(Non-)Perturbative Dynamics of a Light QCD Axion: Dark Matter and the Strong CP Problem

TL;DR

This paper investigates the complex, nonlinear dynamics of a $Z_ $ QCD axion model, revealing effects on dark matter abundance and the probability of solving the strong CP problem through lattice simulations.

Contribution

First lattice simulations of the $Z_ $ QCD axion model show nonlinear effects can significantly alter dark matter relic density and the likelihood of solving the strong CP problem.

Findings

Nonlinear dynamics can reduce axion relic abundance by up to a factor of two.

Probability of solving the strong CP problem deviates from naive $1/\mathcal{N}$ estimate.

Lattice simulations provide accurate predictions for axion dark matter abundance.

Abstract

Considerable theoretical efforts have gone into expanding the reach of the QCD axion beyond its canonical mass--decay-constant relation. The $Z_\mathcal{N}$ QCD axion model reduces the QCD axion mass naturally, by invoking a discrete $Z_\mathcal{N}$ symmetry through which the axion field is coupled to $\mathcal{N}$ copies of the Standard Model. Before the QCD phase transition at temperature $T_{\rm QCD}$, the $Z_\mathcal{N}$ potential has a minimum at misalignment angle $\theta=\pi$. At $T_{\rm QCD}$, $\theta =\pi$ becomes a maximum; the axion potential becomes exponentially suppressed and develops $\mathcal{N}$ minima -- only one of which actually solves the strong CP problem. Before $T_{\rm QCD}$, $\theta$ relaxes towards $\pi$. After $T_{\rm QCD}$, the axion field starts from around the hilltop and may have sufficient kinetic energy to overcome the newly suppressed potential barriers. Such a field evolution leads to nonlinear effects via the self-interactions near the hilltop, which can cause the exponential growth of fluctuations and backreaction on the coherent motion. This behavior can influence the relic density of the field and the minimum in which it settles. We conduct the first lattice simulations of the $Z_{\mathcal{N}}$ QCD axion using ${\mathcal C}$osmo${\mathcal L}$attice to accurately calculate dark matter abundances and find nonlinear dynamics reduce the abundance by up to a factor of two. We furthermore find that the probability of solving the strong CP problem tends to diverge considerably from the naive expectation of $1/\mathcal{N}$.