Pith. sign in

REVIEW 2 major objections 5 minor 106 references

$Z^\prime$ Portal Dark Matter with Observable $\Delta N_{\rm eff}$

T0 review · 2 major / 5 minor · reviewed 2026-07-10 · grok-4.5

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

Pith's one-line read Dirac right-handed neutrinos turn ΔN_eff into a decisive filter on Z' portal dark matter, excluding resonance WIMPs below ~400 GeV and leaving secluded and FIMP regions that future CMB can still test.

desk verdict Solid, incremental B-L portal scan that correctly folds the ν_R–χ channel and latest ΔN_eff bounds into concrete (m_χ, Q_χ) windows for resonance, secluded, and FIMP cases. read the letter →

arxiv 2607.08082 v1 pith:OQM2ULGB submitted 2026-07-09 hep-ph

Ang Liu , Zhi-Long Han , Fei Huang This is my paper
classification hep-ph PACS 95.35.+d14.70.Pw98.80.Cq12.60.Cn
keywords Z'portalDiracneutrinosΔN_effWIMPFIMPU(1)_{B-L}darkmatterrelicdensityCMB-S4
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

Standard Z' portal dark-matter models usually assume Majorana right-handed neutrinos, so the only experimental handles are collider searches for the Z' and direct detection of the dark-matter particle. This paper replaces those neutrinos with Dirac fermions protected by an unbroken U(1)_{B-L} symmetry. The same Z' that couples the dark matter to the Standard Model also keeps the three Dirac neutrinos in (or out of) thermal equilibrium, generating a measurable extra radiation density ΔN_eff. Because dark-matter freeze-out or freeze-in and neutrino decoupling are controlled by the same gauge coupling and charge, every viable dark-matter abundance automatically predicts a definite ΔN_eff. Current bounds already force resonant WIMP dark matter above roughly 400 GeV and charge Q_χ ≳ 0.7; secluded and freeze-in candidates can sit below the thermal floor ΔN_eff = 0.14. Future CMB experiments that reach ΔN_eff ~ 0.03 will either discover the signal or rule out the entire resonant branch, while still leaving open windows for the other two production mechanisms.

What carries the argument

The shared Z' portal: both the dark-matter annihilation (or freeze-in) rate and the ν_R ν_R o f f̄ / χ χ̄ scattering rates are controlled by the same product g' Q, so the temperature at which the Dirac neutrinos decouple—and hence the value of ΔN_eff—is locked to the dark-matter abundance.

What would settle it

A future CMB measurement that sets ΔN_eff < 0.14 with no residual excess would completely exclude the resonant WIMP branch of the model while leaving only the secluded and FIMP windows still open.

Watch

Extended reading notes

Core claim

When right-handed neutrinos are Dirac particles charged under the same U(1)_{B-L} that mediates dark-matter interactions, the requirement that the observed relic density be produced through the Z' portal forces a lower bound ΔN_eff ≥ 0.14 in the resonant WIMP case and permits smaller, still-testable values only for secluded WIMPs and FIMPs; the combined cosmological, direct-detection, indirect-detection and collider constraints therefore carve out sharply defined, experimentally accessible regions in the (m_χ, Q_χ) plane.

Load-bearing premise

The B-L symmetry that keeps the right-handed neutrinos Dirac and generates a light Z' via the Stueckelberg mechanism must remain unbroken; any spontaneous breaking that gives the neutrinos Majorana masses or removes the light Z' collapses the whole ΔN_eff prediction.

Editorial extensions

If this is right

  • Resonant WIMP dark matter is forced into a narrow high-mass window (roughly 400 GeV to 10^5 GeV) with charges between ~1 and a few thousand, all of which will be covered by CMB-S4/HD.
  • Secluded and freeze-in candidates can produce ΔN_eff well below 0.14, so a null CMB result does not kill the entire Z' portal scenario.
  • The same parameter space that survives cosmology is already within reach of next-generation direct-detection experiments for TeV-scale masses and of MeV-scale gamma-ray telescopes for the secluded annihilation channel.
  • Collider searches for a light Z' become secondary once ΔN_eff is measured; the cosmological bound is stronger than present LHC and B-factory limits over most of the interesting range.

