# Axions, Instantons, and the Lattice

## TL;DR

This paper evaluates the uncertainties in the temperature-dependent topological susceptibility of QCD and their impact on axion relic density predictions, combining lattice results and instanton calculations to refine axion mass estimates.

## Contribution

It provides a reassessment of the instanton contribution uncertainty and combines it with models for hi(T) to improve axion relic density predictions.

## Key findings

- Instanton contribution uncertainty is less than 20% in the effective action.
- Combined uncertainties lead to a factor of 2-3 in the zero-temperature axion mass.
- Refined estimates help constrain axion dark matter models.

## Abstract

If the QCD axion is a significant component of dark matter, and if the universe was once hotter than a few hundred MeV, the axion relic abundance depends on the function $\chi(T)$, the temperature-dependent topological susceptibility. Uncertainties in this quantity induce uncertainties in the axion mass as a function of the relic density, or vice versa. At high temperatures, theoretical uncertainties enter through the dilute instanton gas computation, while in the intermediate and strong coupling regime, only lattice QCD can determine $\chi(T)$ precisely. We reassess the uncertainty on the instanton contribution, arguing that it amounts to less than $20\%$ in the effective action, or a factor of 20 in $\chi$ at $T=1.5$ GeV. We then combine the instanton uncertainty with a range of models for $\chi(T)$ at intermediate temperatures and determine the impact on the axion relic density. We find that for a given relic density and initial misalignment angle, the combined uncertainty amounts to a factor of 2-3 in the zero-temperature axion mass.