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arxiv: 2504.16525 · v3 · submitted 2025-04-23 · ✦ hep-ph

Gravitational Positivity Bounds on Higgs-Portal Dark Matter

Kimiko Yamashita This is my paper

Pith reviewed 2026-05-22 18:46 UTC · model grok-4.3

classification ✦ hep-ph
keywords Higgs portal dark mattergravitational positivity boundsforward scatteringfreeze-in mechanismrelic abundanceGUT scale cutoffreheating temperature
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The pith

Gravitational positivity bounds require new physics below 10^10 GeV for light Higgs-portal dark matter or high masses for GUT-scale cutoffs.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper derives gravitational positivity bounds for the Higgs-portal scalar dark matter model by assuming a perturbative string theory ultraviolet completion of gravity. The authors analyze the forward scattering process of dark matter particles to place constraints on the model's parameters. Without a dark matter self-coupling, the bounds force the introduction of new physics below 10^10 GeV whenever the dark matter mass lies below the Higgs mass. Including the self-coupling allows a cutoff near the grand unified theory scale only when the dark matter mass reaches 10^10 to 10^11 GeV, which in turn permits the observed relic density through freeze-in with a portal coupling no larger than about 3.5 times 10 to the minus 11 and caps the reheating temperature below 10^14 GeV.

Core claim

Gravitational positivity bounds on the Higgs-portal scalar dark matter model, derived from forward scattering of dark matter particles, imply that without a dark matter self-coupling new physics must appear below 10^10 GeV if the dark matter mass is below the Higgs mass. With both the portal and self-coupling present, a cutoff at the grand unified theory scale generally requires a dark matter mass of order 10^10 to 10^11 GeV, allowing the observed relic abundance to be reproduced via freeze-in with a Higgs-portal coupling smaller than or equal to 3.5 times 10 to the minus 11 while constraining the reheating temperature to be at most 10^14 GeV.

What carries the argument

Gravitational positivity bounds applied to the forward scattering amplitude of two dark matter scalars in the presence of a massless graviton.

If this is right

  • Without a self-coupling, any Higgs-portal dark matter lighter than the Higgs boson forces new physics below 10^10 GeV.
  • With the self-coupling, dark matter masses of order 10^10 to 10^11 GeV are needed to reach a grand unified theory scale cutoff.
  • Such heavy dark matter reproduces the observed relic density through freeze-in with a portal coupling at most 3.5 times 10 to the minus 11.
  • The positivity bounds limit the reheating temperature to no more than 10^14 GeV.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Light Higgs-portal models become viable only if additional new physics enters at scales well below the grand unified theory.
  • These constraints link ultraviolet gravity requirements directly to the cosmology of dark matter production and reheating.
  • Similar positivity analyses could be applied to other scalar portal models to restrict their viable mass and coupling ranges.

Load-bearing premise

The gravitational theory is ultraviolet-completed by a perturbative string theory that justifies applying positivity bounds to the low-energy effective model.

What would settle it

Observation of scalar dark matter with mass below the Higgs mass, negligible self-coupling, and no new physics appearing below 10^10 GeV would contradict the derived bounds.

Figures

Figures reproduced from arXiv: 2504.16525 by Kimiko Yamashita.

