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

Abstract

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 ${\Sigma }_{med}$ 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 ${\Sigma }_{med}$, 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.

47 pages, 19 figures, some discussion and formulae added, minor typos removed, accepted for publication in Nuclear Physics A

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