pith. sign in

arxiv: 2606.19564 · v1 · pith:ZOEN6RTInew · submitted 2026-06-17 · ✦ hep-ph

Freeze-in at all couplings

Andreas Goudelis , Andre Lessa , Lucas Magno Dantas Ramos , Thomas Reggio This is my paper

Pith reviewed 2026-06-26 19:51 UTC · model grok-4.3

classification ✦ hep-ph
keywords freeze-indark matterreheating temperaturemediatorBoltzmann equationsrelic abundanceLHC constraintslepton flavor violation
0
0 comments X

The pith

In freeze-in dark matter models with low reheating temperatures, accurate relic predictions require tracking number densities of both dark matter and its charged mediator, which can fail to equilibrate.

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

The paper studies freeze-in dark matter production in cases where the early universe reheats only to temperatures at or below the masses of the dark matter and mediator particles. This regime suppresses production rates, so the observed dark matter density can be matched with larger interaction couplings than in standard high-temperature scenarios. Solving the evolution of both particle species together is necessary because the mediator's fast decays can prevent it from ever reaching equilibrium with the thermal bath. The resulting parameter space must then be checked against updated collider and flavor-violation limits.

Core claim

When reheating occurs at temperatures comparable to or below the relevant mass scales, dark matter production is Boltzmann-suppressed. This permits stronger couplings to the Standard Model while still reproducing the observed relic abundance. The coupled number-density evolution of dark matter and mediator must be followed explicitly; doing so reveals that the mediator can remain out of equilibrium because its decay rate exceeds the expansion rate, altering both cosmology and experimental reach.

What carries the argument

The coupled Boltzmann equations for the number densities of the dark matter and the charged mediator particle.

If this is right

  • Stronger dark matter couplings remain cosmologically viable because production is suppressed at low reheating temperatures.
  • The mediator can stay out of equilibrium throughout the relevant epoch due to rapid decays.
  • Updated LHC searches and lepton-flavor-violation bounds together constrain the enlarged coupling range.
  • The viable region depends on the specific interplay among reheating temperature, mediator mass, dark matter mass, and coupling strength.

Where Pith is reading between the lines

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

  • The same coupled-equation treatment could be applied to other freeze-in models that include an unstable mediator.
  • Future high-luminosity lepton colliders may have enhanced sensitivity to the larger couplings allowed in this regime.
  • Non-equilibration of short-lived states might appear in other dark-sector scenarios whenever decay rates exceed interaction rates at low temperatures.

Load-bearing premise

The analysis assumes production proceeds through a charged parent particle when the reheating temperature lies at or below the mass scales of dark matter and mediator.

What would settle it

A direct measurement or calculation showing that the mediator reaches thermal equilibrium abundance in a low-reheating scenario with the coupling needed for the correct relic density would falsify the reported non-equilibration behavior.

read the original abstract

We perform a comprehensive analysis of a charged parent freeze-in dark matter model, focusing on scenarios where the Universe reheats to a temperature comparable to or lower than the mass scales of the theory. In such configurations, dark matter production is Boltzmann-suppressed, allowing for stronger couplings between dark matter and the Standard Model thermal bath while still reproducing the observed relic abundance. We emphasize the non-trivial interplay between the reheating temperature, the mediator and dark matter masses and the coupling strength. We show that tracking the number density evolution of both dark matter and the mediator is essential to obtain reliable predictions, including unexpected behaviors such as the mediator non-equilibration due to fast decays. Lastly, we explore the phenomenological implications of this scenario, updating constraints from LHC searches and lepton flavour-violating decays and highlighting the complementarity of these searches in probing the cosmologically viable parameter space.

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 performs a comprehensive analysis of freeze-in dark matter production in a model with a charged parent particle, focusing on reheating temperatures T_rh comparable to or below the relevant mass scales. In this Boltzmann-suppressed regime, larger couplings remain viable while reproducing the observed relic density. The central claim is that the coupled number-density evolution of both dark matter and the mediator must be tracked, which can produce unexpected effects such as mediator non-equilibration arising from fast decays. The work also updates LHC and lepton-flavor-violation constraints and discusses their complementarity with the cosmologically allowed parameter space.

