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arxiv: 2512.05380 · v1 · submitted 2025-12-05 · ✦ hep-ph · astro-ph.CO· hep-ex

Illuminating sequential freeze-in dark matter with dark photon signal at the CERN SHiP experiment

Xinyue Yin , Sibo Zheng This is my paper

Pith reviewed 2026-05-17 01:59 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.COhep-ex
keywords sequential freeze-indark matterdark photonSHiP experimentkinetic mixingrelic abundanceproton bremsstrahlung
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The pith

Sequential freeze-in dark matter fixes dark charge to 1.3e-12 and restricts mixing parameter to narrow range near 10^{-11}

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

This paper examines sequential freeze-in dark matter in a two-field setup with a dark photon mediator whose mass lies between 0.01 and 10 GeV. It shows that the observed relic abundance together with the requirement that the dark photon stays out of equilibrium fixes the dark charge to e' approximately 1.3 times 10 to the minus 12 and confines the kinetic mixing parameter to the interval from 10 to the minus 11 up to less than 10 to the minus 8 or 10 to the minus 7.5. Within this window the projected 5-year and 15-year proton bremsstrahlung data at the proposed SHiP experiment, under vector-meson or dipole dominance assumptions, exclude most of the higher mixing values at 90 percent confidence level, leaving only a small slice near 10 to the minus 11 open to other probes.

Core claim

We show that the dark charge is fixed to be e'∼1.3×10−12 and the mixing parameter is restricted to 10−11≤ε<10−8−10−7.5, as a result of the out-of-equilibrium condition of dark photon and the observed relic abundance of dark matter. Within this ε region, the 5(15)-year data of proton bremsstrahlung process for the dark photon, assuming vector meson (dipole) dominance, excludes ε≥10−8.5 (10−7.9) at 90% confidence level, implying only a narrow region of ε close to ∼10−11 left for alternative tests.

What carries the argument

Out-of-equilibrium dark photon mediator whose couplings are fixed by relic abundance in the sequential freeze-in mechanism, with detection via proton bremsstrahlung at a fixed-target experiment.

If this is right

  • The dark charge is fixed to e' ∼ 1.3 × 10^{-12}.
  • The mixing parameter ε is restricted to 10^{-11} ≤ ε < 10^{-8}−10^{-7.5}.
  • Five-year SHiP data excludes ε ≥ 10^{-8.5} at 90% CL under vector meson dominance.
  • Fifteen-year SHiP data excludes ε ≥ 10^{-7.9} under dipole dominance.
  • Only the narrow region near ε ∼ 10^{-11} survives for alternative tests.

Where Pith is reading between the lines

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

  • Complementary searches at other fixed-target facilities could target the surviving narrow window.
  • The result highlights how two-field freeze-in scenarios can produce observable mediator signals unlike single-field cases.
  • Non-observation at SHiP would require revisiting the production channel assumptions or the out-of-equilibrium premise.
  • The fixed couplings offer a concrete benchmark for broader dark-sector models with small mixing.

Load-bearing premise

The dark photon remains out of equilibrium and proton bremsstrahlung is dominated by vector mesons or dipoles.

What would settle it

Non-observation of the predicted dark photon events in the proton bremsstrahlung channel after 5 or 15 years of SHiP running would rule out all but the narrowest mixing values near 10^{-11}.

Figures

Figures reproduced from arXiv: 2512.05380 by Sibo Zheng, Xinyue Yin.

