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The $\gamma p \to \pi^0 \eta p$ reaction has been investigated by theCBELSA/TAPS Collaboration, revealing a narrow structure in the $\eta p$invariant mass distributions at a mass of $1700$ MeV. In this study, we explorethe possibility that the narrow structure is caused by a decay cascade via anintermediate nucleon resonance decaying to $\eta p$ final states. Thecandidates for the intermediate nucleon resonances are $N(1700)3/2^{-}$ and$N(1710)1/2^{+}$, with masses near the observed structure. We consider the$t$-channel $\rho$- and $\omega$-exchange diagrams, the $u$-channelnucleon-pole exchange diagram, the contact term, and the $s$-channel polediagrams of nucleon, $\Delta$, and nucleon resonances when constructing thereaction amplitudes to reproduce the stripped individual contribution of thenarrow structure. Our analysis indicates that the signature strength of thedecay cascade $\gamma p \to \pi^{0}N(1700)3/2^{-} \to \pi^{0}\eta p$ is tooweak to reach the experimental curve of the narrow structure due to the smalldecay branching ratio of $N(1700)3/2^{-}$ to $\eta p$. Although the decaycascade $\gamma p \to \pi^{0}N(1710)1/2^{+} \to \pi^{0}\eta p$ canqualitatively reproduce the experimental curve of the invariant massdistributions, its cross-section width is much larger than that of thecorresponding experimental curve. Therefore, we conclude that the decay cascadevia an intermediate nucleon resonance could not be the reason leading to thenarrow structure in the $\eta p$ invariant mass distributions of the $\gamma p\to \pi^0 \eta p$ reaction.

The effect of decay cascade via an intermediate resonance in the $\gamma p \to \pi^0 \eta p $ reaction