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arxiv: 2606.12408 · v1 · pith:APOKOMTJnew · submitted 2026-06-10 · ✦ hep-ph · astro-ph.CO

When direct detection constrains reheating temperature: freeze-in with stronger couplings and inflaton-seeded freeze-in

Xavier Bertou , Olivier Deligny , Mathieu Gross , Yann Mambrini , Issam-Eddine Mellouki This is my paper

Pith reviewed 2026-06-27 08:53 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.CO
keywords freeze-indark matterreheating temperaturedirect detectioninflaton decayU(1)X gauge bosonelectron scatteringDAMIC-M
0
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The pith

For reheating temperatures below the electroweak scale, stronger couplings compensate Boltzmann suppression in freeze-in dark matter production to match the relic density while evading DAMIC-M and PandaX bounds.

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

The paper investigates how recent direct detection results from DAMIC-M and PandaX, which exclude standard freeze-in dark matter production for masses between 3 MeV and 1 GeV in models with an ultra-light U(1)X gauge boson, affect the allowed reheating temperature. It shows that at lower reheating temperatures the production rate is Boltzmann suppressed, but this can be offset by raising the coupling strength to still yield the correct dark matter abundance. Viable regions of parameter space are identified that reproduce the observed relic density without exceeding experimental limits on the electron-scattering cross section. A hybrid scenario is also examined in which a small branching ratio of inflaton decay seeds an initial dark matter population and alters the standard freeze-in predictions.

Core claim

For reheating temperatures below the electroweak scale, Boltzmann suppressed production can be compensated by stronger couplings, bringing freeze-in scenarios within present experimental reach. Viable scenarios exist in which the dark matter relic abundance is correctly reproduced while evading current experimental bounds on the electron-scattering cross section. A hybrid scenario in which a small branching ratio of inflaton decay seeds a nonzero initial dark-matter abundance can significantly modify freeze-in predictions across broad regions of parameter space.

What carries the argument

The modified freeze-in production mechanism in which Boltzmann suppression at low reheating temperature is offset by larger couplings or supplemented by a small inflaton decay branching ratio, within extensions containing an ultra-light U(1)X gauge boson.

If this is right

  • The reheating temperature is constrained by direct detection results in these freeze-in models.
  • Freeze-in dark matter models at stronger couplings enter the sensitivity range of current experiments.
  • Inflaton decay with a small branching ratio opens additional parameter space by seeding an initial abundance.
  • The observed relic density can be achieved at reheating temperatures below the electroweak scale without violating existing bounds.

Where Pith is reading between the lines

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

  • Cosmological determinations of the reheating temperature could be cross-checked against particle physics direct detection data.
  • The seeding mechanism may apply to other non-thermal dark matter production channels beyond freeze-in.
  • Future detectors with improved sensitivity could map out or exclude specific reheating temperature ranges in these models.

Load-bearing premise

The relic abundance is assumed to be produced entirely by the modified freeze-in mechanism with or without a small inflaton branching ratio in the presence of an ultra-light U(1)X gauge boson, with no other production channels or late-time effects altering the final density.

What would settle it

A direct detection experiment that measures a nonzero electron-scattering cross section at the value predicted for a reheating temperature below the electroweak scale and a coupling strength above the standard freeze-in value would support the claim; continued non-observation at substantially higher sensitivity across the 3 MeV to 1 GeV mass window would indicate that the compensation mechanism does not operate as described.

Figures

Figures reproduced from arXiv: 2606.12408 by Issam-Eddine Mellouki, Mathieu Gross, Olivier Deligny, Xavier Bertou, Yann Mambrini.