Reading between the lines

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

  • If Dirac neutrinos are the only light species charged under B-L, a precision ΔN_eff measurement effectively becomes a dark-matter mass and charge spectrometer for any Z' portal model.
  • The same logic can be ported to other anomaly-free U(1) extensions (e.g., L_μ-L_τ) that keep right-handed neutrinos Dirac, potentially turning every future CMB stage into a simultaneous probe of neutrino nature and dark-matter production.
  • A confirmed ΔN_eff excess near 0.14 would favour thermal production of both ν_R and χ, while a value significantly below that floor would point toward freeze-in or secluded dynamics.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper studies a minimal U(1)_{B-L} extension with Dirac right-handed neutrinos u_R (Q_ u R = −1) and a vector-like Dirac dark-matter fermion u_R-protected by unbroken B−L and a Z_2 parity, with the Z′ mass generated by the Stueckelberg mechanism. Free parameters are {m_ u, m_Z′, g′, Q_ u}. Both WIMP (resonant u ū o f f̄ and secluded u ū o Z′Z′) and FIMP production via the Z′ portal are analyzed. The central claim is that thermal and non-thermal u_R contributions to u N_eff, together with perturbativity, direct/indirect detection, and Z′ collider bounds, carve out concrete viable windows: resonant WIMP survives only for roughly 400 GeV ≲ m_ u ≲ 1.54 imes10^5 GeV and 0.7 ≲ Q_ u ≲ 3400 (with u N_eff less 0.14), while secluded and FIMP regions can yield u N_eff < 0.14 and remain testable by CMB-S4/HD. A future null result u N_eff < 0.14 would exclude the resonant case.

Significance. If the results hold, the work supplies a clean, falsifiable link between Z′ portal dark matter and upcoming precision u N_eff measurements. The multi-constraint scans (Figs. 4, 5, 7) and the explicit statement that a null u N_eff < 0.14 kills the resonant WIMP window are concrete predictions that can be tested by CMB-S4/HD, future direct/indirect detection, and colliders. The treatment of the additional u_R ū_R o u ū channel, the piecewise reaction rates, and the consistent use of micrOMEGAs for thermal averages are standard and reproducible within the stated model assumptions. The paper therefore adds a useful, observationally sharp corner to the Z′ portal literature.

major comments (2)
  1. Section II (after Eq. (1) and the Stueckelberg paragraph): the unbroken U(1)_{B-L} that both forbids Majorana masses for u_R and generates the light Z′ is a model-building premise, not an inconsistency. The paper should, however, state more explicitly that any spontaneous breaking that generates Majorana masses or removes the light Z′ collapses the entire u N_eff calculation and the portal structure; a short paragraph quantifying the scale at which this occurs would strengthen the claim’s robustness.
  2. Section III.A, Eqs. (10)–(12) and the discussion of T_ u R^dec vs T_ u^dec: the claim that u_R ū_R o u ū dominates the resonant decoupling for large Q_ u is load-bearing for the floor u N_eff less 0.14. The paper should quantify more carefully the extreme-resonance regime (where phase-space suppression of u Z′ o u ū makes the channel negligible) and show that the quoted mass window 400 GeV ≲ m_ u remains intact when that regime is included.
minor comments (5)
  1. Figure 1 caption and panels: the Unicode/encoding artifacts (e.g. “/uni0000000b”) make the legends hard to read; clean PDF fonts would improve clarity.
  2. Eq. (13) and the surrounding text: the nucleon mass is written m_n less 0.939 GeV; a brief note that the reduced-mass factor is already included would avoid ambiguity.
  3. Section IV.A, freeze-in Boltzmann equations (15)–(16): the neglect of t-channel Z′Z′ and of u ū o u_R ū_R is stated but not quantified; a short numerical check (or reference to the verification mentioned in the text) would be helpful.
  4. Throughout: the notation r_Z′ = m_Z′/m_ u is introduced early but occasionally written inconsistently (r_Z vs r_Z′); unify for readability.
  5. References: a few recent related works on Dirac u_R and u N_eff (e.g. those already cited in the introduction) could be cross-linked more explicitly when the non-thermal results of Ref. [18] are adopted.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: relic-density contours and ΔN_eff floors are computed from free parameters against external experimental bounds.

full rationale

The paper constructs a minimal U(1)_{B-L} model with Dirac ν_R and vector-like DM χ, then solves the Boltzmann equations for freeze-out (WIMP resonance/secluded) and freeze-in (FIMP) production of both χ and ν_R. Relic-density contours (black lines in Figs. 4, 5, 7) are obtained by requiring Ω_χ h^{2} = 0.12 for free parameters {m_χ, m_Z', g', Q_χ}; they are not forced by a normalization chosen to match the target. The thermal ΔN_eff floor of 0.14 follows directly from Eq. (10) once g_*(T_dec) o 106.75, an external SM input. All exclusion regions (DESI, P-ACT, CMB-S4/HD, LZ/XENONnT, AMS/Fermi/HESS, BaBar/LHCb/LEP/CMS/ATLAS) are taken from independent experimental literature. Self-citations (e.g., [53], [54]) supply only prior related calculations and do not close a logical loop that defines the quoted mass/charge windows. The unbroken B-L + Stueckelberg premise is a model-building assumption, not an internal circular construction. The derivation chain is therefore self-contained against external benchmarks.

