Pith. sign in

REVIEW 4 major objections 4 minor 61 references

Measurement of Downward-going Milli-charged particles beyond GZK cutoff at the Pierre Auger Observatory

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read The paper claims that the Pierre Auger Observatory's hybrid spectrum above the GZK cutoff fits a flux of milli-charged particles from superheavy dark matter decay better than standard cosmic-ray nuclei alone, which would open a direct…

desk verdict Interesting channel, but the rate calculation is not shown and the DIS kinematics are mishandled; as written, the limits and the detection claim do not stand. read the letter →

arxiv 2506.07395 v2 pith:ATVJEETL submitted 2025-06-09 astro-ph.HE hep-ph

Ye Xu This is my paper
classification astro-ph.HEhep-ph
keywords milli-chargedparticlessuperheavydarkmatterGZKcutoffPierreAugerObservatoryultrahigh-energycosmicrayshiddenphotonkineticmixingdecay
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

The paper argues that if superheavy dark matter particles of roughly ZeV mass decay to milli-charged particles (MCPs), the resulting ultra-high-energy MCPs raining down through the atmosphere could be detected by the Pierre Auger Observatory. Using 14 years of Auger hybrid data, the author fits the flux above the GZK cutoff with a model where MCPs dominate, and finds that the hybrid spectrum agrees better with the MCP model than with standard cosmic-ray primaries alone. On that basis the paper claims MCPs can be directly probed at Auger for kinetic-mixing couplings as small as $epsilon^{2}$ ~ 2e-6, and that a previously unconstrained region of MCP mass between about $10^{9}$.6 and $10^{11}$.6 eV with epsilon > 2.12e-2 is excluded at 90% C.L. A sympathetic reader would care because this would turn an existing cosmic-ray observatory into a direct detector for a dark-matter decay product, and would be the first exclusion of heavy MCPs in that mass range.

What carries the argument

The load-bearing objects are the MCP flux from SHDM decay, split into galactic and extragalactic contributions (Eqs. 2.1-2.4), and the electromagnetic deep-inelastic-scattering cross-section sigma_chiN approx $epsilon^{2}$ sigma_gamma_eN, with sigma_gamma_eN parametrized from a published table (Eq. 3.5). The expected event count N_det (Eq. 4.1) combines this flux with the probability P = 1 - exp(-D/L_air) that an MCP interacts in the atmosphere and with Auger's effective area S_eff derived from the hybrid exposure. The whole argument depends on identifying the atmospheric air mass above the array as the target and on assuming Auger's detection efficiency for MCP-initiated showers equals that for standard cosmic-ray primaries. The fit to the spectrum above the GZK cutoff is carried out with the method of Ref. [56], using the EPOS-LHC model for the low-Z nuclei and secondaries component.

What would settle it

Run a dedicated Monte Carlo simulation of air showers initiated by MCPs with the assumed cross-section and measure the resulting hybrid detection efficiency and the depth of shower maximum; if the efficiency is not close to the assumed eta(E) for standard nuclei, the expected event counts and exclusion limits in this paper would change, and the claimed preference for an MCP flux above the GZK cutoff would be called into question.

Watch

Extended reading notes

Core claim

The paper's central claim is that downward-going ultra-high-energy milli-charged particles, produced by the decay phi -> chi anti-chi (or gamma chi anti-chi) of superheavy dark matter with m_phi ~ 2e21-2e22 eV and tau_phi ~ 1e27 s, can be observed in the Pierre Auger Observatory's hybrid data. The author evaluates the expected number of MCP events, N_det, using the hidden-photon cross-section sigma_chiN = $epsilon^{2}$ sigma_gamma_eN and Auger's hybrid exposure, and fits the measured spectrum above the GZK cutoff with the sum of standard low-Z nuclei and MCP fluxes. The best fit for the hybrid spectrum uses $epsilon^{2}$ = 1.3e-4; the paper states that this shows better agreement than the standard fit alone and suggests detection of MCPs at energies above about 100 EeV. The paper also derives upper limits on $epsilon^{2}$ of 4.5e-4 (m_phi = 2e21 eV) and 7.18e-4 (m_phi = 2e22 eV) at 90% C.L., and a new exclusion region in the MCP mass-coupling plane.

