a specific reaction, analyzing the line shape and polarization asymmetries to understand the underlying interactions and form factors.

## Contribution

It introduces a detailed effective Lagrangian model including $K^*N ext{Lambda}^*$ interactions and explores their effects on observable signals and polarization asymmetries.

## Key findings

- Lambda* peak is visible with $K^*N extLambda^*$ interaction in photo- and electro-production.
- Photon-polarization asymmetry $ extSigma$ can reveal the $K^*N extLambda^*$ interaction effects.
- Different $Q^2$ dependences lead to distinct behaviors in the production processes.

## Abstract

We study the photo- and electro-productions of the vector kaon off the proton, i.e., $\gamma^{(*)}p\to K^{*+}\pi^0\Sigma^0$, and investigate the line shape of the $\pi^0\Sigma^0$ invariant mass in an effective Lagrangian approach with the inclusion of a $K^*N\Lambda^*$ interaction. Relevant electromagnetic form factors for the neutral hyperons and charged strange mesons are constructed by considering experimental and theoretical information. We find that the $\Lambda^*$ peak is clearly observed for the photo- and electro-productions with the finite $K^*N\Lambda^*$ interaction, whereas the clear peak signals survive only for the electro-production, when we ignore the interaction. These different behaviors can be understood by different $Q^2$ dependences in the $K^*$ electromagnetic and $K^*\to\gamma K$ transition form factors. We suggest a photon-polarization asymmetry $\Sigma$ to extract information of the $K^*N\Lambda^*$ interaction. It turns out that $\Sigma$ near the $\Lambda^*$ peak region becomes negative with a finite $K^*N\Lambda^*$ interaction while positive without it for $Q^2 = 0$, due to the different naturalities of $K$ and $K^*$ exchanges. For $Q^2\ne 0$, we observe more obvious signals in the peak region due to the additional contribution of the longitudinal virtual photon for $\Lambda^*$.