The $N^{\ast }(1710)$ as a resonance in the $\pi \pi N$ system

Abstract

We study the $\pi \pi N$ 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 $\pi \pi$, $\pi N$ 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 $\pi \pi N$ system with a mass of $1704-i375/2$ MeV and with quantum numbers $I=1/2$, $J^{\pi }=1/2^{+}$. We identify this state with the $N^{\ast }(1710)$. This peak is found where the energies of the $\pi \pi$ sub-system fall in the region of the $\sigma$ 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 $5/2$.