What is the structure of the Roper resonance?

Abstract

We investigate the structure of the nucleon resonance $N^{*}\mathrm{}\left(1440\right)\mathrm{}$ (Roper) within a coupled-channel meson exchange model for pion-nucleon scattering. The coupling to $\pi \pi N$ states is realized effectively by the coupling to the $\sigma N,$ $\pi \Delta ,$ and $\rho N$ channels. The interaction within and between these channels is derived from an effective Lagrangian based on a chirally symmetric Lagrangian, which is supplemented by well known terms for the coupling of the $\Delta$ isobar, the $\omega$ meson, and the $“\sigma ,”$ which is the name given here to the strong correlation of two pions in the scalar-isoscalar channel. In this model the Roper resonance can be described by meson-baryon dynamics alone; no genuine $N^{*}\mathrm{}\left(1440\right)\mathrm{}$ (three quark) resonance is needed in order to fit $\pi N$ phase shifts and inelasticities.