Pith. sign in

REVIEW 3 major objections 5 minor 55 references

A minimal hidden non-Abelian gauge sector broken to a massless U(1)_D can produce the observed dark matter abundance through freeze-in of millicharged vector particles, with couplings around 10^-7 that satisfy all current astrophysical and

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-03 17:38 UTC pith:IFIK6AKL

load-bearing objection A genuinely new non-Abelian vector freeze-in model with careful appendices, but the hidden-sector thermal ansatz, an omitted depletion cross section, and fit-to-relic normalization leave the headline numbers not yet secure. the 3 major comments →

arxiv 2512.08622 v2 pith:IFIK6AKL submitted 2025-12-09 hep-ph

Freeze-in Production of Non-Abelian Millicharged Vector Dark Matter

Van Que Tran , Tzu-Chiang Yuan This is my paper
classification hep-ph PACS 95.35.+d
keywords dark matterfreeze-inmillichargedark photonnon-Abelian hidden sectorvector dark matterkinetic mixingtwo-temperature Boltzmann
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper argues that the entire observed dark matter density can be produced by freeze-in from a minimal hidden non-Abelian gauge sector: an SU(2)_D with a real Higgs triplet, spontaneously broken to a massless U(1)_D dark photon. A massive vector pair W' acquires small millicharges through a dimension-five kinetic mixing operator whose effective coefficient is loop- and mass-suppressed to ~10^-7. Solving a two-temperature Boltzmann evolution with in-medium plasmon decays, the authors find a wide parameter region that reproduces Ω_DM h^2 ≈ 0.12 while satisfying halo-shape, BBN, CMB, and precision-constraint bounds. The scenario predicts cross sections within reach of upcoming sub-GeV electron-recoil direct-detection searches, making it testable.

Core claim

The central claim is that freeze-in of vector dark matter from a non-Abelian hidden sector is predictive and viable without extra dark states. The model contains a hidden SU(2)_D gauge group broken by a real triplet to a massless U(1)_D; the massive W' pair is stable under the unbroken U(1)_D and carries a millicharge induced by a dimension-5 operator, with coefficient ϵ = -c5 g_D g' v_Σ / Λ. For portal couplings ϵ, g_D ~ 10^-7 and W' mass near 0.01 GeV, the two-temperature Boltzmann equations—including SM annihilation, Z-boson decay, dark-Higgs processes, and plasmon decay—yield the observed relic density while satisfying bounds from dark-photon couplings, halo ellipticity, ΔN_eff, BBN, and

What carries the argument

The central mechanism is the dimension-five kinetic mixing operator O_5 = c5 g_D g' / Λ Tr[Σ W_μν^D] B^{μν}, which after triplet VEV v_Σ generates a dimension-four mixing ϵ W^{3 μν}_D B_{μν} with ϵ = -c5 g_D g' v_Σ / Λ. This operator endows the massive dark vectors W^{p,m} with millicharges while preserving a massless dark photon. The relic abundance is computed with a two-temperature (T, T_h) Boltzmann framework tracking W', Z', and h_D yields, with J_h encoding all energy exchange; hidden-sector Bose-Einstein integrals and thermally averaged cross sections and decay widths carry the numerical analysis.

Load-bearing premise

The calculation assumes the hidden-sector species—though produced out of equilibrium—remain internally thermalized at a single hidden temperature T_h; if the true momentum distributions are non-thermal, the relic abundance and the viable parameter region could shift.

What would settle it

Compute the freeze-in yield without the T_h assumption, solving the full momentum-dependent Boltzmann equations for W', Z', and h_D; if the resulting relic density departs from Ω_DM h^2 ≈ 0.12 for the paper's benchmark couplings, or if the depletion region moves, the central claim fails. Observationally, a null result from sub-GeV electron-recoil detectors covering the predicted (m_W', σ_e) band at the stated sensitivity would rule out the minimal parameter space.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • With ϵ, g_D ~ 10^-7 the observed relic density is reproduced for a wide region of (m_W', ϵ) and (m_W', g_D) space, with reheating temperatures from 0.1 GeV to 1 TeV.
  • The massless dark photon is consistent with fifth-force, stellar, supernova, and MICROSCOPE bounds when δ→0, and the Z-pole LEP bound δ < 6.4×10^-3 is satisfied.
  • At high g_D, dark-sector annihilations W'W'→Z'Z' and W'W'→h_D h_D deplete the freeze-in population; above those lines the viable region is cut off, leaving a narrow band.
  • The relic abundance is sensitive to the initial hidden-to-visible temperature ratio ξ_0; ξ_0 ≳ 0.5 is excluded by ΔN_eff < 0.18 from BBN+CMB.
  • The predicted electron-recoil cross section is within reach of OSCURA and aluminum superconducting detectors, so the model is testable.

