Polarization of $\mathrm{\Lambda }(1405)$ in the $\gamma p\to K^{+}\pi \mathrm{\Sigma }$ reaction

In this paper, we study the polarization of the $\mathrm{\Lambda }(1405)$ in the $\gamma p\to K^{+}\pi \mathrm{\Sigma }$ reaction within an effective Lagrangian approach and isobar model. In our model, the $\mathrm{\Lambda }(1405)$ is excited through the t-channel $K\mathrm{/}{K}^{\ast }$ 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 $\mathrm{\Lambda }(1405)$. In addition, we also discuss the possibility to verify the proposed two-pole structure of the $\mathrm{\Lambda }(1405)$ using the polarization data. We find that the polarization of the $\mathrm{\Lambda }(1405)$ or the polarization of the final $\mathrm{\Sigma }$ in this reaction is sensitive to the invariant mass $M_{\pi \mathrm{\Sigma }}$. Thus the measurement of the dependence of the $\mathrm{\Lambda }(1405)$ polarization on the $M_{\pi \mathrm{\Sigma }}$ can offer valuable information about the pole structure of the $\mathrm{\Lambda }(1405)$.