pith. sign in

arxiv: 2605.24473 · v1 · pith:LMR4XVREnew · submitted 2026-05-23 · ✦ hep-ph

Freeze-in SU(2) vector dark matter at low reheating temperature

Dilip Kumar Ghosh , Sourav Gope , Xiao-Gang He , Xuan Hong , Sk Jeesun This is my paper

Pith reviewed 2026-06-30 13:13 UTC · model grok-4.3

classification ✦ hep-ph
keywords freeze-invector dark matterSU(2) dark sectorlow reheating temperaturerelic abundancedirect detection
0
0 comments X

The pith

SU(2) vector dark matter achieves the observed relic density with larger couplings at low reheating temperatures because three mass-degenerate states contribute to the yield.

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

The paper shows that a low reheating temperature lets the freeze-in mechanism for SU(2) vector dark matter work with couplings large enough to be probed by direct detection. The non-abelian gauge structure supplies three stable, mass-degenerate vector bosons without extra symmetries, so their combined abundance widens the allowed parameter region compared with a single abelian vector. A reader cares because this setup already excludes part of the space with PandaX-4T and LZ data while leaving other regions accessible to DARWIN.

Core claim

In the SU(2)_HS framework the three vector bosons remain stable without additional discrete symmetries and are produced by freeze-in. At low reheating temperature the observed relic density is obtained with couplings large enough that direct searches already constrain part of the parameter space and future experiments can reach more. The multiplicity of the three states produces a distinctly larger viable region than the corresponding U(1) case.

What carries the argument

The SU(2)_HS gauge symmetry that automatically yields three mass-degenerate stable vector bosons whose freeze-in yield at low T_RH sets the relic density.

If this is right

  • The required DM couplings become sizable, placing part of the space under existing direct-search limits.
  • A significant remaining region lies within the projected sensitivity of DARWIN.
  • The multiplicity of three states enlarges the viable parameter space relative to an abelian vector model.
  • No extra discrete symmetry is required to stabilize the dark matter candidates.

Where Pith is reading between the lines

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

  • Non-abelian dark sectors may systematically offer larger testable windows than abelian ones once low-reheating cosmologies are considered.
  • The same multiplicity could affect the shape of the recoil spectrum or the relative rates in different direct-detection targets.
  • Varying the precise value of T_RH would trace out how the excluded and allowed regions shift with the reheating scale.

Load-bearing premise

The three vector bosons stay stable and never reach thermal equilibrium with the Standard Model bath even when the allowed couplings become larger.

What would settle it

A calculation or measurement showing that the three vectors thermalize with the Standard Model at the couplings needed to match the relic density for a given low T_RH.

read the original abstract

The freeze-in mechanism for dark matter (DM) requires extremely feeble interactions with the Standard Model (SM), preventing thermal equilibrium in the early Universe and typically evading experimental detection. However, for sufficiently low reheating temperatures ($T_{\rm RH}$), the observed relic abundance can be realized with larger couplings, opening prospects for experimental searches. In this work, we investigate freeze-in production of $SU(2)_{\rm HS}$ vector dark matter (VDM) in a low-$T_{\rm RH}$ cosmology. The framework naturally contains three mass-degenerate stable VDM candidates without the need for any additional discrete symmetry. We perform a systematic study of the dark matter phenomenology and identify the parameter space consistent with the observed relic abundance. In contrast to conventional freeze-in scenarios, the required DM couplings can be sizable, rendering part of the parameter space already constrained by existing direct searches like PandaX-4T and LZ, while a significant region remains within the reach of future experiments such as DARWIN. Though one can realize the freeze-in mechanism for an abelian $U(1)_X$ vector DM models as well, we find that the non-abelian structure of the $SU(2)_{\rm HS}$ scenario leads to a distinct feature due to a larger number of dark matter particles, resulting in an enlarged viable parameter space due to the multiplicity of dark matter states.