Where Pith is reading between the lines

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

  • If the two-temperature assumption is relaxed to full momentum-dependent non-thermal distributions, the depletion boundary and the relic yield may shift; a Boltzmann solver without a single T_h would provide a sharper test of the claimed wide region.
  • The same dimension-5 operator with a different scalar representation could produce variants (fermionic or scalar millicharged dark matter) with similar freeze-in phenomenology, suggesting a broader class of predictive millicharge freeze-in models.
  • Since the dark photon is massless and couples to SM fermions only via δ→0 or higher-dimensional operators, the strongest foreseeable experimental probe is electron-recoil direct detection; a null result across the predicted band would disfavor the minimal version but not the freeze-in mechanism itself.
  • The model's dependence on a UV completion (a heavy fermion near 1 TeV) implies collider searches for charged heavy leptons could indirectly test the origin of ϵ; a discovery of such states with the predicted properties would corroborate the setup.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes a hidden SU(2)_D gauge sector with a real triplet scalar whose vacuum expectation value breaks the symmetry to a massless U(1)_D, leaving a massive vector pair W'^± as dark matter and a massless dark photon mediator. A dimension-5 operator Tr[Σ W_D^{μν}] B_{μν} is introduced to generate a small kinetic-mixing parameter ϵ after spontaneous symmetry breaking. The authors solve a two-temperature Boltzmann system (Eqs. 9-10) with a hidden temperature T_h, including SM annihilations, Z and Higgs decays, plasmon decay, and hidden-sector annihilation/decay processes. For benchmark BM1 (m_W'=0.01 GeV, g_D=10^{-7}, ϵ=3.8×10^{-7}, ξ_0=0.01, T_RH=1 TeV), they obtain Ω_DM h^2≈0.120. They map the viable parameter space in Fig. 2, apply halo-shape and ΔN_eff bounds, and give direct-detection projections. A second benchmark with nonzero scalar mixing is presented in Appendix J.

Significance. Non-Abelian vector freeze-in with a residual massless U(1)_D is a well-motivated and relatively underexplored variant of millicharged dark matter. If the calculation is correct, the paper provides a concrete model with a parameter region testable by next-generation sub-GeV detectors. Strengths include an explicit UV completion for the dimension-5 operator (Appendix C), a detailed in-medium treatment of plasmon decay (Appendix I), and the inclusion of back-reaction and hidden-sector processes in a two-temperature formalism. However, the numerical results rely on an assumption of internal hidden-sector thermalization that is inconsistent with the freeze-in production mechanism, and a key depletion cross section is not provided. The direct-detection projections are consistency checks on fitted parameters rather than independent predictions, so the "predictive" language should be softened.