Load-bearing premise

The whole event-rate and exclusion calculation assumes that the Pierre Auger detectors are just as efficient at catching air showers triggered by milli-charged particles as they are for ordinary cosmic-ray nuclei, even though no simulation of MCP-initiated showers is presented.

Editorial extensions

If this is right

  • If the central claim is correct, the Pierre Auger Observatory becomes a direct detector for a dark-matter decay product: downward-going MCPs with coupling squared epsilon^2 down to about 2e-6 would produce roughly one event per 14 years at energies near 100 EeV.
  • The excluded region in the MCP mass-coupling plane, 10^9.6 eV < m_MCP < 10^11.6 eV for epsilon > 2.12e-2, is new and complementary to bounds from accelerators, stars, and cosmology.
  • The preferential fit of the hybrid spectrum above the GZK cutoff with an MCP component implies that the 'GZK cutoff' observed at Auger may be a combined effect of standard nuclei attenuation and a new MCP flux, not a pure feature of cosmic-ray propagation.
  • Because the MCP relic abundance from SHDM decay is orders of magnitude below the Planck bound, these results would not conflict with cosmological constraints, leaving SHDM decay a viable production mechanism.

Reading between the lines

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

  • Editorial inference: the claim of a better fit above the GZK cutoff is based on the author's own combined-flux model rather than a published Auger fit; an unbiased re-analysis by the experiment's own collaboration with an energy-scale nuisance parameter would test whether the improvement is robust.
  • Editorial inference: the detection-efficiency assumption could be checked experimentally by comparing the depth-of-shower-maximum (Xmax) distribution of hybrid events above 100 EeV with hadronic expectations; MCP primaries in the hidden-photon model should produce deeper, more electromagnetic-like showers.
  • Editorial inference: if a future space-based fluorescence detector with much larger aperture (as the author notes) observes a similar high-energy excess with more statistics, the SHDM-decay interpretation would be pushed from a fit preference to a discovery.
  • Editorial inference: the cross-section scaling sigma_chiN = epsilon^2 sigma_gamma_eN assumes a massless hidden photon; extending the calculation to a massive hidden photon would change the energy dependence and could shift the excluded region.
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

4 major / 4 minor

Summary. This paper considers a scenario in which superheavy dark matter (SHDM) particles with ZeV-scale mass decay into relativistic milli-charged particles (MCPs), which then interact in Earth's atmosphere and produce extensive air showers detectable by the Pierre Auger Observatory. Using 14 years of Auger hybrid data, the author fits the flux above the GZK cutoff with MCPs, evaluates expected event numbers, derives 90% C.L. upper limits on the kinetic mixing parameter epsilon^2, and claims a new excluded region in the MCP mass-mixing plane together with a possible indication of MCP/SHDM existence. The central calculation is built on Eq. (4.1), using an MCP-nucleon cross section taken as epsilon^2 times the electron-nucleon electromagnetic DIS cross section, and on an assumed equivalence between MCP-induced showers and standard cosmic-ray showers for the Auger detection efficiency.

Significance. If the calculation were correct, the paper would extend MCP searches to masses around 10^10-10^11.6 eV and would propose SHDM decay as a possible source of super-GZK events at Auger, a potentially interesting and falsifiable scenario. The paper also usefully collects existing MCP bounds from cosmology, astrophysics, accelerators, and laboratory experiments. However, the central event-rate calculation is not shown in sufficient detail, the cross-section treatment omits kinematic effects that are important for the claimed mass range, and the 'detection' statement is based on a fit to the same data that is then used to define the signal. These issues mean that the sensitivity and exclusion claims are not currently established, despite the interesting physical scenario.

