$ρ$-meson properties at finite nuclear density

Abstract

We calculate the momentum dependence of the $ρ$-meson selfenergy based on the dispersion relation for the $ρN$ scattering amplitude $f(ω$) at low nuclear density. The imaginary part of $f(ω)$ is determined from the optical theorem, while the total $ρN$ 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 $ρ$-meson width in the medium especially for low relative momenta $p$ while the real part of the $ρ$ selfenergy is found to change its sign and becomes repulsive already at momenta above 100 MeV/c. Extrapolating to nuclear saturation density $ρ_0$ we find a dropping of the $ρ$-mass for $p \approx$ 0 in line with the QCD sumrule analysis of Hatsuda while at high energy an increase of the $ρ$-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 $ρ$-meson mass shift at $p \approx$ 0 becomes slightly repulsive whereas the width increases substantially.