QCD sum rules at finite density in the large-Nc limit: the coupling of the ρ-nucleon system to the D13(1520)

QCD sum rules are studied for the vector-isovector current at finite baryon density in the limit of large number of colors Nc. For the condensate side it is shown that in this limit the four-quark condensate factorizes also for the finite density case. At the hadronic side the medium dependence is expressed in terms of the current-nucleon forward scattering amplitude. Generalizing vector meson dominance we allow for a direct coupling of the current to the nucleon as well as a coupling via the ρ meson. We discuss the Nc dependence of (a) modifications of the pion cloud of the ρ meson, (b) mixing with other mesons (in particular a1 and ω) and (c) resonance-hole excitations RN−1. We show that only the last effect survives in the large-Nc limit. Saturating the sum rules with a simple hadronic ansatz which allows for the excitation of the D13(1520) we determine the coupling of the latter to the ρ-nucleon and the photon-nucleon system. These couplings are hard to determine from vacuum physics alone.