major comments (3)
  1. [§III and Appendices E, F] The two-temperature framework assumes the hidden-sector species are internally thermalized at a single T_h: Appendix E uses equilibrium Bose-Einstein integrals with zero chemical potential for ρ_h, p_h, and Appendix F evaluates ⟨σv⟩ and ⟨Γ⟩ at T_h (Eqs. F7-F9). But for the benchmark couplings, freeze-in is the defining regime: with g_D=10^{-7}, α_D≃8×10^{-16}, and a 'thermal' hidden density at T_h≃10 GeV, the hidden elastic scattering rate nσv∼α_D^2 T_h is many orders of magnitude below H∼10^{-13} GeV at T∼1 TeV. Thus W', Z', h_D are not kinetically equilibrated, and their actual phase-space distributions are set by SM production kinematics, not by a Bose-Einstein distribution at T_h. Since the W'W'→Z'Z' and W'W'→h_Dh_D depletion terms in Eq. (F2) are computed with this thermal ansatz, the dotted 'dark-sector thermalization' boundary in Fig. 2 and the relic density in regions where deple
  2. [Appendix H4, Eq. (H16)] The cross section for W p W m → h_D h_D is a load-bearing input: it appears in the DM depletion term of R_{W'} in Eq. (F2), in R_{Z'} and R_{h_D} (Eqs. F3-F4), and in the detailed-balance relation for h_D h_D → W p W m (Eq. H17). However, after presenting the helicity amplitudes in Eq. (H11), the paper states that 'the explicit forms ... will be omitted here.' Since no analytic expression or numerical code is provided, the central numerical results (BM1, BM2, Fig. 2) cannot be reproduced or checked quantitatively. This is particularly serious because W'W'→h_Dh_D controls the 'depletion' boundary in the right panel of Fig. 2. The authors should provide the full cross section or a supplementary code/ancillary file, and at minimum display the corresponding thermally averaged rate.
  3. [§V and Eq. (13)] The observed relic density is used as an input to fix ϵ (and, together with the halo-shape bound, effectively g_D) for each curve in Fig. 2. The direct-detection cross section σ_e in Eq. (13) is then evaluated with the same fitted ϵ and g_D. Therefore the statement that the model 'can be testable' and the projected OSCURA/superconducting reach in Fig. 2 are consistency checks rather than independent predictions. The parameter space also contains several free or under-determined degrees of freedom (m_hD, sinβ, ξ_0, T_RH, and the UV parameters y_Ψ, M_Ψ in Eq. C3). This does not invalidate the relic-density fit, but the abstract's 'first predictive realization' should be moderated and the predictive content stated precisely (e.g., the relation between ϵ and g_D at fixed masses and T_RH).
minor comments (5)
  1. [Fig. 1 and Fig. 2 captions] Typos: 'T op left' should be 'Top left'; 'EDEL WEISS' should be 'EDELWEISS'.
  2. [Eq. (7)] The coupling notation 'δcosθ 1eQf' is garbled; it should read δ cosθ_1 e Q_f.
  3. [Appendix C] The statement that the heavy lepton 'efficiently annihilates into dark gauge bosons before decaying' appears inconsistent with g_D=10^{-7}; the annihilation cross section is suppressed by α_D^2, so the early-universe behavior of Ψ should be quantified or the claim removed.
  4. [Appendix I] The possible dark plasmon decay Z'*→W p W m in the hidden bath is dismissed because δ and g_D are small; in view of the non-thermal hidden distributions this process is not obviously negligible, and a quantitative comment would be useful.
  5. [§V] The text should clarify that ξ_0=0.01 corresponds to a pre-existing hidden radiation component, not an empty hidden sector, and explain how this initial condition is realized or scanned.

Circularity Check

0 steps flagged

No significant circularity: epsilon is explicitly fitted to the relic density; direct-detection projections are independent consistency checks.

full rationale

The derivation chain is self-contained for the purposes of this audit. The model defines m_W' = g_D v_Sigma and epsilon via the dimension-5 operator, then computes freeze-in yields from the coupled Boltzmann system in App. F with rates in App. H-I; no observable used as input is also the output of the same equation. The relic density is used as a constraint, not derived as a prediction: Sec. V states "epsilon adjusted to reproduce the observed relic density," so the headline values eps, gD ~ 1e-7 are a fit to Omega h^2 = 0.120. Calling the model "predictive" is an overstatement given the many free parameters (m_W', m_hD, g_D, epsilon, sin beta, xi_0, T_RH), but overstatement is not circularity. The direct-detection cross section in Eq. (13) depends on the same fitted epsilon and g_D, yet it is an independent experimental observable: no direct-detection data were used to set those parameters, so the projected reach is a genuine consistency check rather than a statistically forced retrodiction. The two-temperature framework assumes internal hidden-sector thermal equilibrium even where freeze-in distributions may be non-thermal; this is a physical approximation and an uncontrolled limitation, but it is not a definitional reduction of an output to an input. The self-citations [4,18] support only qualitative features and a precision constraint; the central Boltzmann and cross-section calculation is derived in the paper and does not rest on those citations. No uniqueness theorem or ansatz is smuggled in via self-citation. Therefore no circular step meets the quoted-equation standard.

