Constraints on nuclear matter properties from QCD susceptibilities

We establish the interrelation between the QCD scalar response of the nuclear medium and its response to a scalar probe coupled to nucleons, such as the scalar meson responsible for the nuclear binding. The relation that we derive applies at the nucleonic as well as at the nuclear levels. Non trivial consequences follow. In particular it opens the possibility of relating medium effects in the scalar meson exchange or three-body forces of nuclear physics to QCD lattice studies of the nucleon mass