Scattering versus collider production of dark matter

A low-momentum dark-matter–nucleon elastic cross section and a high-energy collider pair-production cross section are different observables. Crossing of amplitudes does not equate their numerical values. Mediator masses, couplings, nuclear matrix elements, parton distributions and kinematics enter the relation. Collider sensitivity further requires a trigger, visible recoil, acceptance and background treatment. Multiplying a direct-detection cross section by collider luminosity is therefore only a hypothetical dimensional estimate unless a production model justifies the substitution.