Role of a triangle singularity in the π Δ decay of N(1700)(3/2-)

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 nontrivial 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., nucleon, and p as internal loop lines and pi and Delta as external ones. The enhancement is of nonresonant origin but it contributes to the dynamical generation of the N(1700) resonance due to the nonlinear 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.