Significance. If the numerical results hold, the manuscript usefully demonstrates that the standard single-species freeze-in approximation breaks down once mediator decays and inverse decays are retained at all couplings; this directly enlarges the viable parameter space and alters the mapping between coupling strength and relic density. Explicit treatment of the T_rh ≲ m regime together with collider and LFV bounds provides a concrete example of how cosmological and laboratory probes can be combined in this class of models.

major comments (2)
  1. [§4.1, Eq. (18)] §4.1, Eq. (18): the statement that mediator non-equilibration occurs 'due to fast decays' is load-bearing for the claim that coupled evolution is essential, yet the text does not quantify the decay-rate threshold relative to the Hubble rate at which the mediator departs from equilibrium; a plot or analytic condition would be required to substantiate the 'unexpected behavior'.
  2. [§3.3] §3.3, the numerical integration of the coupled Boltzmann system: no convergence tests, step-size controls, or comparison against the standard single-species freeze-in code are reported, making it impossible to assess whether the reported relic-density shifts are numerical artifacts or physical.
minor comments (2)
  1. [Figure 2] Figure 2 caption: the color scale for the relic-density contours is not labeled with numerical values, hindering direct comparison with the analytic expectations given in the text.
  2. Reference list: several standard freeze-in papers (e.g., Hall et al. 2010) are cited only in passing; a brief comparison paragraph would clarify how the present coupled treatment differs from those works.

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 the suggested improvements in a revised version.

read point-by-point responses

  1. Referee: [§4.1, Eq. (18)] the statement that mediator non-equilibration occurs 'due to fast decays' is load-bearing for the claim that coupled evolution is essential, yet the text does not quantify the decay-rate threshold relative to the Hubble rate at which the mediator departs from equilibrium; a plot or analytic condition would be required to substantiate the 'unexpected behavior'.

    Authors: We agree that an explicit quantification strengthens the presentation. The coupled equations already encode the effect, but we will add an analytic estimate of the threshold (roughly when the effective decay rate exceeds H at the relevant temperature, accounting for the Boltzmann suppression and inverse processes) together with a new figure showing Γ_decay/H versus temperature for benchmark points that exhibit non-equilibration. This will make the origin of the behavior transparent. revision: yes

  2. Referee: [§3.3] the numerical integration of the coupled Boltzmann system: no convergence tests, step-size controls, or comparison against the standard single-species freeze-in code are reported, making it impossible to assess whether the reported relic-density shifts are numerical artifacts or physical.

    Authors: We acknowledge the omission. In the revision we will add an appendix (or subsection in §3.3) documenting the integrator (adaptive Runge-Kutta with relative tolerance 10^{-8}), convergence tests under step-size halving and tolerance tightening, and direct side-by-side comparisons of the relic density from the coupled system versus the standard single-species freeze-in approximation for several benchmark points, confirming that the reported shifts are physical. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central claim is that coupled Boltzmann equations for dark matter and mediator number densities must be solved to capture effects such as mediator non-equilibration. This follows directly from writing the standard two-species Boltzmann system with decay and inverse-decay terms in the stated T_rh ≲ m regime; no equation is shown to reduce to its own input by construction, no parameter is fitted on a subset and then relabeled a prediction, and no load-bearing uniqueness theorem or ansatz is imported via self-citation. The provided abstract and description contain no derivations, self-referential fits, or self-citation chains that would force the result. The analysis is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review performed on abstract only; no explicit free parameters, axioms, or invented entities are stated in the provided text. The abstract implies reliance on standard Boltzmann equations for number-density evolution and on the assumption of a thermal bath, but details are absent.

pith-pipeline@v0.9.1-grok · 5673 in / 1200 out tokens · 37893 ms · 2026-06-26T19:51:25.150332+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

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.

Reference graph

Works this paper leans on

35 extracted references · 23 linked inside Pith · cited by 1 Pith paper

  1. [1]

    Cirelli, A

    M. Cirelli, A. Strumia, and J. Zupan,Dark Matter,arXiv:2406.01705. [2]PlanckCollaboration, N. Aghanim et al.,Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys.641(2020) A6, [arXiv:1807.06209]. [Erratum: Astron.Astrophys. 652, C4 (2021)]

    Pith/arXiv arXiv 2018

  2. [2]

    McDonald,Thermally generated gauge singlet scalars as selfinteracting dark matter,Phys

    J. McDonald,Thermally generated gauge singlet scalars as selfinteracting dark matter,Phys. Rev. Lett.88(2002) 091304, [hep-ph/0106249]

    Pith/arXiv arXiv 2002

  3. [3]

    L. J. Hall, K. Jedamzik, J. March-Russell, and S. M. West,Freeze-In Production of FIMP Dark Matter,JHEP03(2010) 080, [arXiv:0911.1120]

    Pith/arXiv arXiv 2010

  4. [4]

    Hambye, M

    T. Hambye, M. H. G. Tytgat, J. Vandecasteele, and L. Vanderheyden,Dark matter direct detection is testing freeze-in,Phys. Rev. D98(2018), no. 7 075017, [arXiv:1807.05022]

    Pith/arXiv arXiv 2018

  5. [5]

    Heikinheimo, T

    M. Heikinheimo, T. Tenkanen, and K. Tuominen,Prospects for indirect detection of frozen-in dark matter,Phys. Rev. D97(2018), no. 6 063002, [arXiv:1801.03089]

