# Triangle mechanisms in the build up and decay of the $N^*(1875)$

## TL;DR

This paper investigates the $N^*(1875)$ resonance using a multichannel unitary approach, revealing significant decay channels and the importance of triangle diagrams, with implications for experimental analysis.

## Contribution

It introduces a multichannel unitary scheme incorporating triangle diagrams to study the $N^*(1875)$ resonance, highlighting the role of specific decay channels and singularities.

## Key findings

- Large decay width to $ ext{Σ}^* K$ channel
- Triangle singularity at the resonance energy
- Significant role of $N \sigma$ in $ ext{π} ext{π}$ mass distributions

## Abstract

We have studied the $N^*(1875) (3/2^-)$ resonance with a multichannel unitary scheme, considering the $\Delta \pi$ and $\Sigma^* K$, with their interaction extracted from chiral Lagrangians, and then have added two more channels, the $N^*(1535) \pi$ and $N \sigma$, which proceed via triangle diagrams involving the $\Sigma^* K$ and $\Delta \pi$ respectively in the intermediate states. The triangle diagram in the $N^*(1535) \pi$ case develops a singularity at the same energy as the resonance mass. We determine the couplings of the resonance to the different channels and the partial decay widths. We find a very large decay width to $\Sigma^* K$, and also see that, due to interference with other terms, the $N \sigma$ channel has an important role in the $\pi \pi$ mass distributions at low invariant masses, leading to an apparently large $N \sigma$ decay width. A discussion is done, justifying the convenience of an experimental reanalysis of this resonance to the light of the findings of the paper, using multichannel unitary schemes.