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

Abstract

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 $ρ$, $ω$ and $ϕ$ in nuclear matter. We find that in-medium modifications of the $ρ$ and $ω$ mesons are essentially dominated by the dependence of the 4-quark condensate on the nucleon density. In particular, the numerical value of a parameter ($κ_N$), which describes the strength of the density dependence of the 4-quark condensate beyond the mean-field approximation, governs the decrease of the $ρ$ mass as a function of the density. For the $ω$ meson the sign of the in-medium mass shift is changed by variations of $κ_N$. To study consistently the in-medium broadening of the light vector mesons we employ $ρN$ and $ωN$ scattering amplitudes derived recently from a covariant unitary coupled channel approach adjusted to pion- and photo-induced reactions. In contrast to the $ρ$ and $ω$ mesons, the in-medium mass of the $ϕ$ 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.