Figure 1
Figure 1. Figure 1: FIG. 1. The observed DM relic abundance arising from the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The values of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The sequential freeze-in DM parameter space corresponding to [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

Single-field freeze-in dark matter barely leaves observable footprints in dark matter direct detection, collider or fixed-target experiments, which can be altered in the two-field context. In this work, we consider sequential freeze-in dark matter through signals of dark photon mediator with a mass range of $m_{A'}\sim 10^{-2}-10$ GeV covered by the proposed SHiP experiment. We show that the dark charge is fixed to be $e'\sim 1.3\times 10^{-12}$ and the mixing parameter is restricted to $10^{-11}\leq \epsilon< 10^{-8}-10^{-7.5}$, as a result of the out-of-equilibrium condition of dark photon and the observed relic abundance of dark matter. Within this $\epsilon$ region, the 5(15)-year data of proton bremsstrahlung process for the dark photon, assuming vector meson (dipole) dominance, excludes $\epsilon\geq 10^{-8.5} (10^{-7.9})$ at 90\% confidence level, implying only a narrow region of $\epsilon$ close to $\sim 10^{-11}$ left for alternative tests.

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

3 major / 2 minor

Summary. The paper examines sequential freeze-in dark matter production mediated by a dark photon with mass in the range 0.01–10 GeV, a window accessible to the proposed SHiP experiment. It claims that matching the observed relic abundance fixes the dark charge to e' ∼ 1.3 × 10^{-12}, while the out-of-equilibrium condition for the dark photon restricts the kinetic mixing to 10^{-11} ≤ ε < 10^{-8}–10^{-7.5}. Projected SHiP sensitivities from proton bremsstrahlung, under vector-meson or dipole dominance, then exclude ε ≥ 10^{-8.5} (10^{-7.9}) at 90% CL for 5 (15) years of data, leaving only a narrow viable window near ε ∼ 10^{-11}.

Significance. If the rate comparisons and dominance assumptions hold, the work supplies a concrete, falsifiable prediction that links cosmological freeze-in production to laboratory dark-photon searches at SHiP, thereby tightening the testable parameter space for two-field dark-matter models.

major comments (3)
  1. [Section deriving out-of-equilibrium condition] The upper limit on ε is obtained by requiring the dark-photon interaction rate to remain below the Hubble rate throughout the relevant temperature window; the manuscript should display the explicit Γ(T)/H(T) comparison (including the ε² scaling and any m_A'-dependent approximations) for the full 0.01–10 GeV range so that the claimed 10^{-11} ≤ ε bound can be verified independently.
  2. [SHiP sensitivity and bremsstrahlung section] The SHiP exclusion contours rest on the assumption that proton bremsstrahlung is dominated by vector-meson or dipole contributions; because this directly determines the projected 90% CL limits of ε ≥ 10^{-8.5} (10^{-7.9}), the paper must quantify the sensitivity of those limits to alternative production mechanisms or provide a justification for dominance across the quoted mass interval.
  3. [Relic abundance calculation] The numerical value e' ∼ 1.3 × 10^{-12} is fixed by matching the sequential freeze-in yield to the observed relic density; the manuscript should report the dependence of this value on the assumed freeze-in temperature window and on possible sub-dominant production channels to establish the robustness of the subsequent ε window.
minor comments (2)
  1. [Abstract] The abstract notation “10^{-8}-10^{-7.5}” for the upper edge of the allowed ε interval is imprecise; a single consistent upper bound or an explicit range should be stated.
  2. [Figures] Figure captions should explicitly state which dominance assumption (vector meson or dipole) is used for each projected exclusion curve.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and will revise the manuscript to incorporate additional details and clarifications where appropriate.

read point-by-point responses

  1. Referee: [Section deriving out-of-equilibrium condition] The upper limit on ε is obtained by requiring the dark-photon interaction rate to remain below the Hubble rate throughout the relevant temperature window; the manuscript should display the explicit Γ(T)/H(T) comparison (including the ε² scaling and any m_A'-dependent approximations) for the full 0.01–10 GeV range so that the claimed 10^{-11} ≤ ε bound can be verified independently.