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

1 major / 1 minor

Summary. The manuscript investigates freeze-in production of SU(2)_HS vector dark matter in a low reheating temperature (T_RH) cosmology. It claims that the non-abelian structure naturally yields three mass-degenerate stable vector DM candidates without additional discrete symmetries, enabling larger portal couplings than in standard freeze-in while still matching the observed relic abundance. This multiplicity enlarges the viable parameter space relative to abelian U(1)_X vector DM models. Portions of the resulting parameter space are already constrained by PandaX-4T and LZ, with more within reach of DARWIN.

Significance. If the relic-density calculation and stability assumptions hold, the work would demonstrate how low-T_RH cosmologies can render freeze-in DM experimentally accessible and how non-abelian gauge structure can produce a distinct multiplicity-driven enlargement of parameter space. This supplies a concrete, falsifiable example of non-abelian versus abelian distinctions in non-standard early-universe scenarios.

major comments (1)
  1. [Model setup and stability discussion] Model setup (implicit in abstract and introduction): The central claim of an enlarged viable parameter space rests on the three vectors remaining stable DM candidates produced purely by freeze-in, without extra discrete symmetries. At the larger portal couplings permitted by low T_RH, the same coupling that sets the freeze-in yield could induce thermalization with the SM bath or open decay channels; the manuscript must explicitly verify that the hidden-sector breaking pattern protects all three states against these effects, otherwise the multiplicity advantage and the Boltzmann-equation solution are invalidated.
minor comments (1)
  1. [Abstract] The abstract states that 'a systematic study' is performed but does not specify the range of T_RH values or the numerical method used for the yield integration; adding these details would improve clarity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive major comment. We address the point below and will revise the manuscript accordingly to strengthen the presentation.

read point-by-point responses

  1. Referee: Model setup (implicit in abstract and introduction): The central claim of an enlarged viable parameter space rests on the three vectors remaining stable DM candidates produced purely by freeze-in, without extra discrete symmetries. At the larger portal couplings permitted by low T_RH, the same coupling that sets the freeze-in yield could induce thermalization with the SM bath or open decay channels; the manuscript must explicitly verify that the hidden-sector breaking pattern protects all three states against these effects, otherwise the multiplicity advantage and the Boltzmann-equation solution are invalidated.

    Authors: We agree that an explicit verification of stability and the absence of thermalization is required to support the central claims, particularly at the larger portal couplings enabled by low T_RH. In the model, the SU(2)_HS is broken by a scalar vev such that the three vector states remain mass-degenerate and stable without additional discrete symmetries, owing to the structure of the hidden-sector gauge interactions and the portal. However, we acknowledge that the current manuscript presents this implicitly. In the revised version we will add a dedicated subsection that (i) details the breaking pattern, (ii) computes the decay widths of the vectors into SM states via the portal, showing they remain negligible throughout the viable parameter space, and (iii) verifies that the interaction rates do not drive thermalization with the SM bath for the couplings consistent with the observed relic density. This will explicitly justify the use of the freeze-in Boltzmann equations and the multiplicity advantage over abelian models. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation self-contained with standard relic-density matching

full rationale

The visible text (abstract) states that the SU(2)_HS model naturally yields three mass-degenerate stable vectors without extra discrete symmetry and that the non-abelian structure enlarges the viable parameter space via multiplicity. No equations, Boltzmann solutions, or self-citations are quoted that reduce a claimed prediction to a fitted input by construction, import uniqueness from prior author work, or smuggle an ansatz. The relic-abundance consistency is the conventional external benchmark procedure in the field and remains falsifiable by direct-detection experiments; it does not meet any of the enumerated circularity patterns. The derivation chain is therefore self-contained.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

Based solely on the abstract: the model assumes standard freeze-in production, automatic stability of the three vectors without extra symmetry, and that low T_RH prevents thermalization at the couplings needed for the observed relic density.