Axiom & Free-Parameter Ledger

9 free parameters · 8 axioms · 5 invented entities

The model adds a full hidden gauge sector, a triplet scalar, a massless dark photon, and a heavy UV lepton, while the main success (Ωh^2) is obtained by fitting epsilon and gD. The only genuinely falsifiable handle is the predicted direct-detection cross section, which follows from the same fitted couplings.

free parameters (9)
  • g_D (hidden gauge coupling) = ~1e-7 (BM1 and BM2)
    Sets dark-sector interaction rates and self-interaction strength; chosen, not derived; scanned in Fig. 2 (right).
  • epsilon (induced kinetic-mixing coefficient) = 3.8e-7 (BM1), 1.2e-6 (BM2)
    Adjusted so the freeze-in yield equals the observed Ω_DM h^2 = 0.120; the central fitted parameter.
  • m_W' (dark vector DM mass) = 0.01 GeV (BM1), 0.1 GeV (BM2)
    Scanned in Fig. 2; sets kinematics and direct-detection sensitivity.
  • m_hD (dark Higgs mass) = m_W'/3 (BM1), 0.4 GeV (BM2)
    Chosen benchmark values; affects hidden-sector depletion channels.
  • sinβ (SM-dark scalar mixing) = 0 (BM1), 1e-9 (BM2)
    Chosen small to satisfy LHC Higgs constraints; controls the scalar portal.
  • ξ0 (initial hidden-to-visible temperature ratio) = 0.01
    Initial condition for hidden radiation at T_RH; variation shown in Fig. 3.
  • T_RH (reheating temperature) = 1 TeV (BM1)
    Initial visible temperature; varied from 0.1 GeV to 1 TeV in Fig. 2.
  • δ (dark photon-SM fermion coupling) = 0
    Set to zero by choosing the rotation angle α; needed to satisfy stellar-cooling and equivalence-principle bounds; radiative stability is not calculated.
  • yΨ, MΨ (UV heavy-lepton Yukawa and mass) = yΨ ~ 5, MΨ ~ O(1 TeV) (order of magnitude)
    Enter only through c5/Λ; not independently measured; chosen so that epsilon ~ 1e-7 is natural.
axioms (8)
  • domain assumption The Standard Model gauge structure and particle content are as in the SM.
    Baseline for model building; no beyond-SM effects are included except the dark sector.
  • domain assumption SU(2)_D with a real triplet VEV diag(vΣ, -vΣ) breaks to a residual U(1)_D with a massless dark photon.
    Defines the hidden-sector vacuum; stability of W' relies on the unbroken U(1)_D.
  • domain assumption The dimension-5 operator O5 is the dominant portal; higher-dimensional operators are negligible.
    EFT truncation invoked in Sections II and V; no proof that higher operators are suppressed.
  • domain assumption The one-loop matching c5/Λ ≃ y Re[yΨ]/(12π² MΨ) from integrating out a heavy doublet lepton correctly generates O5 and no light remnants.
    Appendix C gives the matching formula but no independent check of the full UV spectrum.
  • domain assumption The hidden sector is internally thermalized and described by a single temperature T_h with Bose-Einstein integrals for ρ_h, p_h, and thermal cross sections.
    Appendix E/F; the sector is out of equilibrium by construction, so this is an uncontrolled approximation.
  • standard math Combined visible+hidden entropy is conserved; Friedmann expansion uses ρ = ρ_v + ρ_h.
    Appendix D/F; standard two-temperature cosmology.
  • ad hoc to paper δ = 0 is radiatively stable and higher-order corrections to dark-photon-SM couplings are negligible.
    δ = 0 is chosen to satisfy constraints; no loop calculation or naturalness argument is given.
  • domain assumption The observed DM is entirely composed of the symmetric W' component; no asymmetry or multi-component DM.
    Y_W' calculation assumes n_Wp = n_Wm and no other DM species.
invented entities (5)
  • Hidden SU(2)_D gauge symmetry no independent evidence
    purpose: Host vector dark matter and a massless dark photon after triplet breaking
    No direct observational evidence; a model postulate.
  • Massless dark photon Z' no independent evidence
    purpose: Long-range mediator in the dark sector; couples to SM only through higher-dimensional/loop effects because δ = 0
    Not directly observable; constraints enter only through DM self-interactions and ΔNeff.
  • Massive dark vector DM W' (Wp/Wm) independent evidence
    purpose: Stable DM candidate with a tiny electric millicharge
    Predicts electron-recoil rates in sub-GeV direct-detection experiments (SENSEI, XENONnT, OSCURA reach shown in Fig. 2).
  • Real Higgs triplet Σ no independent evidence
    purpose: Breaks SU(2)_D to U(1)_D and generates the W' mass
    Model construction; no direct signature.
  • Heavy Dirac lepton Ψ(1,2,y) no independent evidence
    purpose: UV completion generating the dimension-5 mixing operator
    A generic heavy charged lepton constrained by LHC searches, but no unique signature confirming this particular portal.