Figure 1
Figure 1. Figure 1: Representative contributions to the low-energy ϕϕ → ϕϕ scattering amplitude. “First,” “second,” and “last” in the subcaptions refer to the corresponding terms in Eq. (9). where we neglect terms not proportional to s 2 . (Including them will restore crossing sym￾metry.) As shown in [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Non-gravitational Feynman diagrams for ϕϕ → ϕϕ Here, ˜a2(t → −0) corresponds to a combination of the Wilson coefficients of dimension-8 operators (for example, see [42]). Eq. (21) shows that these dimension-8 contributions on the LHS arise from heavy states appearing at or above the energy scale Λ. By unitarity of the new physics sector, these states provide positive contributions to the RHS via ImM. This … view at source ↗
Figure 3
Figure 3. Figure 3: t-channel graviton exchange Feynman diagrams for ϕϕ → ϕϕ dominant non-gravitational contribution, Bnon-grav(Λ), is therefore given by B ϕϕ→ϕϕ non-grav = λ 2 hϕ + λ 2 ϕ 16π 2Λ4 . (22) Next, we present the gravitational contribution, Bgrav(Λ), for the ϕϕ → ϕϕ process [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Plots of f(x) (left) and f −1/4 (x) (right). The function f(x) is real and positive in the plotted range. is B ϕϕ→ϕϕ(Λ) = B ϕϕ→ϕϕ non-grav + B ϕϕ→ϕϕ grav ≥ 0, (25) λ 2 hϕ + λ 2 ϕ ≥ 2λ 2 hϕΛ 4 v 2 3M 2 plm4 h f(mϕ/mh), (26) which explicitly gives Λ ≤  3 2 1/4  Mpl v 1/2 [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Parameter space for λϕ/λhϕ versus Λ for light DM with mϕ < mh, satisfying the gravitational positivity bound from the ϕϕ → ϕϕ process. The green region indicates where the bound in Eq. (27) is satisfied. As the figure suggests, heavier DM masses may allow Λ to reach the GUT scale. Indeed, this occurs if the DM mass exceeds approximately 1010 GeV. However, the light DM region with mϕ < mh is more interestin… view at source ↗
Figure 6
Figure 6. Figure 6: Scattering amplitude M(s, t) in the complex s-plane with poles and branch cuts. The integration contour C in the upper-left panel can be deformed into the contours C ′ and C∞ in the upper-right panel, following the analytic structure of the amplitude aside from poles and branch cuts. The bottom-left panel shows how this deformation is achieved by introducing two paths, A and A′ , which can be brought arbit… view at source ↗
read the original 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 $\phi \phi \to \phi \phi$. 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. We further find that, in the presence of both interactions, achieving a cutoff scale at the grand unified theory scale generally requires a dark matter mass of order $10^{10}$-$10^{11}$ GeV (or above), with larger values favored when the four-point self-coupling plays a significant role. For such heavy Higgs-portal dark matter, the observed relic abundance of dark matter in the Universe can be successfully reproduced via the freeze-in mechanism with a tiny Higgs-portal coupling, $\lambda_{h\phi} \lesssim 3.5 \times 10^{-11}$. The reheating temperature is then constrained to be $T_{\mathrm{reh}} \lesssim 10^{14}$ GeV by the positivity bounds on the dark matter mass.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims to derive gravitational positivity bounds for the Higgs-portal scalar dark matter model from the forward φφ → φφ scattering amplitude, assuming a perturbative string theory UV completion of gravity. In the absence of a dark matter self-coupling, it concludes that new physics must appear below 10^{10} GeV when the dark matter mass is below the Higgs mass. With the self-coupling included, a GUT-scale cutoff generally requires dark matter masses of order 10^{10}-10^{11} GeV, allowing the observed relic density to be achieved via freeze-in with a small portal coupling λ_{hφ} ≲ 3.5 × 10^{-11}, and constraining the reheating temperature to T_reh ≲ 10^{14} GeV.

Significance. If valid, these results offer a new way to constrain Higgs-portal dark matter using high-energy theoretical consistency conditions from gravity. The link to the freeze-in mechanism and specific numerical scales for the cutoff and reheating temperature provide concrete, testable implications for cosmology and particle physics. The approach highlights how positivity bounds can restrict renormalizable models when gravity is included.

