Polarization of $\Lambda(1405)$ in the $\gamma p \rightarrow K^+ \pi \Sigma$ reaction

TL;DR

This study investigates the polarization of the $ ext{Lambda}(1405)$ in a photon-induced reaction using an effective Lagrangian model, highlighting the sensitivity of polarization to the $ ext{Lambda}(1405)$'s pole structure and proposing polarization measurements as a diagnostic tool.

Contribution

The paper introduces a contact term in the model and explores polarization as a probe for the two-pole structure of $ ext{Lambda}(1405)$, advancing understanding of its internal structure.

Findings

Polarization is sensitive to the invariant mass $M_{\pi\Sigma}$.

Measurement of polarization dependence can reveal the pole structure.

Inclusion of contact term improves model interpretation.

Abstract

In this paper, we study the polarization of the $\Lambda(1405)$ in the $\gamma p \rightarrow K^+ \pi \Sigma$ reaction within an effective Lagrangian approach and isobar model. In our model, the $\Lambda(1405)$ is excited through the t-channel $K/K^*$ exchanges and u-channel hyperon exchange. Compared to previous studies, we also include the contribution from a contact term, which is necessary for our model to interpret the polarization of the $\Lambda(1405)$. In addition, we also discuss the possibility to verify the proposed two-pole structure of the $\Lambda(1405)$ using the polarization data. We find that the polarization of the $\Lambda(1405)$ or the polarization of the final $\Sigma$ in this reaction is sensitive to the invariant mass $M_{\pi\Sigma}$. Thus the measurement of the dependence of the $\Lambda(1405)$ polarization on the $M_{\pi\Sigma}$ can offer valuable information about the pole structure of the $\Lambda(1405)$.