Chiral condensate at finite density using the chiral Ward identity

Abstract

To study partial restoration of the chiral symmetry at finite density, we investigate the density corrections of the chiral condensate up to the next-to-leading order of density expansion using the chiral Ward identity and an in-medium chiral perturbation theory. In our study, we assume that all the in-vacuum quantities for the pion, the nucleon, and the πN interaction are determined in vacuum and focus on density expansion of the in-medium physical quantities. We perform diagrammatic analysis of the correlation functions which provide the in-medium chiral condensate. This density expansion scheme shows that the medium effect to the chiral condensate beyond the linear density comes from density corrections to the πN σ term as a result of the interactions between pion and nucleon in nuclear matter. We also discuss that higher-density contributions beyond the order of ρ2 cannot be fixed only by the in-vacuum πN dynamics and we encounter divergence in the calculation of the ρ2-order corrections of the chiral condensate. To remove the divergence, we need NN two-body contact interaction, which can be fixed in vacuum.