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The minimal Higgs portal dark matter model is increasingly in tension with recent results form direct detection experiments like LUX and XENON. In this paper we make a systematic study of simple extensions of the Z₂ stabilized singlet scalar Higgs portal scenario in terms of their prospects at direct detection experiments. We consider both enlarging the stabilizing symmetry to Z₃ and incorporating multipartite features in the dark sector. We demonstrate that in these non-minimal models the interplay of annihilation, co-annihilation and semi-annihilation processes considerably relax constraints from present and proposed direct detection experiments while simultaneously saturating observed dark matter relic density. We explore in particular the resonant semi-annihilation channel within the multipartite Z₃ framework which results in new unexplored regions of parameter space that would be difficult to constrain by direct detection experiments in the near future. The role of dark matter exchange processes within multi-component Z₃ Z₃^ framework is illustrated. We make quantitative estimates to elucidate the role of various annihilation processes in the different allowed regions of parameter space within these models.
Bhattacharya et al. (Sun,) studied this question.