Assumptions & free parameters 4 free parameters · 4 assumptions · 2 invented entities

The central claim rests on four free parameters of the minimal U(1)_{B-L} extension, standard cosmological Boltzmann evolution, the assumption that B-L remains unbroken (protecting Dirac u_R and generating Z' via Stueckelberg), and the usual experimental upper limits treated as hard cuts. No additional ad-hoc scales are introduced beyond the free parameters themselves.

free parameters (4)
  • m_χ
    Dark-matter mass; scanned freely and fixed only by the requirement of correct relic density plus experimental bounds.
  • m_Z'
    Z' mass (or equivalently the ratio r_Z' = m_Z'/m_χ); free input that sets the resonance or secluded kinematics.
  • g'
    U(1)_{B-L} gauge coupling; free and constrained by perturbativity, collider searches and relic density.
  • Q_χ
    U(1)_{B-L} charge of the dark-matter fermion; arbitrary free parameter that controls both annihilation and direct-detection rates.
assumptions (4)
  • domain assumption Standard cosmological Boltzmann equations for freeze-out and freeze-in with entropy and Hubble rates that include three Dirac u_R degrees of freedom when thermally populated.
    Used throughout Sections III and IV to compute Y_χ and Y_ u_R; taken as standard without re-derivation.
  • ad hoc to paper Unbroken U(1)_{B-L} that both forbids Majorana masses for u_R and generates the Z' mass via the Stueckelberg mechanism.
    Stated in Section II; if violated the Dirac nature and the light Z' portal disappear.
  • domain assumption Yukawa coupling y ≲ 10^{-11} that generates sub-eV Dirac neutrino masses contributes negligibly to ΔN_eff (≈ 7.5 imes10^{-12}).
    Cited from Luo et al.; used to drop the Yukawa contribution entirely.
  • domain assumption Current experimental upper limits on ΔN_eff (DESI ≲ 0.4, P-ACT ≲ 0.17), σ_SI, ⟨σv⟩ and Z' production can be treated as hard exclusion boundaries.
    Applied throughout the figures; standard practice in the field.
invented entities (2)
  • Vector-like Dirac fermion χ with arbitrary U(1)_{B-L} charge Q_χ and Z_2-odd parity
    purpose: Serves as the dark-matter candidate that couples to the Z' portal.
    Introduced in Section II; stability is imposed by hand via an extra Z_2; no independent evidence outside the model.
  • Massive Z' boson generated by the Stueckelberg mechanism under unbroken B-L
    purpose: Mediates the portal interactions between SM fermions, u_R and χ.
    Stated after Eq. (1); the Stueckelberg choice keeps B-L unbroken so that u_R remain Dirac.

how reviews work

0 comments
Cite this review

Pith. "Pith review of $Z^\prime$ Portal Dark Matter with Observable $\Delta N_{\rm eff}$." pith.science (2026). https://pith.science/paper/OQM2ULGB

@misc{pith2026260708082,
  author       = {Pith},
  title        = {Pith review of: $Z^\prime$ Portal Dark Matter with Observable $\Delta N_\rm eff$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OQM2ULGB}},
  note         = {Machine review of arXiv:2607.08082}
}
abstract

In the conventional $Z^\prime$ portal dark matter scenario, the prediction of detectable dark matter $\chi$ typically relies on the collider sensitivities of $Z^\prime$ and direct detection, where the Majorana type right-handed neutrinos are usually assumed. However, if the right-handed neutrinos $\nu_R$ are Dirac type, they will contribute to the additional effective number of relativistic species $\Delta N_{\rm eff}$, which brings different detectable predictions for $Z^\prime$ portal dark matter. In light of the great improvement of $\Delta N_{\rm eff}$ for the upcoming experiments, we investigate the $Z^\prime$ portal dark matter with Dirac type $\nu_R$. Under the $U(1)_{B-L}$ symmetry, this model includes $\nu_R$ with $U(1)_{B-L}$ charge $Q_{\nu_R}=-1$ and $\chi$ with arbitrary $Q_\chi$ beyond the SM. Based on the relation in the production of $\chi$ and $\nu_R$, both the WIMP and FIMP dark matter through the $Z^\prime$ portal scenario are considered. We perform a comprehensive exploration of the viable parameter space under the constraints from $\Delta N_{\rm eff}$ induced by thermal and non-thermal $\nu_R$, perturbative limit, dark matter direct and indirect detection, and collider searches of $Z^\prime$.

Figures

Figures reproduced from arXiv: 2607.08082 by the authors.