major comments (4)
  1. [Section 5 / Fig. 1 and Eq. (4.1)] The claim that the hybrid spectrum 'shows better agreement with the UHE MCP flux model' and 'suggests detection of MCPs' (Section 6) is circular. The black line in Fig. 1 is a fit with epsilon^2 = 1.3e-4 to the same Auger hybrid data that is later used to define the expected MCP signal; the 'expected numbers of MCPs' in Fig. 2 with epsilon^2 = 1.3e-4 are therefore rescalings of the fitted contribution, not independent predictions. No goodness-of-fit statistic, likelihood comparison, or hypothesis test is reported, so the statement of better agreement is not quantified.
  2. [Section 3, Eqs. (3.3)-(3.5), and Eq. (4.1)] The MCP-nucleon cross section is set equal to epsilon^2 times the electron-nucleon electromagnetic DIS cross section without accounting for the MCP mass in the kinematics. For the claimed mass range 10^9.6 < m_chi/eV < 10^11.6, the minimum Q^2 in the electron calculation is set by the electron mass, whereas for a heavy MCP the lower kinematic limit is of order m_chi^2 y^2/(1-y), which suppresses the low-y contribution that dominates the electron cross section. In addition, a DIS event with inelasticity y produces a hadronic system of energy yE, not E; counting every interaction as a shower at the primary energy E in Eq. (4.1) inflates N_det. Because the 90% upper limit epsilon^2_UL = 4.5e-4 and the excluded region epsilon > 2.12e-2 are derived from this N_det, these central results can change by orders of magnitude once the correct MCP kinematics are used.
  3. [Section 4, Eqs. (4.1)-(4.2)] The exposure and detection-efficiency treatment is not reproducible. The integration limits E_min and E_max in Eq. (4.1) are not specified; the detection efficiency eta is only stated to depend on primary energy, with no functional form; and Eq. (4.2) contains a dimensionally inconsistent chain in which A is first written as dE/dt and E is then called the hybrid exposure. The relation between the Auger hybrid aperture and the effective area S_eff is not derived, and the 90% C.L. upper limits are said to use a 'Gaussian approach' without specifying the observed event count, background, or confidence-interval construction. Since N_det scales linearly with S_eff, the limits depend directly on this unshown conversion.
  4. [Abstract vs. Sections 5-6 and Fig. 4] The paper contains numerical inconsistencies that prevent the reader from identifying the actual claimed result. The abstract states a required sensitivity of epsilon^2 > 3.73e-5 and a ruled-out region with epsilon > 2.02e-2 and 10^10 < m_chi/eV < 10^11.6, while the body (Section 5 and Fig. 4) reports epsilon^2_UL = 4.5e-4, epsilon > 2.12e-2, and 10^9.6 < m_chi/eV < 10^11.6. In addition, Section 6 says the excluded region is 'shown in figure 3' when the actual exclusion plot is Fig. 4. These discrepancies need to be resolved before the claims can be evaluated.
minor comments (4)
  1. [Section 6, Eq. (6.1)] The quantity 'Tre' in Eq. (6.1) is undefined and is presumably meant to be a reheat temperature T_re; the surrounding text also contains typos such as 'recombination-reioniztion' and 'This fall orders of magnitude'.
  2. [Section 4 title] The section title mentions 'expected MCPs and neutrinos', but neutrinos are never defined or used in the calculation; the title should be limited to MCPs.
  3. [References] Reference [31] is cited as 'JHEP (2024) arXiv:2405.00060' without a volume or article number, and the key cross-section input in Eq. (3.3) relies on the author's own Ref. [30] without an independent cross-check.
  4. [Eq. (4.1)] The integral in Eq. (4.1) contains both T and dt, with T already taken to be 14 years, which is redundant and should be simplified.

Circularity Check

3 steps flagged · score 6.0 of 10

MCP event numbers and detection threshold are linear rescalings of the ε² fitted to the same Auger spectrum; the load-bearing cross-section is imported from the author's own prior paper.

  1. fitted input called prediction [Section 5 (Results), Eqs. (4.1)-(4.3), Figs. 1-3]
    "The black solid line represents the fit with the flux of UHE MCPs with ǫ2 = 1.3 × 10−4, mφ = 2 × 1021 eV and τφ = 1027 s exceeding GZK-cutoff energy. ... Figure 2 presents the numbers of expected MCPs in the 1-316 EeV range with ǫ2 = 4.5 × 10−4 ... 1.3 × 10−4 ... and 2 × 10−6 ... The numbers of expected MCPs with 2 × 10−6 ... can reach about 1 at energies with near 100 EeV at Auger."

    Through Eqs. (4.1)-(4.3) and (3.6), N_det ∝ P ∝ σ_χN for a thin atmosphere, and Eq. (3.3) gives σ_χN ∝ ε². Therefore the 'expected numbers of MCPs' in Figs. 2-3 are linear scalings of N_det with ε². The central amplitude ε² = 1.3 × 10−4 is obtained by fitting the MCP flux to the same Auger hybrid spectrum in Fig. 1, so the claimed threshold 'ε² >~ 2 × 10−6' is simply the fitted amplitude rescaled to one expected event. The detection claim is forced by the fit, not an independent prediction.

