In-medium chiral condensate beyond linear density approximation

In-medium chiral perturbation theory is used to calculate the density dependence of the quark condensate 〈q̅ q〉. 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 m_π-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, m_π=0, chiral restoration appears to be reached already at about 1.5 times normal nuclear matter density. By contrast, for the physical pion mass, m_π=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.