Figure 1
Figure 1. FIG. 1. Panel (a): The dependence of DM relic density in the WIMP scenario. Panel (b): Influence of different [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Constraints from DM direct detection experiments and cosmological experiments related to [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The DM indirect detection and [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Comprehensive constraints in the resonance scenario. Panel (a), (b), and (c) correspond to the comprehensive [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Same as Figure 4 but for the secluded scenario. Panels (a), (b), and (c) correspond to cases [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Panel (a): The dependence of DM relic density in the FIMP scenario. Panel (b): The evolution of [PITH_FULL_IMAGE:figures/full_fig_p017_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Same as Figure 4, but for the FIMP scenario. Panel (a), (b), and (c) correspond to cases of [PITH_FULL_IMAGE:figures/full_fig_p019_7.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

106 extracted references · 106 canonical work pages

  1. [1]

    The upcoming results are depicted as a blue dashed line in Figure 2

    will achieve significantly improved sensitivity onσSI, extending the reach downward by approximately one order of magnitude compared to current limits. The upcoming results are depicted as a blue dashed line in Figure 2. In this model, the DM-nucleon scattering process is mediated byZ ′, which can be calculated as σSI = m2 χQ2 χg′4 πm4 Z′(mχ +m n)2 ,(13) ...

    work page

  2. [2]

    J. M. Cline, G. Herrera and J. S. Roux, [arXiv:2603.28859 [hep-ph]]

    work page arXiv

  3. [3]

    Dark Matter

    M. Cirelli, A. Strumia and J. Zupan, [arXiv:2406.01705 [hep-ph]]

    work page Pith review arXiv

  4. [4]

    Evidence for oscillation of atmospheric neutrinos

    Y . Fukudaet al.[Super-Kamiokande], Phys. Rev. Lett.81, 1562-1567 (1998) [arXiv:hep-ex/9807003 [hep-ex]]

    work page Pith review arXiv 1998

  5. [5]

    Q. R. Ahmadet al.[SNO], Phys. Rev. Lett.89, 011301 (2002) [arXiv:nucl-ex/0204008 [nucl-ex]]

    work page Pith review arXiv 2002

  6. [6]

    F. P. Anet al.[Daya Bay], Phys. Rev. Lett.108, 171803 (2012) [arXiv:1203.1669 [hep-ex]]

    work page Pith review arXiv 2012

  7. [7]

    J. K. Ahnet al.[RENO], Phys. Rev. Lett.108, 191802 (2012) [arXiv:1204.0626 [hep-ex]]

    work page Pith review arXiv 2012

  8. [8]

    Particle Dark Matter: Evidence, Candidates and Constraints

    G. Bertone, D. Hooper and J. Silk, Phys. Rept.405, 279-390 (2005) [arXiv:hep-ph/0404175 [hep-ph]]

    work page Pith review arXiv 2005

Show all 106 references
  1. [9]

    Steigman and M

    G. Steigman and M. S. Turner, Nucl. Phys. B253, 375-386 (1985)

    1985

  2. [10]

    Arcadi, M

    G. Arcadi, M. Dutra, P. Ghosh, M. Lindner, Y . Mambrini, M. Pierre, S. Profumo and F. S. Queiroz, Eur. Phys. J. C78, no.3, 203 (2018) [arXiv:1703.07364 [hep-ph]]

    2018 arXiv

  3. [11]

    L. J. Hall, K. Jedamzik, J. March-Russell and S. M. West, JHEP03, 080 (2010) [arXiv:0911.1120 [hep-ph]]. 22

    2010 arXiv

  4. [12]

    Bernal, M

    N. Bernal, M. Heikinheimo, T. Tenkanen, K. Tuominen and V . Vaskonen, Int. J. Mod. Phys. A32, no.27, 1730023 (2017) [arXiv:1706.07442 [hep-ph]]

    2017 arXiv

  5. [13]

    M. J. Dolinski, A. W. P. Poon and W. Rodejohann, Ann. Rev. Nucl. Part. Sci.69, 219-251 (2019) [arXiv:1902.04097 [nucl-ex]]

    2019 arXiv

  6. [14]

    Heeck, Phys

    J. Heeck, Phys. Lett. B739, 256-262 (2014) [arXiv:1408.6845 [hep-ph]]

    2014 arXiv

  7. [15]

    K. N. Abazajian and J. Heeck, Phys. Rev. D100, 075027 (2019) [arXiv:1908.03286 [hep-ph]]

    2019 arXiv

  8. [16]

    Escudero Abenza, JCAP05, 048 (2020) [arXiv:2001.04466 [hep-ph]]

    M. Escudero Abenza, JCAP05, 048 (2020) [arXiv:2001.04466 [hep-ph]]

    2020 arXiv

  9. [17]

    X. Luo, W. Rodejohann and X. J. Xu, JCAP06, 058 (2020) [arXiv:2005.01629 [hep-ph]]

    2020 arXiv

  10. [18]

    X. Luo, W. Rodejohann and X. J. Xu, JCAP03, 082 (2021) [arXiv:2011.13059 [hep-ph]]

    2021 arXiv

  11. [19]

    Adshead, P

    P. Adshead, P. Ralegankar and J. Shelton, JCAP09, 056 (2022) [arXiv:2206.13530 [hep-ph]]

    2022 arXiv

  12. [20]

    K. S. Babu, X. G. He, M. Su and A. Thapa, JHEP08, 140 (2022) [arXiv:2205.09127 [hep-ph]]

    2022 arXiv

  13. [21]