  2. self citation load bearing [Section 3 (UHE MCP interactions with nuclei), Eq. (3.3) and Ref. [30]]
    "The DIS cross section for MCPs on nuclei, computed using the model from Ref. [30], scales as ǫ2 relative to the neutral-current electromagnetic DIS cross section for electrons on nuclei: σχN ≈ǫ2σγ eN (3.3) ... [30] Y. Xu, JHEP 09, 055 (2022) arXiv: 2207.00178"

    This relation is the sole bridge between the MCP parameter ε² and the event rate. The paper does not re-derive σ_χN from first principles; it cites Ref. [30], which is the author's own prior paper. Since all N_det values, the fit amplitude, the 90% upper limits, and the excluded region scale with this cross-section, the central result is load-bearing on a self-citation. Without an independent derivation or external validation of this cross-section, the quoted sensitivity and exclusion reduce to the self-cited input.

1 more flagged steps
  1. other [Section 6 (Discussion and Conclusion)]
    "Compared to the SD data case in figure 5, the hybrid spectrum above the GZK-cut off shows better agreement with the UHE MCP flux model (figure 1). This suggests detection of MCPs at energies /greaterorsimilar100 EeV through Auger’s hybrid measurements, potentially indicating the existence of SHDM in the Universe."

    The 'better agreement' is the result of adding a fitted MCP component with ε² = 1.3 × 10−4 to the same hybrid spectrum. Fitting a one-parameter additive flux to those data bins will generally improve or preserve agreement, so observing better agreement after the fit cannot be used as evidence of detection. The conclusion converts the fit into a detection claim without any out-of-sample prediction, making it circular with respect to the fitted input.

full rationale

The central detection/sensitivity claims are not independent predictions: N_det is proportional to ε² through Eq. (3.3), and the ε² values used in Figs. 2-3 are the same parameter fitted to the Auger spectrum in Fig. 1. The 'expected numbers' and the threshold ε² >~ 2 × 10−6 are rescalings of that fit, not tests against new data. The cross-section that sets the overall scale is taken from the author's own Ref. [30], making the numerical results load-bearing on a self-citation. However, I do not score this as fully circular (8-10) because the 90% upper-limit procedure itself is a standard Gaussian/Poisson limit using public Auger data and external flux references, and the exclusion region could in principle stand even if the detection claim is overstated. The score 6 reflects that the paper's headline 'detection' and 'direct sensitivity' claims reduce by construction to the fitted ε², while the exclusion claim retains some independent statistical content despite resting on the self-cited cross-section.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The paper does not introduce new particles; MCPs and SHDM are already in the literature. However, the specific scenario of SHDM decaying predominantly to MCPs is an assumption, and the cross-section scaling and flux constants are taken from the author's earlier work, so the central calculation is not self-contained.

free parameters (5)
  • m_phi (SHDM mass) = 2 x 10^21 eV and 2 x 10^22 eV
    Assumed superheavy dark matter mass; sets the energy scale of the MCP flux and the decay kinematics.
  • tau_phi (SHDM lifetime) = 10^27 s
    Assumed SHDM lifetime; inversely scales the flux and expected event rate (Section 1).
  • epsilon^2 (kinetic mixing) = Best fit 1.3e-4 for hybrid; upper limit 4.5e-4 (m_phi=2e21)
    Fitted to the Auger hybrid spectrum above the GZK cutoff (Section 5, Fig. 1); this is the main parameter constrained.
  • XS and Delta for baseline fit = XS=2.5, Delta=3 for hybrid; B=0, Delta=1 for SD
    Parameters of the conventional cosmic-ray component in the 'Best fit' taken from Ref [56]; they determine the baseline under which the MCP signal is extracted.
  • Branching ratio of SHDM decay = 50% to chi chi-bar, 50% to gamma chi chi-bar
    Assumed decay fractions for SHDM; affects the MCP flux (Section 1).
assumptions (4)
  • domain assumption Galactic and extragalactic MCP flux formulas and normalization constants from Refs [49,50,44]
    These formulas define the flux in terms of m_phi and tau_phi; the paper adopts them without derivation (Eqs. 2.1-2.4).
  • domain assumption MCP-nucleus cross section equals epsilon^2 times electron-nucleus electromagnetic DIS cross section (Eq. 3.3)
    Taken from the author's previous paper Ref [30]; assumes the massless hidden photon model and that QED-like structure functions apply for MCPs of any mass.
  • domain assumption The GZK cutoff originates from UHE low-Z nuclei (Z <= 8) and their secondaries
    Stated in Section 1 and used in the fit; if the observed cutoff has a different origin, the interpretation of the high-energy tail as MCPs is invalid.
  • standard math Poisson/Gaussian statistics for 90% C.L. limits
    The 'Gaussian approach' is used but not specified; standard practice but needs to be defined.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Measurement of Downward-going Milli-charged particles beyond GZK cutoff at the Pierre Auger Observatory." pith.science (2026). https://pith.science/paper/ATVJEETL

