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, $\Lambda(1405)\rightarrow\Sigma^0\pi^0$. BGOOD's unique 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. The line shape was determined to be in agreement with the previous results of CLAS and ANKE, and appear consistent with two poles derived in $\chi$PT based models. %with hints of a double peak structure which may have been observed in the ANKE results At forward $K^+$ angles the relative strength of the peaks appear to change, however more statistics are required for a firm conclusion. Evidence is provided for the role of a triangle singularity driven by the $N^*(2030)$ resonance, which appears to significantly contribute 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.