Axion cosmology, lattice QCD and the dilute instanton gas

TL;DR

This paper uses lattice QCD to calculate the topological susceptibility relevant for axion dark matter, comparing results with the dilute instanton gas approximation and discussing implications for axion cosmology.

Contribution

It provides the first continuum-extrapolated lattice QCD results for topological susceptibility in the quenched approximation, comparing them with DIGA predictions.

Findings

Good agreement in temperature dependence between lattice results and DIGA

DIGA normalization differs by a factor of ten from lattice results

Implications for axion dark matter abundance are discussed

Abstract

Axions are one of the most attractive dark matter candidates. The evolution of their number density in the early universe can be determined by calculating the topological susceptibility $\chi(T)$ of QCD as a function of the temperature. Lattice QCD provides an ab initio technique to carry out such a calculation. A full result needs two ingredients: physical quark masses and a controlled continuum extrapolation from non-vanishing to zero lattice spacings. We determine $\chi(T)$ in the quenched framework (infinitely large quark masses) and extrapolate its values to the continuum limit. The results are compared with the prediction of the dilute instanton gas approximation (DIGA). A nice agreement is found for the temperature dependence, whereas the overall normalization of the DIGA result still differs from the non-perturbative continuum extrapolated lattice results by a factor of order ten. We discuss the consequences of our findings for the prediction of the amount of axion dark matter.