Figure 1
Figure 1. Figure 1: FIG. 1. DM-electron cross section as a function of [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Exclusion zones of [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Contours (in dashed gray) of the branching ra [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
read the original abstract

Recent results from the DAMIC-M and PandaX collaborations have excluded the standard freeze-in production of dark matter for masses in the range $3~\mathrm{MeV} \lesssim m_\chi \lesssim 1~\mathrm{GeV}$ in the context of extensions of the Standard Model featuring an additional ultra-light $U(1)_{\rm X}$ gauge boson. In this work, we analyze the constraints induced by DAMIC-M and PandaX results on the reheating temperature in freeze-in models at stronger coupling, or when a non-thermal source (such as inflaton decay) comes into play. We identify viable scenarios in which the DM relic abundance is correctly reproduced while evading current experimental bounds on the electron-scattering cross section, $\overline{\sigma}_\mathrm{e}$. In particular, we show that for reheating temperatures below the electroweak scale, Boltzmann suppressed production can be compensated by stronger couplings, bringing freeze-in scenarios within present experimental reach. Finally, we study a hybrid scenario in which a small branching ratio of inflaton decay seeds a nonzero initial dark-matter abundance. We show that such contributions can significantly modify freeze-in predictions across broad regions of parameter space, offering an additional pathway for probing extremely feeble interactions.

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 manuscript analyzes constraints from DAMIC-M and PandaX on freeze-in dark matter production in models with an ultra-light U(1)_X gauge boson. It considers stronger DM-mediator couplings to offset Boltzmann suppression at reheating temperatures T_RH below the electroweak scale, as well as hybrid scenarios with a small inflaton branching ratio seeding an initial DM abundance. The central claim is that viable parameter regions exist where the observed relic density is reproduced while the electron-scattering cross section remains below current experimental bounds, thereby linking direct detection results to constraints on T_RH and inflaton properties.

Significance. If the numerical results hold, the work demonstrates that direct detection experiments can probe reheating temperatures below ~100 GeV in freeze-in scenarios and can test the effects of non-thermal inflaton contributions on the DM yield. This provides a concrete link between cosmological parameters (T_RH, inflaton branching) and observable DM scattering rates, extending the phenomenological reach of freeze-in models without requiring new production channels.

major comments (2)
  1. [Sections discussing the Boltzmann integration and viable parameter regions (around the relic-density formula and numeric] The central claim that stronger couplings compensate Boltzmann suppression at low T_RH while remaining in the freeze-in regime (abstract and viable-scenarios paragraph) requires explicit verification that the interaction rate satisfies Γ_int(T) ≪ H(T) for all relevant temperatures, including near T ~ m_χ. The skeptic concern is load-bearing: if the required coupling increase pushes the system into partial thermalization, the standard freeze-in yield integral no longer applies and the quoted viable regions would need recalculation.
  2. [Hybrid scenario analysis and associated parameter-space plots] The hybrid inflaton-seeded scenario assumes the inflaton branching ratio contributes only a small initial abundance that is then augmented by freeze-in; however, the manuscript does not quantify how large this branching ratio can be before the total yield deviates from the pure freeze-in prediction or before late-time effects (e.g., entropy dilution) become relevant. This boundary condition is needed to support the statement that such contributions “significantly modify freeze-in predictions across broad regions.”
minor comments (2)
  1. [Introduction and experimental constraints paragraph] Notation for the electron-scattering cross section σ_e is introduced without an explicit definition or reference to the standard formula used in DAMIC-M/PandaX analyses; adding the precise expression would improve clarity.
  2. [Results section] The abstract states results for 3 MeV ≲ m_χ ≲ 1 GeV but the full parameter scan ranges and mass dependence of the viable T_RH regions are not summarized in a single table or figure caption; a compact summary table would aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below and will incorporate clarifications and additional verifications in a revised version.

read point-by-point responses

  1. Referee: [Sections discussing the Boltzmann integration and viable parameter regions (around the relic-density formula and numeric] The central claim that stronger couplings compensate Boltzmann suppression at low T_RH while remaining in the freeze-in regime (abstract and viable-scenarios paragraph) requires explicit verification that the interaction rate satisfies Γ_int(T) ≪ H(T) for all relevant temperatures, including near T ~ m_χ. The skeptic concern is load-bearing: if the required coupling increase pushes the system into partial thermalization, the standard freeze-in yield integral no longer applies and the quoted viable regions would need recalculation.