    Authors: We agree that an explicit plot of Γ(T)/H(T) would facilitate independent verification. In the revised version we will add a figure displaying Γ(T)/H(T) versus temperature for representative values of ε and m_{A'} across the full 0.01–10 GeV interval, explicitly showing the ε² scaling and the temperature window used to impose the out-of-equilibrium condition. revision: yes

  2. Referee: [SHiP sensitivity and bremsstrahlung section] The SHiP exclusion contours rest on the assumption that proton bremsstrahlung is dominated by vector-meson or dipole contributions; because this directly determines the projected 90% CL limits of ε ≥ 10^{-8.5} (10^{-7.9}), the paper must quantify the sensitivity of those limits to alternative production mechanisms or provide a justification for dominance across the quoted mass interval.

    Authors: We will expand the relevant section to justify the choice of vector-meson dominance below ~1 GeV and dipole dominance above that scale, citing the relevant literature on dark-photon production at fixed-target facilities. We will also provide a brief estimate of the uncertainty arising from possible sub-dominant direct-quark bremsstrahlung contributions and indicate how the quoted 90% CL contours would shift under a conservative variation of the production rate. revision: yes

  3. Referee: [Relic abundance calculation] The numerical value e' ∼ 1.3 × 10^{-12} is fixed by matching the sequential freeze-in yield to the observed relic density; the manuscript should report the dependence of this value on the assumed freeze-in temperature window and on possible sub-dominant production channels to establish the robustness of the subsequent ε window.

    Authors: We will add a short paragraph and an accompanying plot showing the variation of the required e' when the freeze-in temperature window is shifted by factors of a few and when sub-dominant channels (e.g., direct dark-photon decay contributions) are included at the 10% level. This will confirm that the central value remains stable within the quoted precision under reasonable variations of the integration limits. revision: yes

Circularity Check

0 steps flagged

No significant circularity; parameters fixed via standard relic matching and out-of-equilibrium requirement with independent SHiP projection

full rationale

The derivation fixes e' ≈ 1.3×10^{-12} from the observed relic abundance Ω_DM and restricts 10^{-11} ≤ ε < 10^{-8}–10^{-7.5} via the out-of-equilibrium condition (interaction rate ≲ Hubble) for the dark photon in the sequential freeze-in setup. These are conventional cosmological inputs that determine the viable parameter window before any experimental projection is applied. The SHiP sensitivity to proton bremsstrahlung (under explicit vector-meson or dipole dominance assumptions) is then used to exclude portions of that window, yielding a narrow surviving region near ε ∼ 10^{-11}. No equation reduces to a self-definition, no fitted quantity is relabeled as a first-principles prediction, and no load-bearing step relies on self-citation or smuggled ansatz. The chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claim rests on fitting the dark charge to relic density data and assuming specific equilibrium and production dominance conditions for the dark photon.

free parameters (1)
  • dark charge e' = 1.3e-12
    Fixed by requiring the sequential freeze-in yield to reproduce the observed dark matter relic abundance.
axioms (2)
  • domain assumption The dark photon mediator remains out of equilibrium throughout the freeze-in epoch.
    This condition, together with relic abundance, restricts the allowed range for the mixing parameter ε.
  • domain assumption Proton bremsstrahlung proceeds under vector meson dominance or dipole dominance.
    This choice determines the production rate used to set the SHiP exclusion reach on ε.
invented entities (1)
  • dark photon mediator A' no independent evidence
    purpose: Mediates interactions enabling sequential freeze-in production of dark matter while allowing detectable signals at SHiP.
    Postulated new particle required for the two-field model and the proposed experimental signature.

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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. Exploring non-equilibrium effects in sequential freeze-in

    hep-ph 2026-04 unverdicted novelty 6.0

    In a two-scalar dark sector, non-equilibrium phase-space evolution during sequential freeze-in alters the dark matter relic abundance by up to an order of magnitude relative to the standard number-density treatment.

  2. A new approach to dark photon

    hep-ph 2026-04 unverdicted novelty 5.0

    Dark photon and hypercharge arise from two U(1) groups related by broken mirror symmetry that suppresses their kinetic mixing at one loop.

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