Chiral condensate at finite density using the chiral Ward identity

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 pi N 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 pi N sigma 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 rho(2) cannot be fixed only by the in-vacuum pi N dynamics and we encounter divergence in the calculation of the rho(2)-order corrections of the chiral condensate. To remove the divergence, we need NN two-body contact interaction, which can be fixed in vacuum.