@misc{pith2026250607395,
  author       = {Pith},
  title        = {Pith review of: Measurement of Downward-going Milli-charged particles beyond GZK cutoff at the Pierre Auger Observatory},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ATVJEETL}},
  note         = {Machine review of arXiv:2506.07395}
}
abstract

It is assumed that superheavy dark matter particles (SHDM, $\phi$) with $\mathcal{O}$(ZeV) mass may decay to relativistic milli-charged particles (MCPs, $\chi$) via a channel $\phi\to\chi\bar{\chi}$. The downward-going MCPs passing through the atmosphere can be searched for at the Pierre Auger observatory (Auger). The massless hidden photon model is taken for MCPs to interact with nuclei, so that we evaluated the numbers and fluxes of expected MCPs at Auger assuming 14 years of Auger data. The hybrid data of Auger was fitted with the flux of UHE MCPs exceeding GZK-cutoff energy. Then the corresponding upper limits on $\epsilon^2$ are calculated at 90\% C. L.. These results indicate that MCPs can be searched for with $\epsilon^2\gtrsim 3.73\times10^{-5}$ at Auger, when $m_{\phi}=2\times10^{21}$ eV and $\tau_{\phi}=10^{27}$ s. And a new region of 10$^{10}$ eV < $m_{MCP}$ < 10$^{11.6}$ eV and $\epsilon$ > $2.02\times10^{-2}$ is ruled out in the $m_{MCP}$-$\epsilon$ plane with 14 years of Auger data. These results indicate potential existence of MCPs and SHDM in the Universe.

Figures

Figures reproduced from arXiv: 2506.07395 by the authors.

Figure 1
Figure 1. Fits to the fluxes at Earth. The magenta solid line represents the fit (called "Best fit") with the contributions including the fluxes of UHE (Z ≤ 8) primary nuclei and their secondaries, when XS =2.5 and ∆ = 3. The black solid line represents the fit with the flux of MCPs with ǫ 2 = 1.3×10−4 , mφ = 2 × 1021 eV and τφ = 1027 s exceeding GZK-cutoff energy. The olive dot line represents the total flux who add up the f… view at source ↗
Figure 2
Figure 2. With the different ǫ 2 (= 4.5 × 10−4 , 1.3 × 10−4 and 2 × 10−6 ), the num￾bers of expected MCPs were evaluated assuming 14 years of Auger data, respectively [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. With the different ǫ 2 (= 7.18 × 10−4 , 1.8 × 10−4 and 1.7 × 10−7 ), the num￾bers of expected MCPs were evaluated assuming 14 years of Auger data, respectively [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: If mφ=2 × 1021 eV, with τφ = 1027 s, a new region (shaded region) is ruled out in the mMCP vs. ǫ plane, when 109.6 < mMCP < 1011.6 eV and ǫ > 2.12 × 10−2 (this work). Meanwhile, the bounds from plasmon decay in red giants (RG) [21], plasmon decay in white dwarfs (WD) […
Figure 5
Figure 5. Figure 5: Fits to the fluxes at Earth. The magenta solid line represents the fit (called "Best fit") with the contributions including the fluxes of UHE (Z ≤ 8) primary nuclei and their secondaries, when B=0 and ∆ = 1. The black solid line represents the fit with the flux of MCPs…

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

61 extracted references · 38 canonical work pages

  1. [1]

