Impact of the QCD four-quark condensate on in-medium spectral changes of light vector mesons

Within the Borel QCD sum rule approach at finite baryon density we study the role of the four-quark condensates for the modifications of the vector mesons $\rho$, $\omega$ and $\phi$ in nuclear matter. We find that in-medium modifications of the $\rho$ and $\omega$ mesons are essentially dominated by the dependence of the 4-quark condensate on the nucleon density. In particular, the numerical value of a parameter ($\kappa_N$), which describes the strength of the density dependence of the 4-quark condensate beyond the mean-field approximation, governs the decrease of the $\rho$ mass as a function of the density. For the $\omega$ meson the sign of the in-medium mass shift is changed by variations of $\kappa_N$. To study consistently the in-medium broadening of the light vector mesons we employ $\rho N$ and $\omega N$ scattering amplitudes derived recently from a covariant unitary coupled channel approach adjusted to pion- and photo-induced reactions. In contrast to the $\rho$ and $\omega$ mesons, the in-medium mass of the $\phi$ meson is directly related to the chiral (strange) quark condensate. Measurements of the vector meson spectral change in heavy-ion collisions with HADES can shed light on the yet unknown density dependence of the 4-quark condensate.