$\rho$-meson properties at finite nuclear density

Abstract

We calculate the momentum dependence of the $\rho$-meson selfenergy based on the dispersion relation for the $\rho N$ scattering amplitude $f(\omega$) at low nuclear density. The imaginary part of $f(\omega)$ is determined from the optical theorem, while the total $\rho N$ cross section is obtained within the VDM at high energy and within the resonance model at low energy. Our numerical results indicate a sizeable broadening of the $\rho$-meson width in the medium especially for low relative momenta $p$ while the real part of the $\rho$ selfenergy is found to change its sign and becomes repulsive already at momenta above 100 MeV/c. Extrapolating to nuclear saturation density $\rho_0$ we find a dropping of the $\rho$-mass for $p \approx$ 0 in line with the QCD sumrule analysis of Hatsuda while at high energy an increase of the $\rho$-mass in line with the prediction by Eletsky and Joffe is obtained. However, when including a broadening of the baryonic resonances in the medium, the $\rho$-meson mass shift at $p \approx$ 0 becomes slightly repulsive whereas the width increases substantially.