We explore the possibility that the dark matter relic density is not produced by thermal mechanism directly, but by the decay of other heavier dark sector particles which on the other hand can be produced by the thermal freeze-out mechanism. Using a concrete model with a light dark matter from dark sector decay, we study the collider signature of the dark sector particles in association with Higgs production processes. We find that the future lepton colliders can be a better place to probe the signature of this kind of light dark matter model than the hadron collider such as LHC. Meanwhile, it is found that a Higgs factory with center of mass energy 250 GeV has a better potential to resolve the signature of this kind of light dark matter model than the Higgs factory with center of mass energy 350 GeV.
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