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Phenomenological Constraints on Higgs reheating

T0 review · 3 major / 3 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The paper derives a narrow allowed window for Higgs-portal reheating: vacuum stability, perturbativity, and LHC constraints together force $3.4\times10^6\,\mathrm{GeV}\lesssim T_{\rm rh}\lesssim 3.9\times10^{12}\,\mathrm{GeV}$ and…

desk verdict Useful RG-plus-LHC constraint for the μφ|H|² portal, but the quoted T_rh window relies on a decay-width treatment that thermal effects may invalidate. read the letter →

arxiv 2508.13155 v1 pith:TBOCNDUW submitted 2025-08-18 hep-ph

Yann Cado , Mathieu Gross , Yann Mambrini , Keith Olive This is my paper · ORCID
classification hep-ph
keywords Higgsreheatinginflatontemperaturevacuumstabilityrenormalizationgrouprunningperturbativitycolliderconstraintsdecay
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks what happens when the inflaton reheats the universe by decaying into Higgs bosons through the interaction $\mu \phi |\mathcal{H}|^2$, rather than through the high-scale couplings usually assumed in inflation models. It argues that in potentials where the inflaton is massless without a bare mass term, the inflaton can sit near the electroweak scale, where collider and vacuum-stability constraints become relevant. Combining renormalization-group running of the Higgs quartic coupling with LHC bounds, the paper derives a finite allowed window for the reheating temperature and the inflaton bare mass. If correct, any Higgs-portal reheating mechanism of this type must land inside that window, giving concrete targets for both cosmological and collider searches.

What carries the argument

The load-bearing object is the Higgs-portal interaction $\mu \phi |\mathcal{H}|^2$, where $\phi$ is the inflaton and $\mathcal{H}$ the Standard Model Higgs doublet, together with the standard perturbative relation between the reheating temperature and the inflaton decay width, $T_{\rm rh}\propto \sqrt{M_{\rm Pl}\,\Gamma}$. The paper runs renormalization-group equations for the Higgs quartic coupling, the coupling $\mu$, and the inflaton bare mass, imposing that the Higgs potential remain stable and perturbative to high energies, and then overlays LHC constraints from a public collider code. The two-body decay width for $\phi\to \mathcal{H}\mathcal{H}$ is what carries $\mu$ into the reheating temperature and closes the chain from RG and collider bounds to the quoted temperature window.

What would settle it

Recompute the reheating temperature at a representative allowed point, say $m_\phi=300\,\mathrm{GeV}$ with $\mu$ chosen to give $T_{\rm rh}\approx10^7\,\mathrm{GeV}$, using a lattice or full Boltzmann treatment that includes resonant and backreaction effects; if the resulting radiation temperature differs from the instantaneous-decay formula by an order of magnitude, the window's edge moves. Independently, a collider discovery of a Higgs-coupled scalar at $250\,\mathrm{GeV}$ would directly contradict the $260\,\mathrm{GeV}$ lower bound.

Watch

Extended reading notes

Core claim

The central claim is that the requirement that the Higgs potential stay stable and perturbative up to high energies, together with LHC limits on a new scalar coupled to the Higgs, leaves only a narrow allowed region in the $(m_\phi,\mu)$ plane for the interaction $\mu \phi |\mathcal{H}|^2$. Within that region the reheating temperature is confined to $3.4\times10^6\,\mathrm{GeV}\lesssim T_{\rm rh}\lesssim 3.9\times10^{12}\,\mathrm{GeV}$, and the inflaton bare mass to $260\,\mathrm{GeV}\lesssim m_\phi\lesssim 3.8\times10^{10}\,\mathrm{GeV}$. The paper also provides the resulting relations between $T_{\rm rh}$ and $m_\phi$, and between $\mu$ and $m_\phi$, so that reheating is turned from a free parameter into a derived quantity for this portal.

Load-bearing premise

The load-bearing premise is that reheating is set by the single-particle decay rate $\phi\to\mathcal{H}\mathcal{H}$ with instant thermalization, so that $T_{\rm rh}\propto\sqrt{M_{\rm Pl}\,\Gamma}$; if parametric resonance, backreaction, or a different thermalization history matters, the quoted temperature window need not hold.

