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

TL;DR

This paper solves Faddeev equations for a three-body meson-baryon system using experimental two-body amplitudes, predicting new baryon resonances around 1920, 2080, and 2126 MeV, and identifying them with known states.

Contribution

It introduces a novel method combining experimental two-body data with chiral dynamics to predict baryon resonances in a three-body system.

Findings

Identified a resonance around 2080 MeV as N*(2100).

Found a resonance near 2126 MeV corresponding to Δ(1910).

Discovered a peak around 1920 MeV as a resonance in N a0(980) and N f0(980) systems.

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 $N^*(1710)$ 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 $N^* (2100)$ 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.