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REVIEW 4 major objections 4 minor 96 references

Probing Dark Matter freeze-in with long-lived particle signatures: MATHUSLA, HL-LHC and FCC-hh

T0 review · 4 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper argues that a surface detector at the LHC could cover a wide region of viable freeze-in dark-matter parameter space, probing dark-matter masses up to about 1–10 GeV, and that a forward detector at a 100 TeV collider could reach…

desk verdict Solid, transparent freeze-in LLP study with real technical progress in the relic calculation; read the sensitivity curves with the stated detector idealizations in mind. read the letter →

arxiv 1908.11387 v1 pith:BLQVQAYH submitted 2019-08-29 hep-ph

Jose Miguel No , Patrick Tunney , Bryan Zaldivar This is my paper · ORCID
classification hep-ph
keywords freeze-indarkmatterlong-livedparticlesMATHUSLAHiggsportaldisplacedverticeselectroweakphasetransitionthermalmassesLyman-alphabound
topics Dark Matter
open problems Dark Matter
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

Freeze-in dark matter is produced so feebly that the parent particles decaying into it can be long-lived, and this paper asks whether proposed long-lived-particle detectors could catch those decays. Using a minimal Higgs-portal model in which a fermion singlet mixes with a fermion doublet after electroweak symmetry breaking, it computes the relic density with thermal masses and the electroweak phase transition included, and then projects the reach of MATHUSLA, HL-LHC displaced-vertex searches, and a forward detector at a 100 TeV collider. The central claim is that MATHUSLA could cover a wide slice of the cosmologically allowed freeze-in parameter space between the Lyman-alpha and BBN limits, probing dark-matter masses up to about 1–10 GeV, while the 100 TeV forward detector could probe parent masses up to about 10 TeV. A sympathetic reader would care because freeze-in is one of the few non-thermal dark-matter production mechanisms that leaves a concrete, testable collider imprint, and the projected sensitivities turn a cosmological production mechanism into an experimental target.

What carries the argument

The load-bearing object is the long-lived parent state χ2, a mostly-doublet Dirac fermion whose mixing with the dark-matter singlet is set by yχv/√2(m2 − m1). The production mechanism is freeze-in from decay: bath particles χ2 and ψ± decay into the dark-matter candidate χ1 with a feeble coupling, and the dark-matter yield is set by ΓA/H at temperatures near T ∼ mA/3. The search strategy rests on the decay-length formula cτχ2 ∝ m1/m2² and on the probability Pdecay = exp(−La/βcτ) − exp(−Lb/βcτ) that a boosted parent decays inside a given detector volume; MATHUSLA’s projected reach is computed from this probability times its geometric acceptance, with the 95% C.L. sensitivity set at three signal events in a background-free detector. The relic-density calculation is carried out with a modified version of micrOMEGAS5.0 that includes the thermal masses ΠH(T) and ΠΨ(T) and the electroweak phase-transition temperature TEW.

What would settle it

A full detector-level simulation of MATHUSLA including cosmic-ray and beam backgrounds, applied to the χ2 → h χ1 signal, would settle the reach: if backgrounds exceed about one event in the signal region at 300 fb⁻¹, the three-signal-event sensitivity contours in Figures 6 and 9 do not hold, and simulating decays with m2 close to mh + m1 would test whether the acceptance assumption that decay products hit the tracking layers holds.

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Extended reading notes

Core claim

In the singlet-doublet freeze-in model studied here, the dark-matter candidate χ1 is produced by the decays χ2 → h χ1, χ2 → Z χ1, and ψ± → W± χ1; requiring ΩDM h² = 0.12 fixes the parent decay length to roughly cτ ≈ 4 km × (m1/100 MeV)(500 GeV/m2)² in the limit m2 ≫ m1, so cosmologically viable parameters naturally have macroscopic lifetimes. The paper shows that this lifetime window overlaps the design sensitivity of MATHUSLA, that combined with the ATLAS displaced-vertex-plus-missing-energy search the two probes cover decay lengths from about a meter to 10⁷ meters and dark-matter masses from the Lyman-alpha bound up to a few GeV, and that a forward detector at a 100 TeV hadron collider would extend parent-mass reach to about 10 TeV and lifetimes up to the BBN bound for m2 ≲ 600 GeV. It also establishes that including the thermal masses of the Higgs doublet and the parent doublet, together with the temperature of the electroweak phase transition, changes the predicted relic density by up to a factor of about five in parts of the parameter space.

