Gravitational Positivity Bounds on Higgs-Portal Dark Matter

Abstract: We consider gravitational positivity bounds on the Higgs-portal scalar dark matter model. Applying gravitational positivity bounds with dark matter forward scattering process $\phi \phi \to \phi \phi$ to this DM model, we find that the new physics, besides the Higgs-portal dark matter physics, arises at an energy scale lower than $10^{10}$ GeV without the dark matter self-coupling. With the existence of the dark matter self-coupling, the hierarchical order of magnitude between the self-coupling $\lambda_{\phi}$ and the Higgs-portal coupling $\lambda_{h\phi}$ changes the game. With $\lambda_{\phi}/\lambda_{h\phi} = 10^{12}$, the GUT scale cutoff can realize. In this case, the dark freezeout scenario is possible for realizing the relic density of dark matter in the Universe. We find that $\lambda_{\phi} \sim O(1)$, $\lambda_{h\phi} \sim 10^{-12}$, and sub-GeV dark matter is implicated for the GUT scale cutoff possibility with the Higgs-portal dark matter model.