The $N^*(1710)$ as a resonance in the $ππN$ system

Abstract

We study the $ππN$ system by solving the Faddeev equations, for which the input two-body $t$-matrices are obtained by solving the Bethe-Salpeter equation in the coupled channel formalism. The potentials for the $ππ$, $πN$ sub-systems and their coupled channels are obtained from chiral Lagrangians, which have been earlier used to study resonances in these systems successfully. In this work, we find a resonance in the $ππN$ system with a mass of $1704 - i 375/2$ MeV and with quantum numbers $I=1/2$, $J^π=1/2^+$. We identify this state with the $N^*(1710)$. This peak is found where the energies of the $ππ$ sub-system fall in the region of the $σ$ resonance. We do not find evidence for the Roper resonance in our study indicating a more complex structure for this resonance, nor for any state with total isospin $I=3/2$ or $5/2$.