Semielastic Dark Matter

Many models have recently been proposed in which dark matter (DM) couples to Standard Model fields via a GeV-scale dark sector. We consider scenarios of this type where the DM mass, at the electroweak/TeV scale, is generated by the VEV of a singlet which also couples to the Higgs. Such a setup results in a distinct recoil spectrum with both elastic and inelastic components. We construct an explicit NMSSM-like realization of this setup, discuss constraints coming from the relic density, and include benchmark points which are consistent with current limits, yet visible at upcoming direct detection experiments.