We show that the momentum dependence of dark matter interactions with nuclei
can be probed in direct detection experiments without knowledge of the dark
matter velocity distribution. This is one of the few properties of DM
microphysics that can be determined with direct detection alone, given a signal
of dark matter in multiple direct detection experiments with different targets.
Long-range interactions arising from the exchange of a light mediator are one
example of momentum-dependent DM. For data produced from the exchange of a
massless mediator we find for example that the mediator mass can be constrained
to be ≲10 MeV for DM in the 20-1000 GeV range in a halo-independent
manner.Comment: 15 pages, 4 figures; updated to match published versio
