Coherent $\pi^0\eta d$ photoproduction at forward deuteron angles measured at BGOOD

The coherent reaction, $\gamma d \rightarrow \pi^0\eta d$ was studied with the BGOOD experiment at ELSA from threshold to a centre-of-mass energy of 3200\,MeV. A full kinematic reconstruction was made, with final state deuterons identified in the forward spectrometer and $\pi^0$ and $\eta$ decays in the central BGO Rugby Ball. The strength of the differential cross section exceeds what can be described by models of coherent photoproduction at forward angles by orders of magnitude. The distribution of the differential cross section has an excellent agreement with a model including quasi-free $\Delta \pi$ photoproduction, pion re-scattering and $N(1535)$ formation and subsequent nucleon coalescence to the deuteron. This also gives a reasonable description of the two-body invariant mass distributions and naturally explains the similar magnitudes of this channel and $\pi^0\pi^0 d$ coherent photoproduction.