    Esseili and G

    H. Esseili and G. D. Kribs, JCAP05, 110 (2024) [arXiv:2308.07955 [hep-ph]]

    2024 arXiv

  14. [22]

    Biswas, D

    A. Biswas, D. Borah and D. Nanda, JCAP10, 002 (2021) [arXiv:2103.05648 [hep-ph]]

    2021 arXiv

  15. [23]

    Borah, S

    D. Borah, S. Mahapatra, D. Nanda and N. Sahu, Phys. Lett. B833, 137297 (2022) [arXiv:2204.08266 [hep- ph]]

    2022 arXiv

  16. [24]

    Borah, P

    D. Borah, P. Das and D. Nanda, Eur. Phys. J. C84, no.2, 140 (2024) [arXiv:2211.13168 [hep-ph]]

    2024 arXiv

  17. [25]

    Biswas, D

    A. Biswas, D. Borah, N. Das and D. Nanda, Phys. Rev. D107, no.1, 015015 (2023) [arXiv:2205.01144 [hep- ph]]

    2023 arXiv

  18. [26]

    Borah, S

    D. Borah, S. Mahapatra, D. Nanda, S. K. Sahoo and N. Sahu, JHEP05, 096 (2024) [arXiv:2310.03721 [hep- ph]]

    2024 arXiv

  19. [27]

    Mahapatra, S

    S. Mahapatra, S. K. Sahoo, N. Sahu and V . S. Thounaojam, Phys. Rev. D109, no.5, 055036 (2024) [arXiv:2312.12322 [hep-ph]]

    2024 arXiv

  20. [28]

    Borah, P

    D. Borah, P. Das, B. Karmakar and S. Mahapatra, Phys. Rev. D111, no.3, 035032 (2025) [arXiv:2406.17861 [hep-ph]]

    2025 arXiv

  21. [29]

    Borah, N

    D. Borah, N. Das, S. Jahedi and B. Thacker, JHEP01, 074 (2025) [arXiv:2408.14548 [hep-ph]]

    2025

  22. [30]

    Z. A. Borboruah, D. Borah, L. Malhotra and U. Patel, Phys. Rev. D112, no.1, 015022 (2025) [arXiv:2412.12267 [hep-ph]]

    2025 arXiv

  23. [31]

    Oliveira, P

    V . Oliveira, P. Escalona, L. Angel, C. A. de S. Pires and F. S. Queiroz, JHEP07, 197 (2025) [arXiv:2502.01760 [hep-ph]]

    2025 arXiv

  24. [32]

    A. E. B. Abdelrahim, B. Batell, J. Berger, D. McKeen and B. Shams Es Haghi, JCAP02, 073 (2026) [arXiv:2506.09137 [hep-ph]]

    2026 arXiv

  25. [33]

    Okawa, Y

    S. Okawa, Y . Omura and K. Wu, JHEP03, 039 (2026) [arXiv:2510.04549 [hep-ph]]

    2026

  26. [34]

    Das, [arXiv:2602.09962 [hep-ph]]

    P. Das, [arXiv:2602.09962 [hep-ph]]

  27. [35]

    Adhikary, A

    J. Adhikary, A. Batra, K. Deka and F. R. Joaquim, [arXiv:2603.20145 [hep-ph]]

  28. [36]

    Davidson, Phys

    A. Davidson, Phys. Rev. D20, 776 (1979)

    1979

  29. [37]

    R. N. Mohapatra and R. E. Marshak, Phys. Rev. Lett.44, 1316-1319 (1980) [erratum: Phys. Rev. Lett.44, 1643 (1980)] 23

    1980

  30. [38]

    R. E. Marshak and R. N. Mohapatra, Phys. Lett. B91, 222-224 (1980)

    1980

  31. [39]

    Masiero, J

    A. Masiero, J. F. Nieves and T. Yanagida, Phys. Lett. B116, 11-15 (1982)

    1982

  32. [40]

    R. N. Mohapatra and G. Senjanovic, Phys. Rev. D27, 254 (1983)

    1983

  33. [41]

    Buchmuller, C

    W. Buchmuller, C. Greub and P. Minkowski, Phys. Lett. B267, 395-399 (1991)

    1991

  34. [42]

    Minkowski, Phys

    P. Minkowski, Phys. Lett. B67, 421-428 (1977)

    1977

  35. [43]

    R. N. Mohapatra and G. Senjanovic, Phys. Rev. Lett.44, 912 (1980)

    1980

  36. [44]

    Schechter and J

    J. Schechter and J. W. F. Valle, Phys. Rev. D22, 2227 (1980)

    1980

  37. [45]

    Schechter and J

    J. Schechter and J. W. F. Valle, Phys. Rev. D25, 774 (1982)

    1982

  38. [46]

