Solution to Faddeev equations with two-body experimental amplitudes as input and application to J^P=1/2^+, S=0 baryon resonances

Abstract

We solve the Faddeev equations for the two meson-one baryon system $\pi \pi N$ and coupled channels using the experimental two-body $t$-matrices for the $\pi N$ interaction as input and unitary chiral dynamics to describe the interaction between the rest of coupled channels. In addition to the $N^{\ast }(1710)$ obtained before with the $\pi \pi N$ channel, we obtain, for $J^{\pi }=1/2^{+}$ and total isospin of the three-body system $I=1/2$, a resonance peak whose mass is around 2080 MeV and width of 54 MeV, while for $I=3/2$ we find a peak around 2126 MeV and 42 MeV of width. These two resonances can be identified with the $N^{\ast }(2100)$ and the $\Delta (1910)$, respectively. We obtain another peak in the isospin 1/2 configuration, around 1920 MeV which can be interpreted as a resonance in the $N{a}_0(980)$ and $N{f}_0(980)$ systems.

published version

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