In-medium chiral condensate beyond linear density approximation

In-medium chiral perturbation theory is used to calculate the density dependence of the quark condensate . The corrections beyond the linear density approximation are obtained by differentiating the interaction contributions to the energy per particle of isospin-symmetric nuclear matter with respect to the pion mass. Our calculation treats systematically the effects from one-pion exchange (with mπ-dependent vertex corrections), iterated 1π-exchange, and irreducible 2π-exchange including intermediate Δ(1232)-isobar excitations, with Pauli-blocking corrections up to three-loop order. We find a strong and nonlinear dependence of the ''dropping'' in-medium condensate on the actual value of the pion (or light quark) mass. In the chiral limit, mπ=0, chiral restoration appears to be reached already at about 1.5 times normal nuclear matter density. By contrast, for the physical pion mass, mπ=135 MeV, the in-medium condensate stabilizes at about 60% of its vacuum value above that same density. Effects from 2π-exchange with virtual Δ(1232)-isobar excitations turn out to be crucial in generating such pronounced deviations from the linear density approximation above ρ0. The hindered tendency toward chiral symmetry restoration provides a justification for using pions and nucleons as effective low-energy degrees of freedom at least up to twice nuclear matter density