    Z. L. Han and W. Wang, Eur. Phys. J. C78, no.10, 839 (2018) [arXiv:1805.02025 [hep-ph]]

    2018 arXiv

  39. [47]

    Mahanta and D

    D. Mahanta and D. Borah, Eur. Phys. J. C82, no.5, 495 (2022) [arXiv:2101.02092 [hep-ph]]

    2022 arXiv

  40. [48]

    Berbig, JHEP09, 101 (2022) [arXiv:2203.04276 [hep-ph]]

    M. Berbig, JHEP09, 101 (2022) [arXiv:2203.04276 [hep-ph]]

    2022 arXiv

  41. [49]

    Das and D

    N. Das and D. Borah, Phys. Rev. D109, no.7, 075045 (2024) [arXiv:2312.06777 [hep-ph]]

    2024 arXiv

  42. [50]

    Borah, S

    D. Borah, S. Mahapatra, D. Nanda, S. K. Sahoo and N. Sahu, Phys. Rev. D112, no.5, 055010 (2025) [arXiv:2502.10318 [hep-ph]]

    2025 arXiv

  43. [51]

    Herbermann and M

    T. Herbermann and M. Lindner, JCAP09, 078 (2025) [arXiv:2505.04695 [hep-ph]]

    2025 arXiv

  44. [52]

    E. Ma, P. K. Paul and N. Sahu, [arXiv:2601.05926 [hep-ph]]

  45. [53]

    C. Han, M. L. L ´opez-Ib´a˜nez, B. Peng and J. M. Yang, Nucl. Phys. B959, 115154 (2020) [arXiv:2001.04078 [hep-ph]]

    2020 arXiv

  46. [54]

    A. Liu, F. L. Shao, Z. L. Han, Y . Jin and H. Li, JHEP10, 019 (2024) [arXiv:2407.19730 [hep-ph]]

    2024 arXiv

  47. [55]

    R. N. Mohapatra and N. Okada, Phys. Rev. D102, no.3, 035028 (2020) [arXiv:1908.11325 [hep-ph]]

    2020 arXiv

  48. [56]

    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]]

    2020 arXiv

  49. [57]

    Mangano, G

    G. Mangano, G. Miele, S. Pastor, T. Pinto, O. Pisanti and P. D. Serpico, Nucl. Phys. B729, 221-234 (2005) [arXiv:hep-ph/0506164 [hep-ph]]

    2005 arXiv

  50. [58]

    Grohs, G

    E. Grohs, G. M. Fuller, C. T. Kishimoto, M. W. Paris and A. Vlasenko, Phys. Rev. D93, no.8, 083522 (2016) [arXiv:1512.02205 [astro-ph.CO]]

    2016 arXiv

  51. [59]

    P. F. de Salas and S. Pastor, JCAP07, 051 (2016) [arXiv:1606.06986 [hep-ph]]

    2016 arXiv

  52. [60]

    A. G. Adameet al.[DESI], JCAP02, 021 (2025) [arXiv:2404.03002 [astro-ph.CO]]

    2025 arXiv

  53. [61]

    Louiset al.[Atacama Cosmology Telescope], JCAP11, 062 (2025) [arXiv:2503.14452 [astro-ph.CO]]

    T. Louiset al.[Atacama Cosmology Telescope], JCAP11, 062 (2025) [arXiv:2503.14452 [astro-ph.CO]]

    2025 arXiv

  54. [62]

    Calabreseet al.[Atacama Cosmology Telescope], JCAP11, 063 (2025) [arXiv:2503.14454 [astro-ph.CO]]

    E. Calabreseet al.[Atacama Cosmology Telescope], JCAP11, 063 (2025) [arXiv:2503.14454 [astro-ph.CO]]

    2025 arXiv

  55. [63]

    Abazajian, G

    K. Abazajian, G. Addison, P. Adshead, Z. Ahmed, S. W. Allen, D. Alonso, M. Alvarez, A. Anderson, K. S. Arnold and C. Baccigalupi,et al.[arXiv:1907.04473 [astro-ph.IM]]

    1907 arXiv

  56. [64]

    Aiolaet al.[CMB-HD], [arXiv:2203.05728 [astro-ph.CO]]

    S. Aiolaet al.[CMB-HD], [arXiv:2203.05728 [astro-ph.CO]]

    arXiv

  57. [65]

    J. C. Montero and V . Pleitez, Phys. Lett. B675, 64-68 (2009) [arXiv:0706.0473 [hep-ph]]

    2009 arXiv

  58. [66]

    Feldman, Z

    D. Feldman, Z. Liu and P. Nath, JHEP11, 007 (2006) [arXiv:hep-ph/0606294 [hep-ph]]

    2006 arXiv

  59. [67]

    Belanger, F

    G. Belanger, F. Boudjema, A. Pukhov and A. Semenov, Comput. Phys. Commun.185, 960-985 (2014) [arXiv:1305.0237 [hep-ph]]. 24

