# The QCD topological charge and its thermal dependence: the role of the $\eta'$

## TL;DR

This paper investigates how the $ ext{η'}$ meson influences the topological charge distribution in QCD, analyzing its temperature dependence and comparing theoretical predictions with previous studies.

## Contribution

It provides a detailed calculation of the topological susceptibility and cumulant within U(3) Chiral Perturbation Theory up to NNLO, including temperature effects and isospin breaking corrections.

## Key findings

- The topological susceptibility scales with the quark condensate at finite temperature.
- The $ ext{η'}$ meson significantly affects the higher moments of the topological charge.
- The study confirms the validity of thermal scaling relations in the chiral and large-$N_c$ limits.

## Abstract

We analyze the contribution of the $\eta'(958)$ meson in the first two non-trivial moments of the QCD topological charge distribution, namely, the topological susceptibility and the fourth-order cumulant of the vacuum energy density. We perform our study within U(3) Chiral Perturbation Theory up to next-to-next-to-leading order in the combined chiral and large-$N_c$ expansion. We also describe the temperature dependence of these two quantities and compare them with previous analyses in the literature. In particular, we discuss the validity of the thermal scaling of the topological susceptibility with the quark condensate, which is intimately connected with a Ward Identity relating both quantities. We also consider isospin breaking corrections from the vacuum misalignment at leading order in the U(3) framework.