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We show the important role played by the $\pi\Delta(1232)$ channel in thebuild up of the $N(1700)(3/2^-)$ resonance due to the non-trivial enhancementproduced by a singularity of a triangular loop. The $N(1700)$ is one of thedynamically generated resonances produced by the coupled channel vector-baryoninteraction. The $\pi\Delta$ channel was neglected in previous works but weshow that it has to be incorporated into the coupled channel formalism due toan enhancement produced by a singularity in the triangular loop with $\rho$,nucleon and $\pi$ as internal loop lines and $\pi$ and $\Delta$ as externalones. The enhancement is of non-resonant origin but it contributes to thedynamical generation of the $N(1700)$ resonance due to the non-linear dynamicsinvolved in the coupled channel mechanisms. We obtain an important increase ofthe total width of the $N(1700)$ resonance when the $\pi\Delta$ channel isincluded and provide predictions for the partial widths of the $N(1700)$ decaysinto $VB$ and $\pi\Delta$.

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