Baryon resonance spectroscopy in a unitary isobar model

In an effort to analyze the baryon spectrum in low and medium energies a unitary isobar model (UIM) is proposed. To build the proposed model, we first exhibit the full complex structure of the meson-baryon reaction amplitude in coupled channels approach. By doing so, the reaction amplitude is expressed in a form that may be viewed as the generalization of the well-known Watson's theorem in photoproduction. Furthermore, the reaction amplitude is decomposed into the so-called pole and non-pole parts, corresponding basically to the resonant and background contributions. This allowed us to construct a UIM in which unitarity is maintained automatically.

As the first application of the proposed UIM, we performed simultaneous analyses of the reactions $\pi N \rightarrow \pi N$, $\pi N \rightarrow \eta N$, $\pi N \rightarrow \omega N$, and $\gamma N \rightarrow \omega N$. In total our model required 8 isospin $T = 1/2$ and 4 isospin $T = 3/2$ resonances to describe the $\pi N$ elastic scattering. We found a significant contribution from $N(1520)\frac{3}{2}^-$, $N(1700)\frac{3}{2}^-$, and $N(1680)\frac{5}{2}^+$ to both pion and photon-induced $\omega$ production. Besides those 3 resonances we saw a large contribution from $N(1675)\frac{5}{2}^-$ in $\gamma N \rightarrow \omega N$ reaction. In $\pi N \rightarrow \eta N$ reaction apart from the well known dominant contribution of the $N(1535)\frac{1}{2}^-$ for low energies, we also found a significant contribution of the $N(1680)\frac{5}{2}^+$.