free parameters (3)
  • portal coupling
    Adjusted to reproduce the observed relic abundance for given mass and T_RH
  • DM mass
    Scanned to identify viable regions consistent with direct-search limits
  • reheating temperature T_RH
    Treated as a free input that controls the maximum temperature and thus the freeze-in yield
axioms (2)
  • domain assumption The three SU(2) vector bosons are stable without additional discrete symmetry
    Stated explicitly in the abstract as a natural feature of the non-abelian setup
  • domain assumption Freeze-in production remains valid and does not lead to thermal equilibrium at the larger couplings allowed by low T_RH
    Central to the claim that sizable couplings become viable

pith-pipeline@v0.9.1-grok · 5790 in / 1486 out tokens · 26984 ms · 2026-06-30T13:13:32.879258+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

27 extracted references · 24 canonical work pages · 12 internal anchors

  1. [1]

    Zwicky,Die Rotverschiebung von extragalaktischen Nebeln,Helv

    F. Zwicky,Die Rotverschiebung von extragalaktischen Nebeln,Helv. Phys. Acta6(1933) 110–127

    1933

  2. [2]

    V. C. Rubin and W. K. Ford, Jr.,Rotation of the Andromeda Nebula from a Spectroscopic Survey of Emission Regions,Astrophys. J.159(1970) 379–403

    1970

  3. [3]

    A direct empirical proof of the existence of dark matter

    D. Clowe, M. Bradac, A. H. Gonzalez, M. Markevitch, S. W. Randall, C. Jones et al.,A direct empirical proof of the existence of dark matter,Astrophys. J. Lett.648(2006) L109–L113, [astro-ph/0608407]. [4]Planckcollaboration, N. Aghanim et al.,Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys.641(2020) A6, [1807.06209]. – 16 –

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  4. [4]

    Supersymmetric Dark Matter

    G. Jungman, M. Kamionkowski and K. Griest,Supersymmetric dark matter,Phys. Rept.267 (1996) 195–373, [hep-ph/9506380]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  5. [5]

    Particle Dark Matter: Evidence, Candidates and Constraints

    G. Bertone, D. Hooper and J. Silk,Particle dark matter: Evidence, candidates and constraints, Phys. Rept.405(2005) 279–390, [hep-ph/0404175]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  6. [6]

    J. L. Feng,Dark Matter Candidates from Particle Physics and Methods of Detection,Ann. Rev. Astron. Astrophys.48(2010) 495–545, [1003.0904]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  7. [7]

    The Waning of the WIMP? A Review of Models, Searches, and Constraints

    G. Arcadi, M. Dutra, P. Ghosh, M. Lindner, Y. Mambrini, M. Pierre et al.,The waning of the WIMP? A review of models, searches, and constraints,Eur. Phys. J. C78(2018) 203, [1703.07364]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  8. [8]

    WIMP dark matter candidates and searches - current status and future prospects

    L. Roszkowski, E. M. Sessolo and S. Trojanowski,WIMP dark matter candidates and searches—current status and future prospects,Rept. Prog. Phys.81(2018) 066201, [1707.06277]. [10]PandaX-IIcollaboration, X. Cui et al.,Dark Matter Results From 54-Ton-Day Exposure of PandaX-II Experiment,Phys. Rev. Lett.119(2017) 181302, [1708.06917]. [11]PandaXcollaboration, ...

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  9. [9]

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

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  10. [10]

    The Dawn of FIMP Dark Matter: A Review of Models and Constraints

    N. Bernal, M. Heikinheimo, T. Tenkanen, K. Tuominen and V. Vaskonen,The Dawn of FIMP Dark Matter: A Review of Models and Constraints,Int. J. Mod. Phys. A32(2017) 1730023, [1706.07442]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  11. [11]

    Cosme, F

    C. Cosme, F. Costa and O. Lebedev,Freeze-in at stronger coupling,Phys. Rev. D109(2024) 075038, [2306.13061]

    work page arXiv 2024

  12. [12]

    MeV-scale Reheating Temperature and Thermalization of Neutrino Background

    M. Kawasaki, K. Kohri and N. Sugiyama,MeV scale reheating temperature and thermalization of neutrino background,Phys. Rev. D62(2000) 023506, [astro-ph/0002127]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  13. [13]

    The oscillation effects on thermalization of the neutrinos in the universe with low reheating temperature