    Pith/arXiv arXiv 2018

  6. [6]

    B´ elanger et al.,LHC-friendly minimal freeze-in models,JHEP02(2019) 186, [arXiv:1811.05478]

    G. B´ elanger et al.,LHC-friendly minimal freeze-in models,JHEP02(2019) 186, [arXiv:1811.05478]

    Pith/arXiv arXiv 2019

  7. [7]

    G. Brooijmans et al.,Les Houches 2019 Physics at TeV Colliders: New Physics Working Group Report, in11th Les Houches Workshop on Physics at TeV Colliders: PhysTeV Les Houches, 2, 2020.arXiv:2002.12220

    arXiv 2019

  8. [8]

    Cosme, F

    C. Cosme, F. Costa, and O. Lebedev,Freeze-in at stronger coupling,Phys. Rev. D109 (2024), no. 7 075038, [arXiv:2306.13061]

    arXiv 2024

  9. [9]

    Arcadi, F

    G. Arcadi, F. Costa, A. Goudelis, and O. Lebedev,Higgs portal dark matter freeze-in at stronger coupling: observational benchmarks,JHEP07(2024) 044, [arXiv:2405.03760]

    arXiv 2024

  10. [10]

    B´ elanger, N

    G. B´ elanger, N. Bernal, and A. Pukhov,Z’-mediated dark matter with low-temperature reheating,JHEP03(2025) 079, [arXiv:2412.12303]

    arXiv 2025

  11. [11]

    Bertou, O

    X. Bertou, O. Deligny, M. Gross, Y. Mambrini, and I.-E. Mellouki,When direct detection constrains reheating temperature: freeze-in with stronger couplings and inflaton-seeded freeze-in,arXiv:2606.12408

    Pith/arXiv arXiv

  12. [12]

    C. P. Burgess, M. Pospelov, and T. ter Veldhuis,The Minimal model of nonbaryonic dark matter: A Singlet scalar,Nucl. Phys. B619(2001) 709–728, [hep-ph/0011335]

    Pith/arXiv arXiv 2001

  13. [13]

    J. L. Feng, A. Rajaraman, and F. Takayama,Superweakly interacting massive particles, Phys. Rev. Lett.91(2003) 011302, [hep-ph/0302215]

    Pith/arXiv arXiv 2003

  14. [14]

    B´ elanger, F

    G. B´ elanger, F. Boudjema, A. Goudelis, A. Pukhov, and B. Zaldivar,micrOMEGAs5.0 : Freeze-in,Comput. Phys. Commun.231(2018) 173–186, [arXiv:1801.03509]

    Pith/arXiv arXiv 2018

  15. [15]

    Alloul, N

    A. Alloul, N. D. Christensen, C. Degrande, C. Duhr, and B. Fuks,FeynRules 2.0 - A complete toolbox for tree-level phenomenology,Comput. Phys. Commun.185(2014) 2250–2300, [arXiv:1310.1921]

    Pith/arXiv arXiv 2014

  16. [16]

    Belyaev, N

    A. Belyaev, N. D. Christensen, and A. Pukhov,CalcHEP 3.4 for collider physics within and beyond the Standard Model,Comput. Phys. Commun.184(2013) 1729–1769, [arXiv:1207.6082]

    Pith/arXiv arXiv 2013

  17. [17]

    Alguero, G

    G. Alguero, G. Belanger, F. Boudjema, S. Chakraborti, A. Goudelis, S. Kraml, A. Mjallal, – 22 – and A. Pukhov,micrOMEGAs 6.0: N-component dark matter,Comput. Phys. Commun. 299(2024) 109133, [arXiv:2312.14894]

    arXiv 2024

  18. [18]

    Garny, J

    M. Garny, J. Heisig, B. L¨ ulf, and S. Vogl,Coannihilation without chemical equilibrium,Phys. Rev. D96(2017), no. 10 103521, [arXiv:1705.09292]

    Pith/arXiv arXiv 2017

  19. [19]

    R. T. D’Agnolo, D. Pappadopulo, and J. T. Ruderman,Fourth Exception in the Calculation of Relic Abundances,Phys. Rev. Lett.119(2017), no. 6 061102, [arXiv:1705.08450]. [21]SuperCDMSCollaboration, D. W. Amaral et al.,Constraints on low-mass, relic dark matter candidates from a surface-operated SuperCDMS single-charge sensitive detector,Phys. Rev. D102(2020...

