# Role of a triangle singularity in the $\pi \Delta$ decay of the $N(1700)(3/2^-)$

## TL;DR

This paper demonstrates that a triangle singularity significantly influences the $
(1700)$ resonance's decay, emphasizing the importance of including the $\pi\Delta$ channel in coupled channel models for accurate resonance description.

## Contribution

It introduces the role of a triangle singularity in the $\pi\Delta$ decay channel of the $N(1700)$ resonance, which was previously neglected, showing its impact on the resonance's width and decay predictions.

## Key findings

- Inclusion of the $\pi\Delta$ channel increases the $N(1700)$ width.
- The triangle singularity enhances the coupled channel interaction.
- Predictions for partial decay widths into $VB$ and $\pi\Delta$ are provided.

## Abstract

We show the important role played by the $\pi\Delta(1232)$ channel in the build up of the $N(1700)(3/2^-)$ resonance due to the non-trivial enhancement produced by a singularity of a triangular loop. The $N(1700)$ is one of the dynamically generated resonances produced by the coupled channel vector-baryon interaction. The $\pi\Delta$ channel was neglected in previous works but we show that it has to be incorporated into the coupled channel formalism due to an enhancement produced by a singularity in the triangular loop with $\rho$, nucleon and $\pi$ as internal loop lines and $\pi$ and $\Delta$ as external ones. The enhancement is of non-resonant origin but it contributes to the dynamical generation of the $N(1700)$ resonance due to the non-linear dynamics involved in the coupled channel mechanisms. We obtain an important increase of the total width of the $N(1700)$ resonance when the $\pi\Delta$ channel is included and provide predictions for the partial widths of the $N(1700)$ decays into $VB$ and $\pi\Delta$.