Chiral condensate in nuclear matter beyond linear density using chiral Ward identity

Abstract

We discuss density corrections of the chiral condensate up to a NLO order us- ing the chiral Ward identity and an in-medium chiral perturbation theory. The in-medium chiral condensate is calculated by a correlation function of the axial current and pseu- doscalar density in the nuclear matter as a consequence of the chiral Ward identity. The correlation function is evaluated using the chiral perturbation theory with the hadronic quantities of pion-nucleon dynamics. We assume that the in-vacuum interaction vertices are known, which means that the in-vacuum loop corrections are renormalized to the tree chiral couplings by taking the values of the couplings in chiral Lagrangian as the physical values. We focus on density order in the physical quantities in our perturbative calcula- tion. This study shows that the medium effects to the chiral condensate beyond the linear density come from density corrections to theN sigma term. It implies that calculating the density dependence of the chiral condensate in nuclear matter is essentially equivalent to describe nuclear matter in chiral effective theory.