# Naive versus mirror assignment at finite density: correlator mixing and chiral symmetry restoration

## TL;DR

This paper investigates how chiral symmetry constraints affect hadron correlation functions in dense media, focusing on correlator mixing and partial symmetry restoration, with implications for mesons and nucleons under different chiral assignments.

## Contribution

It analyzes the effects of naive and mirror chiral assignments on correlator mixing and chiral symmetry restoration in dense nuclear matter.

## Key findings

- Correlator mixing reflects partial chiral symmetry restoration.
- Different chiral assignments lead to distinct mixing patterns.
- Soft pion corrections influence quark condensates and hadron properties.

## Abstract

Chiral symmetry imposes some constrains on hadron correlation functions in dense medium. These constraints imply a certain general structure of the two- and three-point correlation functions of chiral partners and lead to the effect of mixing arising from the interaction of the long-ranged nuclear pions with corresponding interpolating currents. It reflects the phenomena of partial restoration of chiral symmetry. We consider soft pion corrections for quark condensates and several possible pairs of chiral partners for both mesons and nucleons and analyse their mixing patterns. We explored both naive and mirror assignments for the chiral partner of nucleon and discussed possible phenomenological consequence.