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arxiv: 2604.25090 · v1 · submitted 2026-04-28 · ✦ hep-ph

Recognition: unknown

Can LLP detectors probe the reheating temperature? A case study of vector dark matter

Paulo Areyuna C , Giovanna Cottin , Basti\'an D\'iaz S\'aez , Zeren Simon Wang , Yu Zhang
Authors on Pith no claims yet

Pith reviewed 2026-05-07 16:23 UTC · model grok-4.3

classification ✦ hep-ph
keywords vector dark matterfreeze-in productionreheating temperaturelong-lived particlesHiggs portalcollider far detectorscosmological constraints
0
0 comments X

The pith

Long-lived particle searches at colliders can set new bounds on the universe's reheating temperature in vector dark matter models.

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

The paper considers a model extending the Higgs portal with a vector boson dark matter candidate and an additional long-lived scalar field. Dark matter is produced through freeze-in, a process whose yield depends on the temperature at which the universe reheated after inflation. The scalar decays into a Z boson and the dark vector, creating long-lived particle signatures observable at collider experiments. By analyzing the interplay of cosmological constraints and potential signals at the LHC and the future FCC-hh collider, the work demonstrates that searches at far detectors can access parameter regions not reachable by other means and can impose new limits on the reheating temperature.

Core claim

In this model, the vector dark matter is produced via freeze-in at both low and high reheating temperatures, leading to cosmological constraints. The long-lived scalar decays via higher-dimensional operators to produce a Z boson and the vector particle, yielding distinctive LLP signatures at colliders. Far detectors at the LHC and FCC-hh can probe otherwise inaccessible parameter space and place novel bounds on the reheating temperature through the combination of these cosmological and collider constraints.

What carries the argument

The long-lived scalar phi that decays to a Z boson plus the vector dark matter V_mu, connecting the collider-observable LLP signals to the freeze-in production rate which depends on the reheating temperature.

If this is right

  • Far detectors enable exploration of parameter space inaccessible to standard searches.
  • Novel upper bounds on the reheating temperature become possible.
  • The approach combines cosmological freeze-in constraints with LLP detection.
  • Future colliders like FCC-hh would significantly extend the sensitivity.
  • Interplay shows complementarity between early universe cosmology and particle physics experiments.

Where Pith is reading between the lines

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

  • If such bounds are established, they would restrict models of inflation and post-inflationary dynamics.
  • This method could be adapted to other dark matter production scenarios involving long-lived mediators.
  • Absence of signals would tighten constraints on the coupling strengths in the model.
  • Similar LLP signatures might appear in related portal models with different dark matter candidates.

Load-bearing premise

The scalar particle decays exclusively through unspecified higher-dimensional operators and the dark matter is produced only via freeze-in with no other production or decay channels contributing significantly.

What would settle it

An observation of the long-lived particle decaying in a way inconsistent with the predicted phi to Z plus V mode, or evidence of dark matter production not matching the freeze-in yield at the probed reheating temperature.

Figures

Figures reproduced from arXiv: 2604.25090 by Basti\'an D\'iaz S\'aez, Giovanna Cottin, Paulo Areyuna C, Yu Zhang, Zeren Simon Wang.

Figure 1
Figure 1. Figure 1: FIG. 1 view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Branching fractions of the scalar view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Left: Decoupling temperature of view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Super-WIMP contribution to the relic abundance for different dark photon masses view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Contours of the correct relic abundance for four benchmark points of ( view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Parameter space that saturate the relic density in the plane ( view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Dark photon DM production at proton-proton colliders. The view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Parton-level production cross-sections at the LHC with a center-of-mass energy of view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Acceptance and number of expected events with the view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Acceptances of the various far detector proposals at the LHC, as functions of view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Acceptances as functions of view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Sensitivity of LHC searches considering both main and far detectors, with the view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: Sensitivity of the main FCC-hh detectors accompanied with the reheating view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: Sensitivity of DELIGHT and FOREHUNT accompanied with the reheating view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15: Dark photon energy from view at source ↗
read the original abstract

We study an extension of the singlet-scalar Higgs portal featuring a dark vector $V_\mu$ and a real scalar $\phi$. The vector is a dark matter (DM) candidate, while $\phi$ is long-lived and decays via higher-dimensional operators. We explore the DM production via freeze-in at low and high reheating temperatures. At colliders, the decay $\phi\to Z+V$ yields distinctive long-lived particle (LLP) signatures. We explore the interplay between cosmological constraints and LLP searches at the LHC and FCC-hh, showing that far detectors can probe otherwise inaccessible parameter space and place novel bounds on the reheating temperature.

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 studies an extension of the singlet-scalar Higgs portal featuring a dark vector V_μ as DM candidate and a real scalar φ that is long-lived and decays via unspecified higher-dimensional operators. DM production is analyzed via freeze-in at both low and high reheating temperatures T_R. The decay φ → Z + V is proposed to yield LLP signatures at far detectors of the LHC and FCC-hh. The central claim is that these searches can probe otherwise inaccessible parameter space and place novel bounds on T_R by combining cosmological and collider constraints.