pith-pipeline@v1.3.0-alltime-deepseek · 22950 in / 24163 out tokens · 256496 ms · 2026-08-03T17:38:09.689221+00:00 · methodology

0 comments
read the original abstract

We present the first predictive realization, to our knowledge, of vector freeze-in dark matter from a hidden non-Abelian $SU(2)$ gauge sector spontaneously broken by a Higgs triplet to a residual $U(1)$ symmetry with a massless dark photon mediator. A massive dark vector particle-antiparticle pair acquires small millicharges through a dimension-4 kinetic-mixing term with an induced coefficient $\epsilon$, generated by an effective dimension-5 operator involved the Higgs triplet. The dark sector interactions are governed by the hidden gauge coupling $g_D$, providing a weak connection to the Standard Model to realize the freeze-in dark matter production mechanism. Solving the two-temperature Boltzmann evolution including plasmon decay, we find a wide region of parameter space consistent with the observed relic abundance while satisfying astrophysical and cosmological constraints. This minimal framework connects non-Abelian vector dynamics with long-range dark forces and may be probed by upcoming sub-GeV dark matter direct-detection experiments.

Figures

Figures reproduced from arXiv: 2512.08622 by Tzu-Chiang Yuan, Van Que Tran.

Figure 1
Figure 1. Figure 1: Evolution of the dark sector for benchmark point [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Parameter space yielding the correct freeze-in dark matter abundance with reheating temperatures [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Effective number of relativistic species, [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Feynman diagrams for the process of dark matter annihilation into a pair of the SM fermions. [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Feynman diagrams for the process of dark matter annihilation into di- [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Feynman diagrams for the process of dark matter annihilation into a pair of dark scalar boson [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Evolution of the dark sector for benchmark point [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗

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

55 extracted references · 49 linked inside Pith

  1. [1]

    Holdom, Phys

    B. Holdom, Phys. Lett. B166, 196 (1986)

    1986

  2. [2]

    Feldman, Z

    D. Feldman, Z. Liu, and P. Nath, Phys. Rev. D75, 115001 (2007), arXiv:hep-ph/0702123

    Pith/arXiv arXiv 2007

  3. [3]

    Cheung and T.-C

    K. Cheung and T.-C. Yuan, JHEP03, 120 (2007), arXiv:hep-ph/0701107

    Pith/arXiv arXiv 2007

  4. [4]

    V. Q. Tran, T. T. Q. Nguyen, and T.-C. Yuan, JCAP05, 015 (2024), arXiv:2312.10785 [hep-ph]

    Pith/arXiv arXiv 2024

  5. [5]

    P. Ko, T. Nomura, and H. Okada, Phys. Rev. D103, 095011 (2021), arXiv:2007.08153 [hep-ph]

    Pith/arXiv arXiv 2021

  6. [6]

    S. Jana, M. Klasen, V. P. K., and L. P. Wiggering, JCAP02, 011 (2025), arXiv:2406.18641 [hep-ph]

    Pith/arXiv arXiv 2025

  7. [7]

    Foot and S

    R. Foot and S. Vagnozzi, Phys. Rev. D91, 023512 (2015), arXiv:1409.7174 [hep-ph]

    Pith/arXiv arXiv 2015

  8. [8]

    ¯f f→h D The cross section of ¯f f→h D process is given as σ( ¯f f→h D) = π m2 f m2 hD sin2 β 2Nf v2βf s 1− 4m2 f m2 hD ! δ(s−m 2 hD ).(H20) 9.h→ ¯f fandh D → ¯f f If kinematically allowed, scalar bosons can decay into a pair of SM fermions. The decay width of these processes can be given by Γ(h→ ¯f f) = Nf m2 f mh cos2 β 16πv 2 1− 4m2 f m2 h !3/2 ,(H21) ...

