Abstract
Nambu-Goldstone bosons, or axions, may be ubiquitous. Some of the axions may have small masses and thus serve as mediators of long-range forces. In this paper, we study the force mediated by an extremely light axion, $\ensuremath{\phi}$, between the visible sector and the dark sector, where dark matter lives. Since nature does not preserve the $CP$ symmetry, the coupling between dark matter and $\ensuremath{\phi}$ is generically $CP$ violating. In this case, the induced force is extremely long range and behaves as an effective magnetic field. If the force acts on electrons or nucleons, the spins of them on Earth precess around a fixed direction toward the Galactic Center. This provides an experimental opportunity for $\ensuremath{\phi}$ with mass, ${m}_{\ensuremath{\phi}}$, and decay constant, ${f}_{\ensuremath{\phi}}$, satisfying ${m}_{\ensuremath{\phi}}\ensuremath{\lesssim}{10}^{\ensuremath{-}25}\text{ }\text{ }\mathrm{eV}$, ${f}_{\ensuremath{\phi}}\ensuremath{\lesssim}{10}^{14}\text{ }\text{ }\mathrm{GeV}$ if the daily modulation of the effective magnetic field signals in magnetometers is measured by using the coherent averaging method. The effective magnetic field induced by an axionic compact object, such as an axion domain wall, is also discussed.
Highlights
Despite the evidence of CP violation, the strong sector has a very good CP-symmetric structure, which is unnatural and dubbed as a strong CP problem
In Appendix A, we show that various sources in concrete models of the dark sector can be COSMIC AXION FORCE
Even if we introduce the QCD axion to solve the strong CP problem, a CP-violating weak interaction drives the minimum of the QCD axion slightly away from the CP-conserving place
Summary
Despite the evidence of CP violation, the strong sector has a very good CP-symmetric structure, which is unnatural and dubbed as a strong CP problem. We study the possibility that an ultralight axion plays the role of cosmically long-range force between the CP-violating dark sector and the visible sector particles. We point out that via the monopole-dipole interaction the cosmic axion force behaves as an effective magnetic field, which induces the spin precessions of axion-coupled SM fermions all over the Earth around a fixed direction (see Fig. 1). This axioninduced magnetic field remains intact when the ordinary magnetic fields are shielded.
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