An ultralight pseudoscalar boson

TL;DR

This paper constructs a two-axion model with a QCD axion and an ultralight axion (ULA) that can serve as dark matter, with detectable cosmological and experimental signatures, addressing small-scale structure issues.

Contribution

It introduces a discrete symmetry-based two-axion model with specific decay constants, providing a natural explanation for dark matter composition and potential detectability.

Findings

The ULA has a mass around 10^{-22} eV suitable for cosmological detection.

The model predicts ULA couplings to fermions within current experimental limits.

The QCD axion remains detectable via standard experimental couplings.

Abstract

Using a fundamental discrete symmetry, $\mathbb{Z}_N$, we construct a two-axion model with the QCD axion solving the strong-$CP$ problem, and an ultralight axion (ULA) with $m_{\rm ULA}\approx 10^{-22}\text{ eV}$ providing the dominant form of dark matter (DM). The ULA is light enough to be detectable in cosmology from its imprints on structure formation, and may resolve the small-scale problems of cold DM. The necessary relative DM abundances occur without fine tuning in constructions with decay constants $f_{\rm ULA}\sim 10^{17}\text{ GeV}$, and $f_{\rm QCD}\sim 10^{11}\text{ GeV}$. An example model achieving this has $N=24$, and we construct a range of other possibilities. We compute the ULA couplings to the Standard Model, and discuss prospects for direct detection. The QCD axion may be detectable in standard experiments through the $\vec{E}\cdot\vec{B}$ and $G\tilde{G}$ couplings. In the simplest models, however, the ULA has identically zero coupling to both $G\tilde{G}$ of QCD and $\vec{E}\cdot\vec{B}$ of electromagnetism due to vanishing electromagnetic and color anomalies. The ULA couples to fermions with strength $g\propto 1/f_{\rm ULA}$. This coupling causes spin precession of nucleons and electrons with respect to the DM wind with period $t\sim$months. Current limits do not exclude the predicted coupling strength, and our model is within reach of the CASPEr-Wind experiment, using nuclear magnetic resonance.