    2014 arXiv

  60. [68]

    Alguero, G

    G. Alguero, G. Belanger, F. Boudjema, S. Chakraborti, A. Goudelis, S. Kraml, A. Mjallal and A. Pukhov, Comput. Phys. Commun.299, 109133 (2024) [arXiv:2312.14894 [hep-ph]]

    2024 arXiv

  61. [69]

    N. Nath, N. Okada, S. Okada, D. Raut and Q. Shafi, Eur. Phys. J. C82, no.10, 864 (2022) [arXiv:2112.08960 [hep-ph]]

    2022 arXiv

  62. [70]

    Okada, S

    N. Okada, S. Okada and Q. Shafi, Phys. Lett. B810, 135845 (2020) [arXiv:2003.02667 [hep-ph]]

    2020 arXiv

  63. [71]

    Agneset al.[DarkSide-50], Eur

    P. Agneset al.[DarkSide-50], Eur. Phys. J. C83, 322 (2023) [arXiv:2302.01830 [hep-ex]]

    2023 arXiv

  64. [72]

    Aprileet al.[XENON], Phys

    E. Aprileet al.[XENON], Phys. Rev. Lett.135, no.22, 221003 (2025) [arXiv:2502.18005 [hep-ex]]

    2025

  65. [73]

    Boet al.[PandaX], Phys

    Z. Boet al.[PandaX], Phys. Rev. Lett.134, no.1, 011805 (2025) [arXiv:2408.00664 [hep-ex]]

    2025 arXiv

  66. [74]

    Aalberset al.[LZ], Phys

    J. Aalberset al.[LZ], Phys. Rev. Lett.135, no.1, 011802 (2025) [arXiv:2410.17036 [hep-ex]]

    2025 arXiv

  67. [75]

    Agneset al.[Global Argon Dark Matter], Phys

    P. Agneset al.[Global Argon Dark Matter], Phys. Rev. D107, no.11, 112006 (2023) [arXiv:2209.01177 [physics.ins-det]]

    2023 arXiv

  68. [76]

    Agneseet al.[SuperCDMS], Phys

    R. Agneseet al.[SuperCDMS], Phys. Rev. D95, no.8, 082002 (2017) [arXiv:1610.00006 [physics.ins-det]]

    2017 arXiv

  69. [77]

    D. S. Akeribet al.[LZ], [arXiv:1509.02910 [physics.ins-det]]

    arXiv

  70. [78]

    Cirelli, N

    M. Cirelli, N. Fornengo, J. Koechler, E. Pinetti and B. M. Roach, JCAP07, 026 (2023) [erratum: JCAP08, E02 (2025)] [arXiv:2303.08854 [hep-ph]]

    2023 arXiv

  71. [79]

    Lopez-Honorez, O

    L. Lopez-Honorez, O. Mena, S. Palomares-Ruiz and A. C. Vincent, JCAP07, 046 (2013) [arXiv:1303.5094 [astro-ph.CO]]

    2013 arXiv

  72. [80]

    T. R. Slatyer, Phys. Rev. D93, no.2, 023527 (2016) [arXiv:1506.03811 [hep-ph]]

    2016 arXiv

  73. [81]

    R. K. Leane, T. R. Slatyer, J. F. Beacom and K. C. Y . Ng, Phys. Rev. D98, no.2, 023016 (2018) [arXiv:1805.10305 [hep-ph]]

    2018 arXiv

  74. [82]

    Dutta, A

    K. Dutta, A. Ghosh, A. Kar and B. Mukhopadhyaya, JCAP08, 071 (2023) [arXiv:2212.09795 [hep-ph]]

    2023 arXiv

  75. [83]

    Aguilaret al.[AMS], Phys

    M. Aguilaret al.[AMS], Phys. Rev. Lett.113, 121102 (2014)

    2014

  76. [84]

    Aguilaret al.[AMS], Phys

    M. Aguilaret al.[AMS], Phys. Rev. Lett.122, no.4, 041102 (2019)

    2019

  77. [85]

    Albertet al.[Fermi-LAT and DES], Astrophys

    A. Albertet al.[Fermi-LAT and DES], Astrophys. J.834, no.2, 110 (2017) [arXiv:1611.03184 [astro-ph.HE]]

    2017 arXiv

  78. [86]

    Abdallahet al.[H.E.S.S.], Phys

    H. Abdallahet al.[H.E.S.S.], Phys. Rev. Lett.117, no.11, 111301 (2016) [arXiv:1607.08142 [astro-ph.HE]]

    2016 arXiv

  79. [87]

    Abdallaet al.[H.E.S.S.], Phys

    H. Abdallaet al.[H.E.S.S.], Phys. Rev. Lett.129, no.11, 111101 (2022) [arXiv:2207.10471 [astro-ph.HE]]

    2022

  80. [88]

