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We consider a simple class of models in which the relic density of dark matter is determined by the baryon asymmetry of the Universe. In these models a B-L asymmetry generated at high temperatures is transferred to the dark matter, which is charged under B-L. The interactions that transfer the asymmetry decouple at temperatures above the dark matter mass, freezing in a dark matter asymmetry of order the baryon asymmetry. This explains the observed relation between the baryon and dark matter densities for the dark matter mass in the range 5--15 GeV. The symmetric component of the dark matter can annihilate efficiently to light pseudoscalar Higgs particles a or via t-channel exchange of new scalar doublets. The first possibility allows for h^0 decays, while the second predicts a light charged Higgs-like scalar decaying to. Direct detection can arise from Higgs exchange in the first model or a nonzero magnetic moment in the second. In supersymmetric models, the would-be lightest supersymmetric partner can decay into pairs of dark matter particles plus standard model particles, possibly with displaced vertices.
Kaplan et al. (Tue,) studied this question.