Observation of a structure in the M$_{p\eta}$ invariant mass distribution near 1700 MeV in the $\mathbf{\gamma p \rightarrow p \pi^0 \eta} $ reaction

The reaction $\gamma p \rightarrow p \pi^0 \eta$ has been studied with the CBELSA/TAPS detector at the electron stretcher accelerator ELSA in Bonn for incident photon energies from threshold up to 3.1 GeV. This paper has been motivated by the recently claimed observation of a narrow structure in the M$_{N\eta}$ invariant mass distribution at a mass of 1678 MeV. The existence of this structure cannot be confirmed in the present work. Instead, for E$_{\gamma}$ = 1400 - 1500 MeV and the cut M$_{p\pi^0} \le 1190 $ MeV a statistically significant structure in the M$_{p\eta}$ invariant mass distribution near 1700 MeV is observed with a width of $\Gamma\approx 35$ MeV while the mass resolution is $\sigma_{res}$ = 5 MeV. Increasing the incident photon energy from 1420 to 1540 MeV this structure shifts in mass from $\approx 1700 $ to 1725 MeV; the width increases to about 50 MeV and decreases thereafter. The cross section associated with this structure reaches a maximum of $\approx$ 100 nb around E$_{\gamma} \approx$ 1490 MeV (W $\approx $ 1920 MeV), which coincides with the $p a_0$ threshold. Three scenarios are discussed which might be the origin of this structure in the M$_{p\eta}$ invariant mass distribution. The most likely interpretation is that it is due to a triangular singularity in the $\gamma p \rightarrow p a_0 \rightarrow p \pi^0 \eta$ reaction