# Patterns and partners for chiral symmetry restoration

## TL;DR

This paper introduces new Ward Identities to distinguish different patterns of chiral symmetry restoration in QCD, predicting degeneracies among meson partners and supporting specific mixing scenarios, with validation against lattice data.

## Contribution

It provides a novel set of Ward Identities that clarify the relationship between $O(4)$ and $U(1)_A$ symmetry restoration patterns in QCD, including predictions for meson partner degeneracies.

## Key findings

- Degeneracy of chiral partners around $O(4)$ restoration.
- Predicted degeneracy of $U(1)_A$ partners near $O(4)$ restoration.
- Support for ideal mixing in certain meson sectors at $O(4)\times U(1)_A$ restoration.

## Abstract

We present and analyze a new set of Ward Identities which shed light on the distinction between different patterns of chiral symmetry restoration in QCD, namely $O(4)$ vs $O(4)\times U(1)_A$. The degeneracy of chiral partners for all scalar and pseudoscalar meson nonet members are studied through their corresponding correlators. Around chiral symmetry degeneration of $O(4)$ partners, our analysis predicts that $U(1)_A$ partners are also degenerated. Our analysis also leads to $I=1/2$ scalar-pseudoscalar partner degeneration at exact chiral restoration, and supports ideal mixing between the $\eta$-$\eta^\prime$ and the $f_0(500)$-$f_0(980)$ mesons at $O(4)\times U(1)_A$ restoration, with a possible range where the pseudoscalar mixing vanishes if the two transitions are well separated. We test our results with lattice data and provide further relevant observables regarding chiral and $U(1)_A$ restoration for future lattice and model analyses.