    Caputoet al.[AMEGO], [arXiv:1907.07558 [astro-ph.IM]]

    R. Caputoet al.[AMEGO], [arXiv:1907.07558 [astro-ph.IM]]

    1907 arXiv

  81. [89]

    C. A. Kierans [AMEGO Team], Proc. SPIE Int. Soc. Opt. Eng.11444, 1144431 (2020) [arXiv:2101.03105 [astro-ph.IM]]

    2020 arXiv

  82. [90]

    Caputo, M

    R. Caputo, M. Ajello, C. A. Kierans, J. S. Perkins, J. L. Racusin, L. Baldini, M. G. Baring, E. Bissaldi, E. Burns and N. Cannady,et al.J. Astron. Telesc. Instrum. Syst.8, no.4, 044003 (2022) [arXiv:2208.04990 [astro-ph.IM]]

    2022 arXiv

  83. [91]

    De Angeliset al.[e-ASTROGAM], Exper

    A. De Angeliset al.[e-ASTROGAM], Exper. Astron.44, no.1, 25-82 (2017) [arXiv:1611.02232 [astro- ph.HE]]

    2017 arXiv

  84. [92]

    De Angeliset al.[e-ASTROGAM], JHEAp19, 1-106 (2018) [arXiv:1711.01265 [astro-ph.HE]]

    A. De Angeliset al.[e-ASTROGAM], JHEAp19, 1-106 (2018) [arXiv:1711.01265 [astro-ph.HE]]

    2018 arXiv

  85. [93]

    Dzhatdoev and E

    T. Dzhatdoev and E. Podlesnyi, Astropart. Phys.112, 1-7 (2019) [arXiv:1902.01491 [astro-ph.HE]]

    2019 arXiv

  86. [94]

    Cirelli and A

    M. Cirelli and A. Kar, SciPost Phys.19, no.3, 080 (2025) [arXiv:2503.04907 [hep-ph]]. 25

    2025

  87. [95]

    Profumo, F

    S. Profumo, F. S. Queiroz, J. Silk and C. Siqueira, JCAP03, 010 (2018) [arXiv:1711.03133 [hep-ph]]

    2018 arXiv

  88. [96]

    J. P. Leeset al.[BaBar], Phys. Rev. Lett.113, no.20, 201801 (2014) [arXiv:1406.2980 [hep-ex]]

    2014 arXiv

  89. [97]

    Aaijet al.[LHCb], Phys

    R. Aaijet al.[LHCb], Phys. Rev. Lett.120, no.6, 061801 (2018) [arXiv:1710.02867 [hep-ex]]

    2018 arXiv

  90. [98]

    Aaijet al.[LHCb], Phys

    R. Aaijet al.[LHCb], Phys. Rev. Lett.124, no.4, 041801 (2020) [arXiv:1910.06926 [hep-ex]]

    2020

  91. [99]

    S. K.A., A. Das, G. Lambiase, T. Nomura and Y . Orikasa, Eur. Phys. J. C84, no.11, 1224 (2024) [arXiv:2308.14483 [hep-ph]]

    2024 arXiv

  92. [100]

    Schaelet al.[ALEPH, DELPHI, L3, OPAL and LEP Electroweak], Phys

    S. Schaelet al.[ALEPH, DELPHI, L3, OPAL and LEP Electroweak], Phys. Rept.532, 119-244 (2013) [arXiv:1302.3415 [hep-ex]]

    2013 arXiv

  93. [101]

    A. M. Sirunyanet al.[CMS], JHEP07, 208 (2021) [arXiv:2103.02708 [hep-ex]]

    2021 arXiv

  94. [102]

    Aadet al.[ATLAS], Phys

    G. Aadet al.[ATLAS], Phys. Lett. B796, 68-87 (2019) [arXiv:1903.06248 [hep-ex]]

    2019 arXiv

  95. [103]

    J. P. Leeset al.[BaBar], Phys. Rev. Lett.119, no.13, 131804 (2017) [arXiv:1702.03327 [hep-ex]]

    2017 arXiv

  96. [104]

    Ferber, C

    T. Ferber, C. Garcia-Cely and K. Schmidt-Hoberg, Phys. Lett. B833, 137373 (2022) [arXiv:2202.03452 [hep- ph]]

    2022 arXiv

  97. [105]

    M. J. Dolan, T. Ferber, C. Hearty, F. Kahlhoefer and K. Schmidt-Hoberg, JHEP12, 094 (2017) [erratum: JHEP 03, 190 (2021)] [arXiv:1709.00009 [hep-ph]]

    2017 arXiv

  98. [106]

    Karliner, M

    M. Karliner, M. Low, J. L. Rosner and L. T. Wang, Phys. Rev. D92, no.3, 035010 (2015) [arXiv:1503.07209 [hep-ph]]

    2015 arXiv

Pith tools

Reviewed July 10, 2026 · model on record in the stance chip above.