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$K^+\Lambda(1405)$ photoproduction has been studied at the BGOOD experimentvia the all neutral decay, $\Lambda(1405)\rightarrow\Sigma^0\pi^0$. The uniqueBGOOD 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 atprevious 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 angulardistributions and the integrated cross section which was determined withunprecedented energy resolution. The measured line shape is also in agreementwith the previous results of CLAS and ANKE, and is consistent with two polesderived in $\chi$PT based models.

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