Axion phenomenology and $\theta$-dependence from $N_f = 2+1$ lattice QCD

TL;DR

This study uses lattice QCD simulations to analyze the topological properties of $N_f=2+1$ QCD at various temperatures, providing insights into axion phenomenology and the temperature dependence of topological susceptibility.

Contribution

It offers the first continuum-extrapolated results for topological susceptibility and charge distribution moments in $N_f=2+1$ QCD at finite temperature, refining axion dark matter predictions.

Findings

Topological susceptibility differs from instanton predictions at high temperatures.

The fourth moment of the topological charge aligns with dilute instanton gas expectations.

Results suggest a shift in the axion dark matter window by nearly an order of magnitude.

Abstract

We investigate the topological properties of $N_f = 2+1$ QCD with physical quark masses, both at zero and finite temperature. We adopt stout improved staggered fermions and explore a range of lattice spacings $a \sim 0.05 - 0.12$ fm. At zero temperature we estimate both finite size and finite cut-off effects, comparing our continuum extrapolated results for the topological susceptibility $\chi$ with predictions from chiral perturbation theory. At finite temperature, we explore a region going from $T_c$ up to around $4\, T_c$, where we provide continuum extrapolated results for the topological susceptibility and for the fourth moment of the topological charge distribution. While the latter converges to the dilute instanton gas prediction the former differs strongly both in the size and in the temperature dependence. This results in a shift of the axion dark matter window of almost one order of magnitude with respect to the instanton computation.