Load-bearing premise

The projections assume MATHUSLA and the FCC-hh forward detector are background-free with perfect detection efficiency, so the 95% C.L. limit is set at three signal events, and that the visible χ2 decay products always hit the tracking layers whenever the parent trajectory does; if backgrounds, reconstruction efficiencies, or that acceptance assumption are worse, the projected reach shrinks.

Editorial extensions

If this is right

  • MATHUSLA100 and MATHUSLA200 could probe dark-matter masses from the Lyman-alpha bound up to m1 ∼ 1–10 GeV, covering a wide region of the viable freeze-in parameter space between the Lyman-alpha and BBN constraints.
  • For decay lengths cτχ2 ≲ 100 m, the ATLAS displaced-vertex-plus-missing-energy search is the most sensitive probe, while MATHUSLA dominates at larger decay lengths; together they cover decay lengths from about a meter to 10⁷ meters.
  • A forward detector at a 100 TeV proton-proton collider with 3 or 30 ab⁻¹ of integrated luminosity could probe parent masses up to about 10 TeV and reach lifetimes up to the BBN bound for m2 ≲ 600 GeV.
  • Including thermal masses and the electroweak phase transition changes the predicted relic density by up to a factor of about five, so earlier freeze-in-from-decay relic computations that omitted these effects can be off by that amount in parts of the parameter space.
  • The super-WIMP contribution becomes sizable only for m2 > 1.1 TeV and m1 ≳ 300 GeV, and in that region the freeze-in and super-WIMP contributions must be added together when matching the observed dark-matter abundance.

Reading between the lines

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

  • If the background-free, perfect-efficiency assumption is relaxed, the same approach applied to other freeze-in parents, such as dark photons or heavy neutral leptons, would likely preserve the qualitative complementarity between a surface detector and displaced-vertex searches, but the reach would shrink roughly as the square root of the required event count.
  • The thermal-mass correction identified here is generic to freeze-in from decay, so existing relic-density calculations for other long-lived-parent models may need a similar revision; the paper states this generality but does not quantify it for other models.
  • The forward detector’s geometric acceptance of about 0.5 at 100 TeV suggests that even a moderate detector volume placed down the beam line could outperform a large surface detector for very long lifetimes, which could motivate optimising forward geometry in future collider designs.
  • The assumption that the visible decay products hit the tracking layers whenever the parent trajectory does is only justified for m2 ≫ mh + m1; for compressed spectra near m2 ≈ mh + m1, a full detector simulation could either validate or shrink the claimed sensitivity contours.
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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

4 major / 4 minor

Summary. The paper studies freeze-in dark matter production through the decay of a neutral parent particle, using as a concrete model a singlet-doublet fermion extension of the Standard Model with the Higgs as the visible decay product. It computes the dark matter relic density with modified micrOMEGAs code including thermal masses and a temperature-dependent treatment of electroweak symmetry breaking, and it derives cosmological constraints from Big Bang Nucleosynthesis and Lyman-alpha observations. The main phenomenological results are projected 95% C.L. sensitivities for the MATHUSLA100/MATHUSLA200 surface detectors, for ATLAS/CMS searches at the HL-LHC (mono-jet, disappearing tracks, and displaced vertices plus missing transverse energy), and for a forward detector at a future 100 TeV FCC-hh. The authors find that MATHUSLA can probe a wide region between the Lyman-alpha and BBN constraints, that the FCC-hh forward detector could extend the reach to parent masses up to about 10 TeV, and that thermal-mass corrections can change the freeze-in relic abundance by up to a factor of about five in parts of the parameter space.

Significance. If the projections hold, the paper provides a useful and fairly complete case study of how long-lived particle searches can probe freeze-in dark matter, including a well-documented recast of the ATLAS displaced-vertex search and the use of NLO+NLL Higgsino production cross sections. The treatment of thermal masses and of the electroweak phase transition addresses a gap in earlier freeze-in studies, and the comparison among MATHUSLA, LHC searches, and the FCC-hh forward detector gives a clear picture of complementarity. The authors are also unusually explicit about the limitations of their assumptions, which makes the paper easier to evaluate. The headline sensitivity claims, however, rest on idealized detector assumptions and on a benchmark electroweak transition temperature that is not realized in the minimal model, so the quantitative conclusions should be treated as conditional.

