We perform a comprehensive analysis for the light scalar dark matter (DM)in the Inert two Higgs doublet model (i2HDM) with compressed mass spectra, small mass splittings among three $mathbb{Z}_2$ odd particles---scalar $S$, pseudo-scalar $A$, and charged Higgs $H^pm$. In such a case, the co-annihilation processes play a significant role to reduce DM relic density. As long as a co-annihilation governs the total interaction rate in the early universe, a small annihilation rate is expected to reach a correct DM relic density and its coupling $lambda_S$ between DM pair and Higgs boson shall be tiny. Consequently, a negligible DM-nucleon elastic scattering cross section is predicted at the tree-level. In this work, we include the one-loop quantum corrections of the DM-nucleon elastic scattering cross section. We found that the quartic self-coupling $lambda_2$ between $mathbb{Z}_2$ odd particles indeed contributes to the one-loop quantum correction and behaves non-trivially for the co-annihilation scenario. Interestingly, the parameter space, which is allowed by the current constraints considered in this study, can predict the DM mass and annihilation cross section at the present compatible with the AMS-02 antiproton excess. The parameter space can be further probed at the future high luminosity LHC.
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