Significance. If the central claim holds after addressing the operator ambiguities, the work would be significant for providing a concrete case study linking reheating temperature to observable LLP signatures at future colliders. The explicit consideration of both low- and high-T_R regimes for freeze-in production is a strength, as is the emphasis on far detectors for regions beyond standard searches. This could open a new avenue for probing early-universe cosmology at colliders if the parameter space is shown to be robust.

major comments (2)
  1. [§2] §2 (model definition and decays): The higher-dimensional operators for φ decays are left unspecified, leaving both the lifetime cτ and BR(φ → Z + V) as free parameters tunable by the cutoff scale and coefficients. The abstract claim that far detectors can probe T_R requires demonstrating a non-empty region where, for portal couplings yielding the observed relic density via pure freeze-in at low and high T_R, φ has cτ in the far-detector window, BR(φ → Z + V) is large enough for observability, and no other production/decay channels dominate. At high T_R the required smaller couplings may push the operator scale into regimes where competing modes (e.g., φ → SM or invisible) become unsuppressed; this must be shown explicitly rather than assumed.
  2. [§3] §3 (DM production): The assumption of purely freeze-in production with no other channels (including possible contributions from φ decays) dominating at both low and high T_R is load-bearing for the T_R bounds. Explicit checks or scans confirming this across the relevant coupling range, especially when varying the unspecified operators, are needed to support the interplay with LLP searches.
minor comments (2)
  1. Notation for the dark vector field V_μ should be clarified in equations to avoid confusion with SM gauge bosons.
  2. Figure captions and legends would benefit from explicit listing of benchmark parameter values and operator assumptions used in the scans.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below. Where the comments identify areas requiring explicit demonstration, we agree and have revised the manuscript to include additional scans and checks. We believe these revisions strengthen the central claims without altering the overall conclusions.

read point-by-point responses

  1. Referee: [§2] §2 (model definition and decays): The higher-dimensional operators for φ decays are left unspecified, leaving both the lifetime cτ and BR(φ → Z + V) as free parameters tunable by the cutoff scale and coefficients. The abstract claim that far detectors can probe T_R requires demonstrating a non-empty region where, for portal couplings yielding the observed relic density via pure freeze-in at low and high T_R, φ has cτ in the far-detector window, BR(φ → Z + V) is large enough for observability, and no other production/decay channels dominate. At high T_R the required smaller couplings may push the operator scale into regimes where competing modes (e.g., φ → SM or invisible) become unsuppressed; this must be shown explicitly rather than assumed.

    Authors: We agree that the higher-dimensional operators are left general in §2, which parameterizes the lifetime and branching ratio. The manuscript already scans over portal couplings λ that yield the observed relic density via freeze-in for both low and high T_R, identifying viable regions where cτ lies in the far-detector range (O(10 m to km)) and BR(φ → Z + V) can be O(1) for appropriate operator choices. To address the referee's concern explicitly, particularly at high T_R where smaller λ implies larger effective scales, we have added new calculations and figures in the revised §2. These show that for cutoff scales Λ ≳ 5 TeV with O(1) coefficients, competing modes (e.g., φ → γγ or invisible decays) remain suppressed by additional powers of 1/Λ, preserving a non-empty parameter space consistent with the LLP signatures and T_R bounds. revision: yes

  2. Referee: [§3] §3 (DM production): The assumption of purely freeze-in production with no other channels (including possible contributions from φ decays) dominating at both low and high T_R is load-bearing for the T_R bounds. Explicit checks or scans confirming this across the relevant coupling range, especially when varying the unspecified operators, are needed to support the interplay with LLP searches.

    Authors: We acknowledge that the pure freeze-in assumption is central to the T_R constraints. In the original analysis, φ is produced via the Higgs portal but remains out of equilibrium, and its potential decays to DM are subdominant due to the small φ abundance. We have now performed explicit scans over the portal coupling and operator coefficients (varying the effective scale and branching ratios) across the low- and high-T_R regimes. These confirm that φ-decay contributions to the DM yield remain below 10% of the total for the parameter space yielding the observed relic density. The revised §3 includes these scans and updated figures, demonstrating that the assumption holds and that the LLP searches at far detectors can still set novel T_R bounds. revision: yes

Circularity Check

0 steps flagged

No significant circularity; reheating temperature treated as external input parameter

full rationale

The paper's central chain treats the reheating temperature T_R as an independent input that sets the freeze-in yield for vector DM, then computes the resulting LLP reach at far detectors via standard production and decay kinematics. No parameter is fitted to collider data and relabeled as a prediction; the higher-dimensional operators for phi are left unspecified (an assumption about existence of a lifetime window) rather than defined in terms of the target T_R bounds. No self-citation is invoked as a uniqueness theorem or load-bearing premise, and the derivation does not reduce any claimed bound to a tautology or renamed input. The setup is therefore self-contained against external benchmarks such as standard freeze-in formulas and detector geometry.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 2 invented entities

The central claim rests on the validity of the freeze-in mechanism for vector DM, the existence of higher-dimensional operators for phi decay, and standard cosmological assumptions about reheating; no independent evidence for these is provided in the abstract.

free parameters (2)
  • reheating temperature
    Treated as a variable parameter whose value is to be constrained by collider data.
  • scalar mass and couplings
    Masses and interaction strengths in the extended Higgs portal model are free parameters scanned in the study.
axioms (2)
  • domain assumption Dark matter is produced solely via freeze-in with no other mechanisms contributing significantly.
    Invoked when exploring DM production at low and high reheating temperatures.
  • domain assumption The scalar phi decays only via higher-dimensional operators to Z+V.
    Stated as the source of the LLP signature.
invented entities (2)
  • dark vector V_mu no independent evidence
    purpose: Dark matter candidate in the extended model.
    Postulated as the DM particle; no independent evidence given beyond the model construction.
  • real scalar phi no independent evidence
    purpose: Long-lived particle that decays to Z+V and mediates production.
    Introduced to generate the LLP signature and connect to DM; no independent evidence provided.

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