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

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

2008-04-29

arxiv.org/abs/0804.4670v1

Eur.Phys.J.A37:233-243,2008

Physics

Nuclear Physics

Nuclear Theory

Scientific paper

10.1140/epja/i2008-10625-3

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 $1704 - i 375/2$ MeV and with quantum numbers $I=1/2$, $J^\pi =1/2^+$. We identify this state with the $N^*(1710)$. 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 $5/2$.

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