Gravitational Positivity Bounds on Higgs-Portal Light Dark Matter

TL;DR

This paper derives gravitational positivity bounds for a Higgs-portal real scalar dark matter model, assuming a string-theory UV completion of gravity. The authors compute the forward scattering amplitude for $\phi\phi\to\phi\phi$ and decompose the low-energy contribution into a non-gravitational part and a gravitational part, obtaining a bound that links the cutoff scale $\Lambda$ to the portal and self-couplings. For light DM with $m_\phi < m_h$, the bound without self-interaction requires new physics below $\sim 10^{10}$ GeV; introducing a large hierarchy $\lambda_\phi/\lambda_{h\phi}$ can raise $\Lambda$ to the GUT/string scale, enabling dark freeze-out to reproduce the observed relic abundance. A concrete benchmark with $\lambda_\phi \sim O(1)$, $\lambda_{h\phi} \sim 10^{-12}$, and $m_\phi \lesssim 1$ GeV demonstrates a viable parameter space where the gravitational positivity bounds are satisfied and the correct relic density can be achieved.

Abstract

Gravitational positivity bounds are constraints on a renormalizable theory in the presence of a massless graviton, under the assumption that the gravitational theory is ultraviolet-completed by a perturbative string theory. We derive these bounds for the Higgs-portal scalar dark matter model using the forward scattering process $φφ\to φφ$. We find that, in the absence of a dark matter self-coupling, new physics beyond the Higgs-portal dark matter interaction must appear below an energy scale of $10^{10}$ GeV if the dark matter mass is smaller than the Higgs boson mass. The presence of a dark matter self-coupling alters this situation. A hierarchy between the dark matter four-point self-coupling $λ_φ$ and a tiny Higgs-portal coupling $λ_{hφ}$ is required to raise the energy scale at which the new physics appears. If $λ_φ/λ_{hφ} = 10^{12}$, the dark matter model can remain valid up to the grand unified theory (GUT) scale or the typical string scale. In this case, the relic abundance of dark matter in the Universe can be reproduced via the dark freeze-out scenario. A parameter set with $λ_φ \sim O(1)$, $λ_{hφ} \sim 10^{-12}$, and a sub-GeV dark matter mass can accommodate the GUT-scale $Λ$ within the Higgs-portal light dark matter framework.

Figures (13)

• Figure 1: first: $\tilde{a}_2(t) s^2$
• Figure 2: first: $\tilde{a}_2(t) s^2$
• Figure 3: second: $-g_2(t)s^2/M^2_{\text{pl}}$
• Figure 4: last: $-Cs^2/(M^2_\text{pl} t)$
• Figure 6: Non-gravitational Feynman diagrams for $\phi \phi \to \phi \phi$