Editorial extensions

If this is right

  • For this portal, reheating temperatures below about $3\times10^6\,\mathrm{GeV}$ and above about $4\times10^{12}\,\mathrm{GeV}$ are excluded, so viable models must reheat inside that band.
  • The inflaton mass is forced above $260\,\mathrm{GeV}$ and below $3.8\times10^{10}\,\mathrm{GeV}$, ruling out electroweak-scale inflatons below $260\,\mathrm{GeV}$ under the stated stability plus collider logic.
  • Vacuum stability and perturbativity alone already bracket the allowed $\mu$–$m_\phi$ relation, with LHC data further tightening it.
  • The explicit $T_{\rm rh}$–$m_\phi$ and $\mu$–$m_\phi$ relations make the reheating temperature a derived quantity rather than a freely chosen model parameter for this reheating portal.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: the $260\,\mathrm{GeV}$ lower bound turns collider searches for new scalars in Higgs final states into a direct test of reheating; a discovery of a Higgs-coupled scalar below that mass would break the claimed window.
  • Beyond the paper: if the window holds, high-temperature mechanisms requiring $T_{\rm rh}\gtrsim10^{12}\,\mathrm{GeV}$, such as some leptogenesis scenarios, are disfavoured for this portal because the upper edge sits near $3.9\times10^{12}\,\mathrm{GeV}$.
  • Beyond the paper: a full preheating simulation including parametric resonance and backreaction would provide a sharper test, because the perturbative two-body decay assumption is the step that maps $\mu$ and $m_\phi$ onto $T_{\rm rh}$.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 3 minor

Summary. The manuscript studies the scenario in which reheating proceeds through the interaction μ φ |H|^2 between a light inflaton φ and the Standard Model Higgs doublet H, with a bare inflaton mass m_phi. The authors combine renormalization-group requirements that the Higgs potential remain stable and perturbative up to high scales with LHC constraints evaluated with HiggsTools, and they translate the resulting constraints on (μ, m_phi) into a prediction for the reheating temperature using the two-body decay φ→HH. Their headline result is 3.4×10^6 GeV ≲ T_rh ≲ 3.9×10^12 GeV and 260 GeV ≲ m_phi ≲ 3.8×10^10 GeV. The version of the full text supplied to me is heavily corrupted, so the underlying equations and numerical steps could not be independently checked; the abstract is legible and is the basis for this report.

Significance. If the claimed window is correct, the paper gives a sharp, falsifiable correlation between an electroweak-scale inflaton mass, the Higgs-inflaton coupling, and the reheating temperature, which is directly relevant for Higgs-portal reheating models and for LHC searches. The use of the public code HiggsTools and the explicit RG analysis are strengths, and the constraints appear to be externally imposed benchmarks rather than derived from the desired T_rh interval, so there is no evident circularity. The main caveats are that the central derivation is not legible in the supplied text and that the zero-temperature decay treatment needs justification at the quoted high reheating temperatures.

major comments (3)
  1. [Abstract / reheating calculation] The quoted window rests on the standard mapping T_rh ~ sqrt(Γ M_Pl) with the zero-temperature two-body width Γ(φ→HH). At the claimed endpoints T_rh is many orders of magnitude above m_phi (3.4×10^6 GeV vs. 260 GeV; 3.9×10^12 GeV vs. 3.8×10^10 GeV), so at the epoch H ~ Γ the ambient plasma has T ≫ m_phi/2. The SM Higgs then acquires a thermal mass m_h(T) ~ O(0.1–0.6)T, which typically exceeds m_phi/2 and kinematically blocks at-rest φ→HH decays. The manuscript, in the legible parts, does not address this. Please either solve the Boltzmann equation with a temperature-dependent width (e.g., Γ_eff = Γ_0 Θ(m_phi − 2 m_h(T))), or provide a concrete argument that decays complete before the thermal bath is established. Without this, the T_rh bounds are not established beyond the zero-temperature approximation.
  2. [RG analysis / Section 2 (unreadable in supplied text)] Because the full text I received is corrupted, I cannot verify the β-functions, the treatment of the dimensionful coupling μ, or the threshold corrections used to conclude that the Higgs potential remains stable and perturbative. Please make sure the published version explicitly lists the renormalization-group equations, the matching scale, and the criteria for 'stable' and 'perturbative' (including the upper bound on μ). These are load-bearing for the derived allowed region.
  3. [LHC constraints / HiggsTools implementation] The abstract states that LHC constraints are applied through HiggsTools, but the legible text does not specify which observables are used (e.g., Higgs signal strengths, exotic Higgs decays, or direct searches for a new scalar) or how the code translates a given (μ, m_phi) into an exclusion. Please spell out the relevant processes and give the numerical likelihood or chi-square treatment, since the lower bound m_phi > 260 GeV appears to follow from this step.
minor comments (3)
  1. [Overall presentation] The supplied full text is garbled; please ensure the final manuscript has intact display equations and section numbers, since this prevented verification.
  2. [Reheating definition] Define T_rh precisely (e.g., T at H = Γ versus instantaneous decay temperature) and state whether the quoted range assumes instant thermalization.
  3. [References] The mention of the 'HiggsTools public code' should include a version or arXiv reference and the specific input parameters used.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: stability, perturbativity, and LHC constraints are external inputs; the T_rh window is a derived output.

