  We study direct detection in simplified models of Dark Matter (DM) in which
interactions with Standard Model (SM) fermions are mediated by a heavy vector
boson. We consider fully general, gauge-invariant couplings between the SM, the
mediator and both scalar and fermion DM. We account for the evolution of the
couplings between the energy scale of the mediator mass and the nuclear energy
scale. This running arises from virtual effects of SM particles and its
inclusion is not optional. We compare bounds on the mediator mass from direct
detection experiments with and without accounting for the running. In some
cases the inclusion of these effects changes the bounds by several orders of
magnitude, as a consequence of operator mixing which generates new interactions
at low energy. We also highlight the importance of these effects when
translating LHC limits on the mediator mass into bounds on the direct detection
cross section. For an axial-vector mediator, the running can alter the derived
bounds on the spin-dependent DM-nucleon cross section by a factor of two or
more. Finally, we provide tools to facilitate the inclusion of these effects in
future studies: general approximate expressions for the low energy couplings
and a public code runDM to evolve the couplings between arbitrary energy
scales.
