Axion forces in axion backgrounds

Abstract

Axions can naturally be very light due to the protection of an (approximate) shift symmetry. Because of their pseudoscalar nature, the long-range force mediated by the axion at tree level is spin dependent, which cannot lead to observable effects between two unpolarized macroscopic objects. At the one-loop level, however, the exchange of two axions does mediate a spin-independent force. This force is coherently enhanced in the presence of an axion background. In this work, we study the two-axion exchange force in a generic axion background. We find that the breaking of the axion shift symmetry plays a crucial role in determining this force. The background-induced axion force $V_{\rm bkg}$ vanishes in the shift-symmetry restoration limit. The shift symmetry can be broken either explicitly by non-perturbative effects or effectively by the axion background. When the shift symmetry is broken, $V_{\rm bkg}$ scales as $1/r$ and could be further enhanced by a large occupation number of the background axions. We investigate possible experimental probes of this effect in two distinct scenarios: an axion dark matter background and a solar axion flux, using fifth-force searches and atomic spectroscopy experiments. In the axion dark matter case, we find that the background-induced axion force can place strong constraints on axion couplings and masses, comparable to existing astrophysical bounds.

Figures (13)

• Figure 1: Feynman diagrams of two-axion exchange between two fermions $\psi_1$ and $\psi_2$. Each of them can be affected by an axion background.
• Figure 2: Effective box diagrams in the medium of axions that contribute to the background-induced axion force through coherent scattering. The four diagrams in the first line correspond to the "Box 1" diagram in Fig. \ref{['fig:Feyn']}, while those in the second line correspond to the "Box 2" diagram in Fig. \ref{['fig:Feyn']}. See App. \ref{['app:coherent-scattering']} for detailed calculations.
• Figure 3: The comparison between the background-induced axion force $V_{\rm bkg}$ in the coherent region [Eq. (\ref{['eq:Vcoh']})] and its vacuum counterpart $V_{2a}$ [Eq. (\ref{['eq:V2a']})]. Note that the dependence on both $\mu$ and $f_a$ is cancelled in the ratio $V_{\rm bkg}/V_{2a}$, indicating that these two terms are of the same order from the view of effective field theories. We have fixed $\rho_a = \rho_{\rm DM} \approx 0.4~{\rm GeV}/{\rm cm}^3$ as the local density of DM. We also take the typical de Broglie wavelength as $\lambda_{\rm dB} = 1/(m_a v_a)$, with $v_a \approx 10^{-3}$ the average velocity of the axion DM. Different curves in the plot correspond to the comparison at different length scales.
• Figure 4: The phase-space form factor ${\cal F}_{\rm PS}$. Left panel: the scaling behavior of the magnitude of ${\cal F}_{\rm PS}$ with $r$ for different values of $\alpha$. Note the cusps correspond to the place where ${\cal F}_{\rm PS}$ changes sign. Right panel: the contour plot of ${\cal F}_{\rm PS}$ as a function of $r$ and $\alpha$.
• Figure 5: The schematic plot of the axion force in the background of the axion DM wind between a finite-size source and a point-like target.