full rationale

At the level of the readable abstract, the derivation chain is: (i) adopt the interaction term mu phi |H|^2; (ii) impose Higgs vacuum stability and perturbativity on the RG running of the couplings in the presence of this portal; (iii) impose LHC constraints via the public HiggsTools code; (iv) convert the surviving (mu, m_phi) parameter region into a reheating temperature through the standard relation T_rh ~ sqrt(Gamma(phi -> HH) M_Pl). Steps (ii) and (iii) are independent external benchmarks: the stability and perturbativity conditions and the collider data do not presuppose any value of T_rh, and the quoted T_rh window is an output of the calculation, not an input used to select parameters. No readable equation defines mu or m_phi in terms of T_rh, and no fit to the final T_rh range is described. The only concerns that can be raised from the material supplied, such as whether finite-temperature Higgs masses suppress phi -> HH when T_rh >> m_phi or whether the instantaneous-decay reheating formula is adequate, are physics-correctness questions rather than circularity: they do not make the claimed T_rh window equal to an input by construction. A full equation-by-equation audit was not possible because most of the body text is corrupted, but unreadability is not evidence of circularity; no self-definitional reduction, fitted-input-as-prediction, or load-bearing self-citation chain can be exhibited from the readable text.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

No new particles, forces, or dimensions are introduced; the inflaton is part of the pre-existing inflation framework and the Higgs is Standard Model. The central claim rests on the two free parameters m_phi and mu, plus the perturbative reheating and RG-stability assumptions listed above.

free parameters (2)
  • m_phi (inflaton bare mass) = 260 GeV to 3.8e10 GeV (allowed range)
    The inflaton bare mass is a free model parameter that the paper scans and constrains through stability and collider limits.
  • mu (inflaton-Higgs coupling) = Constrained function of m_phi; no single value quoted
    The trilinear portal coupling is a free parameter of the model; the RG analysis determines the values that keep the Higgs potential stable and perturbative.
assumptions (3)
  • domain assumption Standard Model couplings run perturbatively, and the Higgs quartic can become negative or non-perturbative at high scales.
    The abstract states that an RG analysis is used to require Higgs potential stability and perturbativity.
  • domain assumption The inflaton is a Standard Model singlet whose only interaction relevant for reheating is mu phi |H|^2 plus its own bare mass.
    The abstract defines this interaction and mass as the model under investigation.
  • domain assumption Reheating proceeds through perturbative inflaton decay, with T_rh derived from the decay width.
    The abstract reports a reheating temperature range, which requires a decay-to-thermal-bath relation not stated in the abstract.

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Cite this review

Pith. "Pith review of Phenomenological Constraints on Higgs reheating." pith.science (2026). https://pith.science/paper/TBOCNDUW

@misc{pith2026250813155,
  author       = {Pith},
  title        = {Pith review of: Phenomenological Constraints on Higgs reheating},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TBOCNDUW}},
  note         = {Machine review of arXiv:2508.13155}
}
abstract

In many models of inflation, reheating is realized through a coupling between the inflaton and the Higgs boson. Often, the mass of the inflaton is of order $10^{13}~$GeV determined by the amplitude of the scalar fluctuation spectrum. However, in models where the inflaton potential is of the form $V \sim \phi^k$ about its minimum, the inflaton is massless for $k\ge 4$ unless a bare mass term, $\frac12 m_\phi^2 \phi^2$, is present. In this case, the inflaton mass may be of order the electroweak scale and may be subject to existing collider constraints. In particular, we investigate the constraints on the inflaton mass and reheating temperature $T_{\rm rh}$ arising from the decay of $\phi$ into $\mathcal{H}$ through an interaction term $\mu \phi |\mathcal{H}|^2$. We perform a renormalization group analysis to determine the relative values of $\mu$ and $m_\phi$ such that the Higgs potential remains stable (and perturbative) at high energy. Taking into account the running of the Higgs quartic self-coupling and the experimental constraints from the LHC via the $\texttt{HiggsTools}$ public code, we find that $3.4 \times 10^6 $ GeV $\lesssim T_{\rm rh}\lesssim 3.9 \times 10^{12} $ GeV with a corresponding constraint on the inflaton bare mass $260~{\rm GeV} \lesssim m_\phi \lesssim 3.8 \times 10^{10}~{\rm GeV}$. The dependencies between $T_{\rm rh}$ and the inflaton bare mass $m_\phi$ as well as between $\mu$ and $m_\phi$ are provided.

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Reviewed August 15, 2026 · model on record in the stance chip above.