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

Understand

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.