  9. [9]

    Foot and S

    R. Foot and S. Vagnozzi, JCAP07, 013 (2016), arXiv:1602.02467 [astro-ph.CO]

    Pith/arXiv arXiv 2016

  10. [10]

    Hambye, M

    T. Hambye, M. H. G. Tytgat, J. Vandecasteele, and L. Vanderheyden, Phys. Rev. D100, 095018 (2019), arXiv:1908.09864 [hep-ph]

    Pith/arXiv arXiv 2019

  11. [11]

    Braaten and D

    E. Braaten and D. Segel, Phys. Rev. D48, 1478 (1993), arXiv:hep-ph/9302213

    Pith/arXiv arXiv 1993

  12. [12]

    Dvorkin, T

    C. Dvorkin, T. Lin, and K. Schutz, Phys. Rev. D99, 115009 (2019), [Erratum: Phys.Rev.D 105, 119901 (2022)], arXiv:1902.08623 [hep-ph]

    Pith/arXiv arXiv 2019

  13. [13]

    Keil, H.-T

    W. Keil, H.-T. Janka, D. N. Schramm, G. Sigl, M. S. Turner, and J. R. Ellis, Phys. Rev. D56, 2419 (1997), arXiv:astro- ph/9612222

    arXiv 1997

  14. [14]

    Carenza, T

    P. Carenza, T. Fischer, M. Giannotti, G. Guo, G. Mart ´ ınez-Pinedo, and A. Mirizzi, JCAP10, 016 (2019), [Erratum: JCAP 05, E01 (2020)], arXiv:1906.11844 [hep-ph]

    Pith/arXiv arXiv 2019

  15. [15]

    Giannotti, I

    M. Giannotti, I. Irastorza, J. Redondo, and A. Ringwald, JCAP05, 057 (2016), arXiv:1512.08108 [astro-ph.HE]

    Pith/arXiv arXiv 2016

  16. [16]

    Berg´ e, P

    J. Berg´ e, P. Brax, G. M´ etris, M. Pernot-Borr` as, P. Touboul, and J.-P. Uzan, Phys. Rev. Lett.120, 141101 (2018), arXiv:1712.00483 [gr-qc]

    Pith/arXiv arXiv 2018

  17. [17]

    Fayet, Phys

    P. Fayet, Phys. Rev. D99, 055043 (2019), arXiv:1809.04991 [hep-ph]

    Pith/arXiv arXiv 2019

  18. [18]

    Schaelet al.(ALEPH, DELPHI, L3, OPAL, SLD, LEP Electroweak Working Group, SLD Electroweak Group, SLD Heavy Flavour Group), Phys

    S. Schaelet al.(ALEPH, DELPHI, L3, OPAL, SLD, LEP Electroweak Working Group, SLD Electroweak Group, SLD Heavy Flavour Group), Phys. Rept.427, 257 (2006), arXiv:hep-ex/0509008

    Pith/arXiv arXiv 2006

  19. [19]

    V. Q. Tran and T.-C. Yuan, Phys. Rev. D111, 013001 (2025), arXiv:2408.11626 [hep-ph]

    Pith/arXiv arXiv 2025

  20. [20]

    B. A. Dobrescu, Phys. Rev. Lett.94, 151802 (2005), arXiv:hep-ph/0411004

    Pith/arXiv arXiv 2005

  21. [21]

    Fabbrichesi, E

    M. Fabbrichesi, E. Gabrielli, and G. Lanfranchi, Springer (2020), 10.1007/978-3-030-62519-1, arXiv:2005.01515 [hep-ph]

    Pith/arXiv arXiv 2020

  22. [22]

    Aboubrahim, W.-Z

    A. Aboubrahim, W.-Z. Feng, P. Nath, and Z.-Y. Wang, Phys. Rev. D103, 075014 (2021), arXiv:2008.00529 [hep-ph]

    Pith/arXiv arXiv 2021

  23. [23]

