QCD Sum Rules and Vector Mesons in Nuclear Matter

Based on an effective Lagrangian which combines chiral SU(3) dynamics with vector meson dominance, we have developed a model for the s-wave vector meson-nucleon scattering amplitudes. We use this as an input for the low energy part of the current-current correlation function in nuclear matter. Its spectrum enters directly in the ``left hand side'' of QCD sum rules. For the isovector channel we find a significant enhancement of the in-medium spectral density below the $\rho$ resonance while the mass of $\rho$ meson itself decreases only slightly. The situation is different in the isoscalar channel. Here the mass and therefore the peak position of the $\omega$ meson decreases strongly while the width increases less drastically than in the $\rho$ meson case. For the $\phi$ meson we find almost no mass shift, the width of the peak broadens due to the imaginary part of the scattering length. We find a remarkable degree of consistency with the operator product expansion of QCD sum rules in all three channels.