Chiral condensate at finite density using chiral Ward identity

TL;DR

This paper investigates how the chiral condensate changes at finite density using chiral Ward identities and in-medium chiral perturbation theory, focusing on density corrections up to next-leading order.

Contribution

It introduces a density expansion scheme for the in-medium chiral condensate that accounts for interactions between pions and nucleons beyond linear density.

Findings

Medium effects beyond linear density originate from pi N sigma term corrections.

Higher density contributions require NN two-body dynamics for divergence fixing.

Density corrections beyond order rho^2 involve complex in-medium interactions.

Abstract

In order to study partial restoration of the chiral symmetry at finite density, we investigate the density corrections of the chiral condensate up to next-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 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 medium effects to the chiral condensate beyond the linear density come 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 order of rho^2 cannot be fixed only by the in-vacuum pi N dynamics but we need NN two-body dynamics in vacuum to fix divergence appearing in the calculation of the rho^2 dependence of the chiral condensate with the pi N dynamics.