Scattering of vector mesons off nucleons

Abstract

We construct a relativistic and unitary approach to 'high' energy pion- and photon-nucleon reactions taking the $\pi N, \pi \Delta$, $\rho N$, $\omega N$, $\eta N, K \Lambda, K \Sigma$ final states into account. Our scheme dynamically generates the s- and d-wave nucleon resonances N(1535), N(1650) and N(1520) and isobar resonances $\Delta(1620)$ and $\Delta(1700)$ in terms of quasi-local interaction vertices. The description of photon-induced processes is based on a generalized vector-meson dominance assumption which directly relates the electromagnetic quasi-local 4-point interaction vertices to the corresponding vertices involving the $\rho$ and $\omega$ fields. We obtain a satisfactory description of the elastic and inelastic pion- and photon-nucleon scattering data in the channels considered. The resulting s-wave $\rho$- and $\omega$-nucleon scattering amplitudes are presented. Using these amplitudes we compute the leading density modification of the $\rho$ and $\omega$ energy distributions in nuclear matter. We find a repulsive energy shift for the $\omega $ meson at small nuclear density but predict considerable strength in resonance-hole like $\omega$-meson modes. Compared to previous calculations our result for the $\rho$-meson spectral function shows a significantly smaller in-medium effect. This reflects a fairly small coupling strength of the N(1520) resonance to the $\rho N$ channel.