major comments (4)
  1. [Section 5, Eqs. (5.2)-(5.4), Fig. 6] The MATHUSLA projections are obtained by assuming that visible decay products of chi2 hit the tracking layers whenever the chi2 trajectory does, and the text explicitly states that this is only automatic for m2 much larger than mh + m1. For m2 approaching mh + m1 the authors acknowledge that a more detailed event and detector simulation is needed. This is a load-bearing assumption because Figure 6 and the conclusions use it to claim coverage of a wide region of the freeze-in parameter space, including parts where m2 is not large compared with mh. The authors should either provide a detector-level or conservative geometric treatment of this region or explicitly restrict the coverage claim to the regime where collinearity holds.
  2. [Section 7, Eq. (5.4) and Fig. 10] The FCC-hh forward detector sensitivity is computed under the assumptions of perfect detector performance and a background-free environment, with the 95% C.L. reach set at three signal events, but no background estimate is given for the forward volume z in [20,40] m, rho in [5,30] m at a 100 TeV pp collider. Neutral hadron interactions, pile-up, and fake displaced vertices could produce backgrounds in this geometry, and the central claims of reaching parent masses up to 10 TeV and lifetimes up to the BBN bound for m2 below about 600 GeV are derived directly from this assumption. A background estimate or a well-justified background-free argument is needed before these projections can be considered robust.
  3. [Appendix B, Figs. 13-14 and Fig. 9] The recast validation shows that the authors' derived limits are stronger than those of ATLAS in the compressed gluino region, and the text acknowledges that the corresponding freeze-in region is m2 close to mh. The DV + Emiss_T exclusion contours in Figure 9 therefore overestimate the true sensitivity precisely where the Higgs decay channel is phase-space suppressed. Since these contours are used in the comparison with MATHUSLA and in the complementarity discussion, this region should be marked as approximate or the recast should be improved.
  4. [Section 3.2, Figs. 2-3] The statement that thermal masses change the relic density by up to a factor of about five relies on the benchmark TEW = 50 GeV, which the authors describe as corresponding to a strongly super-cooled first-order electroweak phase transition. The model defined by Eq. (3.2) contains no additional scalar dynamics that would turn the Standard Model crossover into such a transition, so the largest thermal-mass effect is not realized in the minimal model. The authors should either justify how TEW = 50 GeV arises within the model or present the factor-five result as an illustration for a non-minimal extension rather than as a property of the specific freeze-in scenario studied here.
minor comments (4)
  1. [Section 5, Eq. (5.1)] The decay-length estimate uses '4 Km'; for consistency with the rest of the paper and the figures, this should be '4 km'.
  2. [Section 6.1, Eq. (6.1)] The mono-jet rescaling uses up-type quark couplings only, and the text notes that a full treatment would re-weight down-type contributions; this approximation should be stated directly in the equation or its caption so that readers do not mistake Eq. (6.1) for the exact signal strength.
  3. [Figure 1, right panel] The caption lists branching-ratio values but does not explain how to read the color scale or contours in the (m2, ctau_chi2) plane; a brief description would improve interpretability.
  4. [Section 7] The geometric acceptance epsilon_geometric ~ 0.5 for the forward detector is quoted without a derivation or a definition of whether it includes the decay-product geometry; stating the definition used in the simulation would make the result reproducible.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the relic-density and sensitivity calculations are anchored in external codes, published LHC data, and validated recasts, with no fitted parameter renamed as a prediction.

full rationale

The central derivation chain is self-contained rather than circular. The relic-density curves are computed with micrOMEGAs5.0 [46], a public code whose freeze-in implementation is documented and widely used; one of the present authors is a co-author of that code, but the code is an independently maintained tool and its use does not make the paper's conclusion equivalent to its input. The observed relic abundance Omega h^2 = 0.12 is imposed as an external cosmological constraint to draw benchmark lines in the (m2, c_tau_chi2) plane, and the DM Yukawa coupling is not fitted to the projected reach; it is simply the model parameter that fixes the parent-particle lifetime through the freeze-in condition. The MATHUSLA and FCC-hh sensitivity contours are obtained from NLO+NLL Higgsino pair-production cross sections computed with Resummino-2.0.1, from Madgraph/Pythia/Delphes simulations, and from published ATLAS/CMS analyses, with the ATLAS displaced-vertex recast validated against ATLAS's own long-lived-gluino model in Appendix B. The two assumptions highlighted in the skeptical reading, namely collinear decay products entering the MATHUSLA tracking layers for m2 >> mh + m1 and a background-free FCC-hh forward detector, are optimistic detector-modeling assumptions; they may affect the numerical reach, but they are not fitted inputs, definitions, or self-citations that make any prediction reduce to its input. No equation is reused as both input and output, no uniqueness theorem is imported from the authors' prior work, and no fitted parameter is renamed as a prediction. The self-citation to micrOMEGAs5.0 is therefore minor and non-load-bearing, and the central claims retain independent physical content.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central analysis imports the singlet-doublet model, micrOMEGAs, Resummino cross sections, and ATLAS and CMS data. The only parameter tuned to data is the dark matter Yukawa coupling, fixed by the relic abundance, and the electroweak phase transition temperature is scanned. The main additional assumptions are the cosmological history and idealized detector performance listed above.

