Dark-Matter-Induced Violation of the Weak Equivalence Principle

A long-range fifth force coupled to dark matter can induce a coupling to ordinary matter if the dark matter interacts with standard model fields. We consider constraints on such a scenario from both astrophysical observations and laboratory experiments. We also examine the case where the dark matter is a weakly interacting massive particle, and derive relations between the coupling to dark matter and the coupling to ordinary matter for different models. Currently, this scenario is most tightly constrained by galactic dynamics, but improvements in Eötvös experiments can probe unconstrained regions of parameter space.

Figure 1

Constraints on the strength of fifth forces coupled to ordinary matter and/or dark matter. The horizontal axis is the effective coupling to ordinary matter $g_{*}$ divided by the proton mass $m_p$, while the vertical axis is the Yukawa coupling to DM $g_{\chi }$ divided by the mass $m_{\chi }$ of the DM, both in units of inverse GeV. The vertical line (in blue) is the constraint from Eötvös experiments with ordinary-matter sources; the horizontal line (in red) is from DM tidal tails; and the diagonal line in the top right quadrant (in green) is from the searches for anomalous accelerations in the direction of the Galactic center. The diagonal band running from bottom left to top right (in yellow) is the range of predictions from the WIMP models we consider.

Figure 2

Two-loop graph inducing an interaction between a massless scalar $\varphi$ and a Dirac fermion $\psi$, mediated by a WIMP $\chi$ and hypercharge gauge bosons $B$.

Figure 3

Two-loop ‘‘Compton scattering” graph inducing an interaction between a massless scalar $\varphi$ and a Dirac fermion $\psi$, mediated by a WIMP $\chi$ and electroweak gauge bosons.

Figure 4

One-loop graph involving scalar sfermions $\tilde{\psi }$.