Axions, Instantons, and the Lattice

Understand

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.