free parameters (2)
  • y_ch (singlet-doublet Yukawa coupling) = set by Omega_DM h^2 = 0.12; around 1e-10 for the m1 = 1 GeV benchmark in Fig. 2
    Determines the parent decay width and thereby the freeze-in yield; fixed by requiring the observed dark matter relic abundance.
  • T_EW (electroweak phase transition temperature) = 50, 100, and 160 GeV (scanned)
    Controls which decay channels contribute above and below the phase transition and affects the relic density by up to a factor of about five in parts of the parameter space.
assumptions (5)
  • domain assumption Standard cosmological history: radiation domination during production, negligible initial dark matter abundance, and entropy conservation.
    Invoked in Section 2, Eqs. (2.2) through (2.7) and footnote 4; a modified expansion or reheating history would change the yield and the c-tau lines.
  • domain assumption The parent particles chi2 and psi+/- are in thermal equilibrium with the SM bath during freeze-in.
    Used in Section 2 and throughout the relic density calculation; equilibrium fixes the parent abundance n_A^eq in Eq. (2.3).
  • domain assumption Above the electroweak phase transition, electroweak symmetry is restored, so Z and W interactions with dark matter vanish and only Psi -> H chi operates, with thermal masses given by Eqs. (3.8) through (3.10).
    Section 3.2 and Appendix A rely on this to decide which channels contribute at high temperature and to regulate Z-mediated 2 to 2 scattering.
  • domain assumption The Lyman-alpha bound for freeze-in from two-body decay, Eq. (4.3), derived in Refs. [69,70], applies to this model.
    Section 4 uses this to set the lower bound on m1 and the corresponding lower bound on c-tau; if the mapping is not valid for this model, the allowed parameter band changes.
  • ad hoc to paper MATHUSLA and the FCC-hh forward detector are background-free with perfect detection efficiency, giving exclusion at Nevents = 3.
    Sections 5 and 7, Eq. (5.4), translate cross section and decay probability into sensitivity curves under this optimistic detector assumption, which is not verified with full detector simulation.

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Pith. "Pith review of Probing Dark Matter freeze-in with long-lived particle signatures: MATHUSLA, HL-LHC and FCC-hh." pith.science (2026). https://pith.science/paper/BLQVQAYH

@misc{pith2026190811387,
  author       = {Pith},
  title        = {Pith review of: Probing Dark Matter freeze-in with long-lived particle signatures: MATHUSLA, HL-LHC and FCC-hh},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BLQVQAYH}},
  note         = {Machine review of arXiv:1908.11387}
}
abstract

Collider searches for long-lived particles yield a promising avenue to probe the freeze-in production of Dark Matter via the decay of a parent particle. We analyze the prospects of probing the parameter space of Dark Matter freeze-in from the decay of neutral parent particles at the LHC and beyond, taking as a case study a freeze-in Dark Matter scenario via the Standard Model Higgs. We obtain the projected sensitivity of the proposed MATHUSLA surface detector (for MATHUSLA100 and MATHUSLA200 configurations) for long-lived particle searches to the freeze-in Dark Matter parameter space, and study its complementarity to searches by ATLAS and CMS at HL-LHC, as well as the interplay with constraints from Cosmology: Big-Bang Nucleosynthesis and Lyman-$\alpha$ forest observations. We then analyze the improvement in sensitivity that would come from a forward detector within a future 100 TeV $pp$-collider. In addition, we discuss several technical aspects of the present Dark Matter freeze-in scenario: the role of the electroweak phase transition; the inclusion of thermal masses, which have been previously disregarded in freeze-in from decay studies; the impact of $2\to 2$ scattering processes on the Dark Matter relic abundance; and the interplay between freeze-in and super-WIMP Dark Matter production mechanisms.

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