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Scattering of Dark Particles with Light Mediators

We present a treatment of the high energy scattering of dark Dirac fermions from nuclei, mediated by the exchange of a light vector boson. The dark fermions are produced by proton-nucleus interactions in a fixed target and, after traversing shielding that screens out strongly interacting products, appear similarly to neutrino neutral current scattering in a detector. Using the Fermilab experiment E613 as an example, we place limits on a secluded dark matter scenario. Visible scattering in the detector includes both the familiar regime of large momentum transfer to the nucleus ($Q^2$) described by deeply inelastic scattering, as well as small $Q^2$ kinematics described by the exchanged vector mediator fluctuating into a quark-antiquark pair whose interaction with the nucleus is described by a saturation model. We find that the improved description of the low $Q^2$ scattering leads to important corrections, resulting in more robust constraints in a regime where a description entirely in terms of deeply inelastic scattering cannot be trusted.