In-medium chiral condensate beyond linear density approximation

Abstract

In-medium chiral perturbation theory is used to calculate the density dependence of the quark condensate $<\bar qq>$. 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 non-linear 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 $ρ_0$. The hindered tendency towards 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.