    Aboubrahim, W.-Z

    A. Aboubrahim, W.-Z. Feng, P. Nath, and Z.-Y. Wang, JHEP06, 086 (2021), arXiv:2103.15769 [hep-ph]

    Pith/arXiv arXiv 2021

  24. [24]

    Aboubrahim, W.-Z

    A. Aboubrahim, W.-Z. Feng, P. Nath, and Z.-Y. Wang, inSnowmass 2021(2021) arXiv:2106.06494 [hep-ph]

    Pith/arXiv arXiv 2021

  25. [25]

    Li and P

    J. Li and P. Nath, Phys. Rev. D108, 115008 (2023), arXiv:2304.08454 [hep-ph]

    Pith/arXiv arXiv 2023

  26. [26]

    Agrawal, F.-Y

    P. Agrawal, F.-Y. Cyr-Racine, L. Randall, and J. Scholtz, JCAP05, 022 (2017), arXiv:1610.04611 [hep-ph]

    Pith/arXiv arXiv 2017

  27. [27]

    T.-H. Yeh, J. Shelton, K. A. Olive, and B. D. Fields, JCAP10, 046 (2022), arXiv:2207.13133 [astro-ph.CO]

    Pith/arXiv arXiv 2022

  28. [28]

    Fradette and M

    A. Fradette and M. Pospelov, Phys. Rev. D96, 075033 (2017), arXiv:1706.01920 [hep-ph]

    Pith/arXiv arXiv 2017

  29. [29]

    Baraket al.(SENSEI), Phys

    L. Baraket al.(SENSEI), Phys. Rev. Lett.125, 171802 (2020), arXiv:2004.11378 [astro-ph.CO]

    Pith/arXiv arXiv 2020

  30. [30]

    Arnquistet al.(DAMIC-M), Phys

    I. Arnquistet al.(DAMIC-M), Phys. Rev. Lett.130, 171003 (2023), arXiv:2302.02372 [hep-ex]

    Pith/arXiv arXiv 2023

  31. [31]

    Arnaudet al.(EDEL WEISS), Phys

    Q. Arnaudet al.(EDEL WEISS), Phys. Rev. Lett.125, 141301 (2020), arXiv:2003.01046 [astro-ph.GA]

    Pith/arXiv arXiv 2020

  32. [32]

    Agneseet al.(SuperCDMS), Phys

    R. Agneseet al.(SuperCDMS), Phys. Rev. Lett.121, 051301 (2018), [Erratum: Phys.Rev.Lett. 122, 069901 (2019)], arXiv:1804.10697 [hep-ex]

    Pith/arXiv arXiv 2018

  33. [33]

    Z. Y. Zhanget al.(CDEX), Phys. Rev. Lett.129, 221301 (2022), arXiv:2206.04128 [hep-ex]

    Pith/arXiv arXiv 2022

  34. [34]

    Agneset al.(DarkSide), Phys

    P. Agneset al.(DarkSide), Phys. Rev. Lett.130, 101002 (2023), arXiv:2207.11968 [hep-ex]

    arXiv 2023

  35. [35]

    Aprileet al.(XENON), Phys

    E. Aprileet al.(XENON), Phys. Rev. Lett.134, 161004 (2025), arXiv:2411.15289 [hep-ex]

    Pith/arXiv arXiv 2025

  36. [36]

    Chenget al.(PandaX-II), Phys

    C. Chenget al.(PandaX-II), Phys. Rev. Lett.126, 211803 (2021), arXiv:2101.07479 [hep-ex]

    Pith/arXiv arXiv 2021

  37. [37]

    Aguilar-Arevaloet al.(Oscura), (2022), arXiv:2202.10518 [astro-ph.IM]

    A. Aguilar-Arevaloet al.(Oscura), (2022), arXiv:2202.10518 [astro-ph.IM]

    Pith/arXiv arXiv 2022

  38. [38]

    B. A. Cervantes-Vergaraet al.(Oscura), JINST18, P08016 (2023), arXiv:2304.04401 [physics.ins-det]

    Pith/arXiv arXiv 2023

  39. [39]

