# Role of a triangle singularity in the $\pi N(1535)$ contribution to $\gamma p \to p \pi^0 \eta$

## TL;DR

This paper investigates the role of a triangle singularity in the $ o p o p o p o p$ reaction, demonstrating its impact on cross section calculations and highlighting the importance of including such singularities in partial wave analyses.

## Contribution

It introduces a quantitative evaluation of the triangle singularity's effect on the $ o p o p o p o p$ reaction, emphasizing the need to incorporate these singularities in standard analyses.

## Key findings

- The cross section aligns with experimental data when including the triangle singularity.
- Standard partial wave analysis may miss effects from triangle singularities.
- Explores extending analysis methods to account for triangle singularities.

## Abstract

We have studied the $\gamma p \to p \pi^0 \eta$ reaction paying attention to the two main mechanisms at low energies, the $\gamma p \to \Delta(1700) \to \eta \Delta(1232)$ and the $\gamma p \to \Delta(1700) \to \pi N(1535)$. Both of them are driven by the photoexcitation of the $\Delta(1700)$ 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 to explore possible triangle singularities in other reactions and how a standard partial analysis can be extended to accommodate them.