major comments (2)
  1. [§2] The central claims depend on the assumption that the gravitational theory admits a perturbative string theory completion to justify the positivity bounds on the dimension-4 operators in the Higgs-portal model. While the assumption is stated, the manuscript does not provide an independent verification or discuss the sensitivity of the 10^{10} GeV scale to this choice versus weaker conditions like causality and unitarity.
  2. [§3.2] The quantitative bounds, such as the energy scale of 10^{10} GeV and the dark matter mass range of 10^{10}-10^{11} GeV, are presented without visible step-by-step derivation, error analysis, or checks against post-hoc parameter choices in the forward scattering calculation. Explicit expressions for the amplitude and the resulting positivity inequality would allow verification of these scales.
minor comments (2)
  1. Consider adding a table summarizing the key bounds for different cases (with/without self-coupling) for clarity.
  2. [Abstract] The abstract mentions 'generally requires' for the mass range; a more precise statement on the conditions would improve readability.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which help clarify the presentation and assumptions. We address each major comment below and outline the revisions we will make.

read point-by-point responses

  1. Referee: [§2] The central claims depend on the assumption that the gravitational theory admits a perturbative string theory completion to justify the positivity bounds on the dimension-4 operators in the Higgs-portal model. While the assumption is stated, the manuscript does not provide an independent verification or discuss the sensitivity of the 10^{10} GeV scale to this choice versus weaker conditions like causality and unitarity.

    Authors: The gravitational positivity bounds applied here follow the standard framework in the literature, which requires a perturbative string theory UV completion to constrain the dimension-4 operators via the forward scattering amplitude. An independent verification of such a completion for the specific Higgs-portal model would necessitate a full string-theoretic construction, which is outside the scope of this phenomenological study. We agree that a discussion of the sensitivity to weaker assumptions (such as causality and unitarity alone) would be valuable, as the bounds could relax under those conditions. We will add a dedicated paragraph in the introduction and/or conclusions to explicitly state the assumption, reference the relevant literature, and comment on the potential impact of alternative UV assumptions on the derived scale of 10^{10} GeV. revision: partial

  2. Referee: [§3.2] The quantitative bounds, such as the energy scale of 10^{10} GeV and the dark matter mass range of 10^{10}-10^{11} GeV, are presented without visible step-by-step derivation, error analysis, or checks against post-hoc parameter choices in the forward scattering calculation. Explicit expressions for the amplitude and the resulting positivity inequality would allow verification of these scales.

    Authors: We apologize if the derivation steps were not sufficiently transparent. The bounds originate from the forward limit of the φφ → φφ amplitude in the effective theory, where the gravitational contribution and the portal/self-coupling terms are included. The positivity condition requires the coefficient of s² in the low-energy expansion to be non-negative, yielding the quoted scales after imposing the cutoff. We will revise Section 3.2 (and add an appendix if needed) to include the explicit analytic expression for the amplitude, the step-by-step derivation of the positivity inequality, and a clear mapping from the inequality to the numerical values of 10^{10} GeV and 10^{10}–10^{11} GeV for the dark matter mass. As these are theoretical consistency bounds rather than fits to data, a statistical error analysis does not apply; however, we will explicitly verify the results for representative parameter choices to confirm robustness. revision: yes

standing simulated objections not resolved
  • Independent verification of a perturbative string theory UV completion for the Higgs-portal model, which lies beyond the scope of this work.

Circularity Check

0 steps flagged

Minor external assumption on string UV completion; derivation applies bounds independently via forward scattering

full rationale

The paper states the assumption of perturbative string theory UV completion explicitly to justify gravitational positivity bounds on the renormalizable EFT. It then computes the constraints for the Higgs-portal model by analyzing the forward φφ→φφ amplitude, yielding the reported scales (10^10 GeV etc.) and relic abundance statements. No quoted step reduces these outputs to fitted parameters from the same data, self-definitional loops, or a load-bearing self-citation chain that forces the result by construction. The forward-scattering calculation supplies independent content once the (external) assumption is granted. This qualifies as low circularity per the guidelines.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption of a perturbative string theory ultraviolet completion for gravity and the use of forward scattering amplitudes in a renormalizable effective theory; no free parameters are explicitly fitted in the abstract, and no new entities are postulated.

axioms (1)
  • domain assumption The gravitational theory is ultraviolet-completed by a perturbative string theory
    Explicitly stated as the basis for deriving gravitational positivity bounds on the renormalizable model.

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Reference graph

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