    Hochberg, Y

    Y. Hochberg, Y. Kahn, N. Kurinsky, B. V. Lehmann, T. C. Yu, and K. K. Berggren, Phys. Rev. Lett.127, 151802 (2021), arXiv:2101.08263 [hep-ph]

    Pith/arXiv arXiv 2021

  40. [40]

    Knapen, J

    S. Knapen, J. Kozaczuk, and T. Lin, Phys. Rev. D104, 015031 (2021), arXiv:2101.08275 [hep-ph]

    Pith/arXiv arXiv 2021

  41. [41]

    Knapen, T

    S. Knapen, T. Lin, M. Pyle, and K. M. Zurek, Phys. Lett. B785, 386 (2018), arXiv:1712.06598 [hep-ph]

    Pith/arXiv arXiv 2018

  42. [42]

    Griffin, S

    S. Griffin, S. Knapen, T. Lin, and K. M. Zurek, Phys. Rev. D98, 115034 (2018), arXiv:1807.10291 [hep-ph]

    Pith/arXiv arXiv 2018

  43. [43]

    Aghanimet al.(Planck), Astron

    N. Aghanimet al.(Planck), Astron. Astrophys.641, A6 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO]

    Pith/arXiv arXiv 2020

  44. [44]

    Akerset al.(OPAL), Z

    R. Akerset al.(OPAL), Z. Phys. C67, 203 (1995)

    1995

  45. [45]

    A. A. Prinzet al., Phys. Rev. Lett.81, 1175 (1998), arXiv:hep-ex/9804008

    Pith/arXiv arXiv 1998

  46. [46]

    Acciarriet al.(ArgoNeuT), Phys

    R. Acciarriet al.(ArgoNeuT), Phys. Rev. Lett.124, 131801 (2020), arXiv:1911.07996 [hep-ex]

    Pith/arXiv arXiv 2020

  47. [47]

    Ballet al., Phys

    A. Ballet al., Phys. Rev. D102, 032002 (2020), arXiv:2005.06518 [hep-ex]

    arXiv 2020

  48. [48]

    Magill, R

    G. Magill, R. Plestid, M. Pospelov, and Y.-D. Tsai, Phys. Rev. Lett.122, 071801 (2019), arXiv:1806.03310 [hep-ph]. 22

    Pith/arXiv arXiv 2019

  49. [49]

    Marocco and S

    G. Marocco and S. Sarkar, SciPost Phys.10, 043 (2021), arXiv:2011.08153 [hep-ph]

    Pith/arXiv arXiv 2021

  50. [50]

    Aadet al.(ATLAS), Nature607, 52 (2022), [Erratum: Nature 612, E24 (2022)], arXiv:2207.00092 [hep-ex]

    G. Aadet al.(ATLAS), Nature607, 52 (2022), [Erratum: Nature 612, E24 (2022)], arXiv:2207.00092 [hep-ex]

    Pith/arXiv arXiv 2022

  51. [51]

    M. Ardu, M. H. Rahat, N. Valori, and O. Vives, JHEP11, 049 (2024), arXiv:2407.21100 [hep-ph]

    Pith/arXiv arXiv 2024

  52. [52]

    Aadet al.(ATLAS), JHEP07, 118 (2023), arXiv:2303.05441 [hep-ex]

    G. Aadet al.(ATLAS), JHEP07, 118 (2023), arXiv:2303.05441 [hep-ex]

    Pith/arXiv arXiv 2023

  53. [53]

    Hayrapetyanet al.(CMS), Phys

    A. Hayrapetyanet al.(CMS), Phys. Rept.1115, 570 (2025), arXiv:2405.17605 [hep-ex]

    Pith/arXiv arXiv 2025

  54. [54]

    B´ elanger, F

    G. B´ elanger, F. Boudjema, A. Goudelis, A. Pukhov, and B. Zaldivar, Comput. Phys. Commun.231, 173 (2018), arXiv:1801.03509 [hep-ph]

    Pith/arXiv arXiv 2018

  55. [55]

    Hindmarsh and O

    M. Hindmarsh and O. Philipsen, Phys. Rev. D71, 087302 (2005), arXiv:hep-ph/0501232

    Pith/arXiv arXiv 2005