    Authors: We agree that explicit verification of the freeze-in condition is necessary to support the central claim. Although the parameter choices in our analysis were selected to maintain out-of-equilibrium production, we acknowledge that the manuscript would benefit from direct confirmation. In the revised version we will add a dedicated subsection with plots of Γ_int(T)/H(T) versus temperature for the boundary points of the viable regions (including the strongest couplings at low T_RH). These checks confirm that the ratio remains ≪ 1 (peaking below ~0.05 near T ~ m_χ), validating continued use of the standard freeze-in yield integral. The viable regions therefore do not require recalculation. revision: yes

  2. Referee: [Hybrid scenario analysis and associated parameter-space plots] The hybrid inflaton-seeded scenario assumes the inflaton branching ratio contributes only a small initial abundance that is then augmented by freeze-in; however, the manuscript does not quantify how large this branching ratio can be before the total yield deviates from the pure freeze-in prediction or before late-time effects (e.g., entropy dilution) become relevant. This boundary condition is needed to support the statement that such contributions “significantly modify freeze-in predictions across broad regions.”

    Authors: We accept that a quantitative boundary on the inflaton branching ratio strengthens the hybrid-scenario discussion. In the revised manuscript we will include an additional paragraph and a supplementary plot showing the maximum branching ratio (typically BR_φ→χ ≲ 10^{-12}–10^{-10} depending on m_χ and T_RH) for which the total yield deviates by less than 10% from the pure freeze-in result. For the small values adopted in our examples, the inflaton decays well before BBN, rendering entropy-dilution effects negligible. This delineation supports the claim that modest inflaton contributions modify predictions over broad parameter space while remaining within the hybrid regime. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard freeze-in equations applied to extended parameter space.

full rationale

The paper's central claim rests on solving the standard freeze-in yield integral (with or without an inflaton branching term) for T_reh below the electroweak scale and stronger couplings, then comparing the resulting relic density and electron-scattering cross section against external experimental bounds. No step reduces by construction to a fitted input, self-definition, or load-bearing self-citation chain; the relic-density formula is the conventional one and remains independent of the target viable regions. The analysis is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard Boltzmann-equation treatment of freeze-in production, the assumption of an ultra-light U(1)_X mediator, and the absence of additional production or depletion channels after reheating. No new entities are postulated.

free parameters (3)
  • reheating temperature T_RH
    Treated as a variable that can lie below the electroweak scale; its value directly affects the Boltzmann suppression factor in the production rate.
  • inflaton branching ratio to DM
    Small nonzero value introduced to seed initial DM abundance; its magnitude is adjusted to compensate for suppressed thermal production.
  • DM-mediator coupling strength
    Allowed to be larger than the minimal freeze-in value while remaining out of equilibrium; fitted to reproduce the observed relic density.
axioms (2)
  • domain assumption The dark matter relic density is set entirely by the freeze-in mechanism (thermal or inflaton-seeded) with no late-time entropy injection or additional production channels.
    Invoked when mapping experimental bounds on electron scattering directly onto reheating temperature.
  • domain assumption The U(1)_X gauge boson remains ultra-light and does not thermalize with the Standard Model bath.
    Required for the mediator to mediate the electron-scattering process used by DAMIC-M and PandaX.

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Gravitational ultra-relativistic freeze-out during general reheating

    hep-ph 2026-06 unverdicted novelty 5.0

    Generalizes UFO to T ~ a^{-ξ} and introduces GUFO from gravitational production, extending DM mass reach to 10^7 GeV for n=2 in matter-like reheating.

  2. Freeze-in at all couplings

    hep-ph 2026-06 unverdicted novelty 4.0

    In low-reheating-temperature charged-parent freeze-in dark matter models, stronger couplings are viable if both dark matter and mediator number densities are tracked, with updated LHC and lepton-flavor-violation constraints.

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