Photoproduction of $K^+\Lambda(1405) \rightarrow K^+\pi^0\Sigma^0$ extending to forward angles and low momentum transfer

$K^+\Lambda(1405)$ photoproduction has been studied at the BGOOD experiment via the all neutral decay, $\Lambda(1405)\rightarrow\Sigma^0\pi^0$. The unique BGOOD experimental setup allows both the cross section and $\Lambda(1405)$ invariant mass distribution (line shape) to be measured over a broad $K^+$ polar angle range, extending to extreme forward $K^+$ angles unattainable at previous experiments. Evidence is provided for the role of a triangle singularity driven by the $N^*(2030)$ resonance, which appears to contribute significantly to $K^+\Lambda(1405)$ photoproduction. This is observed in both the angular distributions and the integrated cross section which was determined with unprecedented energy resolution. The measured line shape is also in agreement with the previous results of CLAS and ANKE, and is consistent with two poles derived in $\chi$PT based models.