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RESEARCH PRODUCT

Role of a triangle singularity in the πN(1535) contribution to γp→pπ0η

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We have studied the $\ensuremath{\gamma}p\ensuremath{\rightarrow}p{\ensuremath{\pi}}^{0}\ensuremath{\eta}$ reaction paying attention to the two main mechanisms at low energies, the $\ensuremath{\gamma}p\ensuremath{\rightarrow}\mathrm{\ensuremath{\Delta}}(1700)\ensuremath{\rightarrow}\ensuremath{\eta}\mathrm{\ensuremath{\Delta}}(1232)$ and the $\ensuremath{\gamma}p\ensuremath{\rightarrow}\mathrm{\ensuremath{\Delta}}(1700)\ensuremath{\rightarrow}\ensuremath{\pi}N(1535)$. Both are driven by the photoexcitation of the $\mathrm{\ensuremath{\Delta}}(1700)$ and the second one involves a mechanism that leads to a triangle singularity. We are able to evaluate quantitatively the cross section for this process and show that it agrees with the experimental determination. Yet there are some differences with the standard partial wave analysis which does not include explicitly the triangle singularity. The exercise also shows the convenience of exploring possible triangle singularities in other reactions and how a standard partial wave analysis can be extended to accommodate them.