Photoproduction of $\Lambda (1405)$ with the $N^*$ and $t$-channel Regge contributions

We investigate the photoproduction of $\Lambda(1405)\equiv\Lambda^*$ hyperon resonance, i.e., $\gamma p\to K^+\Lambda^*$, employing the effective Lagrangian approach with the $t$-channel Regge trajectories at tree level. We extensively explore the effects from the nucleon resonances in the vicinity of the threshold $\sqrt{s}_\mathrm{th}\approx1900$ MeV, i.e., $N(2000)$, $N(2030)$, $N(2055)$, $N(2095)$, and $N(2100)$, and observe that they are of great importance to reproduce the recent CLAS/Jlab experimental data. Total and differential cross sections are given as numerical results and compared with the experimental data, in addition to the $t$-channel momentum transfer and photon-beam asymmetry. The invariant-mass plots for $\gamma p\to K^+\pi^0\Sigma^0$ via $\Lambda^*$ are also extracted from the two-body process results, showing a qualitative agreement with the data. We also discuss the constituent-counting rule for the internal structure of $\Lambda^*$, resulting in that $\Lambda^*$ appears to be different from a simple three-quark $(uds)$ state.