An ultralight pseudoscalar boson

Abstract

Using a fundamental discrete symmetry, ${\mathbf{Z}}_{N}$, we construct a two-axion model with the QCD axion solving the strong-$CP$ problem, and an ultralight axion (ULA) with ${m}_{\mathrm{ULA}}\ensuremath{\approx}1{0}^{\ensuremath{-}22}\text{ }\text{ }\mathrm{eV}$ 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 ${f}_{\mathrm{ULA}}\ensuremath{\sim}{10}^{17}\text{ }\text{ }\mathrm{GeV}$, and ${f}_{\mathrm{QCD}}\ensuremath{\sim}{10}^{11}\text{ }\text{ }\mathrm{GeV}$. 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 $\stackrel{\ensuremath{\rightarrow}}{E}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{B}$ and $G\stackrel{\texttildelow{}}{G}$ couplings. In the simplest models, however, the ULA has identically zero coupling to both $G\stackrel{\texttildelow{}}{G}$ of QCD and $\stackrel{\ensuremath{\rightarrow}}{E}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{B}$ of electromagnetism due to vanishing electromagnetic and color anomalies. The ULA couples to fermions with strength $g\ensuremath{\propto}1/{f}_{\mathrm{ULA}}$. This coupling causes spin precession of nucleons and electrons with respect to the DM wind with period $t\ensuremath{\sim}$ 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.