Role of a triangle singularity in the $\gamma p\rightarrow K^+ \Lambda(1405)$ reaction

We show the effects of a triangle singularity mechanism for the $\gamma p \to K^+\Lambda(1405)$ reaction. The mechanism has a $N^*$ resonance around 2030 MeV, which decays into $K^* \Sigma$. The $K^*$ decays to $K^+ \pi$, and the $\pi \Sigma$ merge to form the $\Lambda(1405)$. This mechanism produces a peak around $\sqrt{s} = 2110$ MeV, and has its largest contribution around cos$\theta=0$. The addition of this mechanism to other conventional ones, leads to a good reproduction of ${\rm d}\sigma/{\rm dcos}\theta$ and the integrated cross section around this energy, providing a solution to a problem encountered in previous theoretical models.