# Topology in the SU(N_f) chiral symmetry restored phase of unquenched QCD and axion cosmology II

## TL;DR

This paper explores the effects of the U(1)_A anomaly in the chiral symmetric phase of unquenched QCD, revealing singular behaviors in free energy and susceptibilities that challenge recent numerical simulation results.

## Contribution

It demonstrates that the U(1)_A anomaly effects persist in the chiral symmetric phase and predicts divergent susceptibilities, providing new insights into QCD phase structure.

## Key findings

- Free energy density is singular in the chiral limit at T ≥ T_c.
- Susceptibilities of σ and π diverge in the chiral limit.
- Difference between π and δ susceptibilities diverges, conflicting with recent simulations.

## Abstract

We investigate the physical consequences of the survival of the effects of the U(1)_A anomaly in the chiral symmetric phase of QCD, and show that the free energy density is a singular function of the quark mass m, in the chiral limit, and that the $\sigma$ and $\bar\pi$ susceptibilities diverge in this limit at any $T\ge T_c$. We also show that the difference between the $\bar\pi$ and $\bar\delta$ susceptibilities diverges in the chiral limit at any $T\ge T_c$, a result which seems to be excluded by recent results of Tomiya et al. from numerical simulations of two-flavor QCD. We also discuss on the generalization of these results to the $N_f\ge 3$ model.