Connection between a Possible Fifth Force and the Direct Detection of Dark Matter

If there were a fifth force in the dark sector and dark matter (DM) particles interacted nongravitationally with ordinary matter, quantum corrections generically would lead to a fifth force in the visible sector. We show how the strong experimental limits on fifth forces in the visible sector produce bounds on the cross section for DM detection and the strength of the fifth force in the dark sector. For a fifth force comparable in strength to gravity, the spin-independent direct detection cross section must typically be $\lesssim {10}^{-55}{\mathrm{cm}}^2$. The anomalous acceleration of ordinary matter falling towards dark matter would also be constrained: ${\eta }_{\mathrm{OM}-\mathrm{DM}}\lesssim {10}^{-8}$.

Figure 1

(a) Direct detection four-fermion vertex coupling quarks and dark matter fermions $\chi$. (b) Fifth force Yukawa interaction for fermionic dark matter.

Figure 2

An effective Yukawa interaction of ordinary matter particles arises due to a quantum correction.