The $\rho$ Spectral Function in a Relativistic Resonance Model

We calculate the spectral function $A_{\rho }$ of the $\rho$ meson in nuclear matter. The calculation is performed in the {\it low density} approximation, where the in-medium self energy ${\mathrm{\Sigma }}_{med}$ is completely determined by the vacuum $\rho N$ forward scattering amplitude. This amplitude is derived from a relativistic resonance model. In comparison to previous non-relativistic calculations we find a much weaker momentum dependence of ${\mathrm{\Sigma }}_{med}$, especially in the transverse channel. Special attention is paid to uncertainties in the model. Thus, we compare the impact of different coupling schemes for the $RN\rho$ interaction on the results and discuss various resonance parameter sets.