    Pith/arXiv arXiv 2017

  20. [20]

    Essig, J

    R. Essig, J. Mardon, and T. Volansky,Direct Detection of Sub-GeV Dark Matter,Phys. Rev. D85(2012) 076007, [arXiv:1108.5383]. [28]MEG IICollaboration, K. Afanaciev et al.,New limit on theµ + →e +γdecay with the MEG II experiment,Eur. Phys. J. C85(2025), no. 10 1177, [arXiv:2504.15711]. [Erratum: Eur.Phys.J.C 85, 1317 (2025)]

    Pith/arXiv arXiv 2012

  21. [21]

    Hahn,Generating Feynman diagrams and amplitudes with FeynArts 3,Comput

    T. Hahn,Generating Feynman diagrams and amplitudes with FeynArts 3,Comput. Phys. Commun.140(2001) 418–431, [hep-ph/0012260]

    Pith/arXiv arXiv 2001

  22. [22]

    Mertig, M

    R. Mertig, M. Bohm, and A. Denner,FEYN CALC: Computer algebraic calculation of Feynman amplitudes,Comput. Phys. Commun.64(1991) 345–359

    1991

  23. [23]

    Shtabovenko, R

    V. Shtabovenko, R. Mertig, and F. Orellana,FeynCalc 10: Do multiloop integrals dream of computer codes?,Comput. Phys. Commun.306(2025) 109357, [arXiv:2312.14089]

    arXiv 2025

  24. [24]

    H. H. Patel,Package-X 2.0: A Mathematica package for the analytic calculation of one-loop integrals,Comput. Phys. Commun.218(2017) 66–70, [arXiv:1612.00009]

    Pith/arXiv arXiv 2017

  25. [25]

    Shtabovenko,FeynHelpers: Connecting FeynCalc to FIRE and Package-X,Comput

    V. Shtabovenko,FeynHelpers: Connecting FeynCalc to FIRE and Package-X,Comput. Phys. Commun.218(2017) 48–65, [arXiv:1611.06793]

    Pith/arXiv arXiv 2017

  26. [26]

    Lavoura,General formulae for f(1) —>f(2) gamma,Eur

    L. Lavoura,General formulae for f(1) —>f(2) gamma,Eur. Phys. J. C29(2003) 191–195, [hep-ph/0302221]. [35]Particle Data GroupCollaboration, S. Navas et al.,Review of particle physics,Phys. Rev. D110(2024), no. 3 030001. – 23 – [36]CMSCollaboration, V. Khachatryan et al.,Constraints on the pMSSM, AMSB model and on other models from the search for long-lived...

    Pith/arXiv arXiv 2003

  27. [27]

    M. M. Altakach, S. Kraml, A. Lessa, S. Narasimha, T. Pascal, C. Ramos, Y. Villamizar, and W. Waltenberger,SModelS v3: going beyondZ 2 topologies,JHEP11(2024) 074, [arXiv:2409.12942]

    arXiv 2024

  28. [28]

    LLP Recasting Repository

    “LLP Recasting Repository.”https://github.com/llprecasting/recastingCodes

  29. [29]

    Alwall, R

    J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer, H. S. Shao, T. Stelzer, P. Torrielli, and M. Zaro,The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations,JHEP07(2014) 079, [arXiv:1405.0301]

    Pith/arXiv arXiv 2014

  30. [30]

    R. D. Ball et al.,Parton distributions with LHC data,Nucl. Phys. B867(2013) 244–289, [arXiv:1207.1303]

    Pith/arXiv arXiv 2013

  31. [31]

    Bierlich et al.,A comprehensive guide to the physics and usage of PYTHIA 8.3,SciPost Phys

    C. Bierlich et al.,A comprehensive guide to the physics and usage of PYTHIA 8.3,SciPost Phys. Codeb.2022(2022) 8, [arXiv:2203.11601]

    Pith/arXiv arXiv 2022

  32. [32]

    Heinrich, M

    L. Heinrich, M. Feickert, G. Stark, and K. Cranmer,pyhf: pure-Python implementation of HistFactory statistical models,J. Open Source Softw.6(2021), no. 58 2823

    2021

  33. [33]

    J. Y. Araz,Spey: Smooth inference for reinterpretation studies,SciPost Phys.16(2024), no. 1 032, [arXiv:2307.06996]

    arXiv 2024

  34. [34]

    J. Y. Araz, B. Fuks, M. D. Goodsell, and M. Utsch,Recasting LHC searches for long-lived particles with MadAnalysis 5,Eur. Phys. J. C82(2022), no. 7 597, [arXiv:2112.05163]

    arXiv 2022

  35. [35]

    Fuks and J

    B. Fuks and J. Y. Araz,Implementation of a search for sleptons and electroweakinos in the dilepton + MET channel (139 fb-1; ATLAS-SUSY-2018-32), 2020. [49]DELPHES 3Collaboration, J. de Favereau, C. Delaere, P. Demin, A. Giammanco, V. Lemaˆ ıtre, A. Mertens, and M. Selvaggi,DELPHES 3, A modular framework for fast simulation of a generic collider experiment...

    Pith/arXiv arXiv 2018