$2\pi$ production in the Giessen coupled-channel model

Abstract

We present a coupled-channel Lagrangian approach (GiM) to describe the $\pi N\to \pi N$, $2\pi N$ scattering in the resonance energy region. The $2\pi N$ production has been significantly improved by using the isobar approximation with $\sigma N$ and $\pi \Delta (1232)$ in the intermediate state. The three-body unitarity is maintained up to interference pattern between the isobar subchannels. The scattering amplitudes are obtained as a solution of the Bethe-Salpeter equation in the $K$ matrix approximation. As a first application we perform a partial wave analysis of the $\pi N\to \pi N$, ${\pi }^0{\pi }^{0}N$ reactions in the Roper resonance region. We obtain $R_{\sigma N}(1440)=27_{-9}^{+4}$\,\% and $R_{\sigma N}(1440)=12_{-3}^{+5}$\,\% for the $\sigma N$ and $\pi \Delta$ decay branching ratios of $N^{\ast }(1440)$ respectively. The extracted $\pi N$ inelasticities and reaction amplitudes are consistent with the results from other groups.

Comments: replaced with the published version