    K. Ichikawa, M. Kawasaki and F. Takahashi,The Oscillation effects on thermalization of the neutrinos in the Universe with low reheating temperature,Phys. Rev. D72(2005) 043522, [astro-ph/0505395]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  14. [14]

    Silva-Malpartida, N

    J. Silva-Malpartida, N. Bernal, J. Jones-P´ erez and R. A. Lineros,From WIMPs to FIMPs with low reheating temperatures,JCAP09(2023) 015, [2306.14943]

    work page arXiv 2023

  15. [15]

    Koutroulis, O

    F. Koutroulis, O. Lebedev and S. Pokorski,Gravitational production of sterile neutrinos,JHEP 04(2024) 027, [2310.15906]

    work page arXiv 2024

  16. [16]

    S. Khan, J. Kim and H. M. Lee,Higgs portal vector dark matter at a low reheating temperature, JCAP06(2025) 040, [2503.17621]

    work page arXiv 2025

  17. [17]

    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, [2405.03760]. – 17 –

    work page arXiv 2024

  18. [18]

    K. K. Boddy, K. Freese, G. Montefalcone and B. Shams Es Haghi,Minimal dark matter freeze-in with low reheating temperatures and implications for direct detection,Phys. Rev. D 111(2025) 063537, [2405.06226]

    work page arXiv 2025

  19. [19]

    Arcadi, D

    G. Arcadi, D. Cabo-Almeida and O. Lebedev,Z’-mediated dark matter freeze-in at stronger coupling,Phys. Lett. B861(2025) 139268, [2409.02191]

    work page arXiv 2025

  20. [20]

    B´ elanger, N

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

    work page arXiv 2025

  21. [21]

    Arias, B

    P. Arias, B. D´ ıaz S´ aez, L. Duarte, J. Jones-P´ erez, W. Rodriguez and D. Z. Herrera,Probing displaced (dark)photons from low reheating freeze-in at the LHC,JHEP01(2026) 135, [2507.15930]

    work page arXiv 2026

  22. [22]

    Minimal Freeze-in Dark Matter: Reviving electroweak doublet dark matter with Boltzmann suppressed freeze-in

    N. Bernal, S. Mukherjee and J. Unwin,Minimal Freeze-in Dark Matter: Reviving electroweak doublet dark matter with Boltzmann suppressed freeze-in,2602.10112

    work page internal anchor Pith review Pith/arXiv arXiv

  23. [23]

    Hidden vector dark matter

    T. Hambye,Hidden vector dark matter,JHEP01(2009) 028, [0811.0172]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  24. [24]

    Baouche, A

    N. Baouche, A. Ahriche, G. Faisel and S. Nasri,Phenomenology of the hidden SU(2) vector dark matter model,Phys. Rev. D104(2021) 075022, [2105.14387]. [31]Particle Data Groupcollaboration, S. Navas et al.,Review of particle physics,Phys. Rev. D 110(2024) 030001. [32]ATLAS, CMScollaboration, G. Aad et al.,Measurements of the Higgs boson production and decay...

    work page arXiv 2021

  25. [25]

    A. et. al.,Measurement of separate cosmic-ray electron and positron spectra with the fermi large area telescope,Physical Review Letters108(Jan., 2012)

    2012

  26. [26]

    Calore, M

    F. Calore, M. Cirelli, L. Derome, Y. Genolini, D. Maurin, P. Salati et al.,AMS-02 antiprotons and dark matter: Trimmed hints and robust bounds,SciPost Phys.12(2022) 163, [2202.03076]. [37]DAR WINcollaboration, J. Aalbers et al.,DARWIN: towards the ultimate dark matter detector,JCAP11(2016) 017, [1606.07001]

    work page arXiv 2022

  27. [27]

    Frigerio, N

    M. Frigerio, N. Grimbaum-Yamamoto and T. Hambye,Dark matter from the centre of SU(N), SciPost Phys.15(2023) 177, [2212.11918]. – 18 –

    work page arXiv 2023