    Bergstrom, Rept

    L. Bergstrom, Rept. Prog. Phys. 63,793 (2000) arXiv: hep -ph/0002126

    work page arXiv 2000

  2. [2]

    Bertone, D

    G. Bertone, D. Hooper and J.Silk, Phys. Rep. 405, 279 (200 5) arXiv: hep- ph/0404175 7 Acknowledgements 8

    arXiv

  3. [3]

    Abe, et al., Planck collaboration, A&A 594, A13 (2 015) arXiv:1502.01589

    P.A.R. Abe, et al., Planck collaboration, A&A 594, A13 (2 015) arXiv:1502.01589

    arXiv

  4. [4]

    J.D.Lewin, P.F.Smith, Astropart. Phys. 6, 87 (1996)

    work page 1996

  5. [5]

    E.Aprile, et al., XENON1T Collaboration, Phys. Rev. Let t. 119, 181301 (2017)

    work page 2017

  6. [6]

    X.Y.Cui, et al., PandaX-II Collaboration, Phys. Rev. Le tt. 119, 181302 (2017)

    work page 2017

  7. [7]

    Limits on Dark Matter Annihilation Signals from the Fermi LAT 4-year Measurement of the Isotropic Gamma-Ray Background

    M. Ackermann, et al., Fermi-LAT Collaborations, JCAP 09 , 008 (2015) arXiv: 1501.05464

    work page Pith review arXiv 2015

  8. [8]

    Albert, M

    A. Albert, M. Andre, et al., ANTARES and IceCube Collabor ation, Phys. Rev. D 102, 08002 (2020) arXiv: 2003.06614

    arXiv 2020

Show all 61 references
  1. [9]

    Adrian-Matinez, et al., ANTARES Collaboration, Phys

    S. Adrian-Matinez, et al., ANTARES Collaboration, Phys . Lett. B 759, 69-74, (2016), arXiv: 1603.02228

    2016 arXiv

  2. [10]

    M. G. Aartsen, et al., IceCube Collaboration, Euro. Phy s. J. C 77, 146 (2017) arXiv: 1612.05949

    2017 arXiv

  3. [11]

    Anastassopoulos, et al., CAST Collaboration, Natur e Physics 13, 584 (2017)

    V. Anastassopoulos, et al., CAST Collaboration, Natur e Physics 13, 584 (2017)

    2017

  4. [12]

    Adhikari, C.S

    S. Adhikari, C.S. Akondi, GlueX Collaboration, Phys. R ev. D 105, 052007 (2022) arXiv: 2109.13439

    2022 arXiv

  5. [13]

    Reynolds et al., Astrophys

    C.S. Reynolds et al., Astrophys. J. 890, 59 (2020)

    2020

  6. [14]

    Abrahao, et al., Double Chooz Collaboration, Eur

    T. Abrahao, et al., Double Chooz Collaboration, Eur. Ph ys. J. C 81, 775 (2021) arXiv: 2009.05515

    2021 arXiv

  7. [15]

    Adamson, F.P

    P. Adamson, F.P. An, et al., Daya Bay, MINOS+ Collaborat ion, Phys. Rev. Lett. 125, 071801 (2020) arXiv: 2002.00301

    2020

  8. [16]

    Goldberg and L.J

    H. Goldberg and L.J. Hall, Phys. Lett. B 174, 151 (1986)

    1986

  9. [17]

    Yuan, JHEP 0703, 120 (2007) arXiv: hep -ph/0701107

    K.Cheung and T.C. Yuan, JHEP 0703, 120 (2007) arXiv: hep -ph/0701107

    2007

  10. [18]

    Feldman, Z

    D. Feldman, Z. Liu and P. Nath, Phys. Rev. D 75, 115001 (20 07) arXiv: hep-ph/0702123

    arXiv

  11. [19]

    Holdom, Phys

    B. Holdom, Phys. Lett. B 166, 196 (1986)

    1986

  12. [20]

    J. H. Chang, R. Essig, and S. D. McDermott, J. High Energy Phys. 09, 051 (2018)

    2018

  13. [21]

    Davidson, S

    S. Davidson, S. Hannestad, and G. Raffelt, J. High Energy Phys. 05, 003 (2000)

    2000

  14. [22]

    Dubovsky, D

    S. Dubovsky, D. Gorbunov and G. Rubtsov, JETP Lett. 79 (2 004) arXIv: hep-ph/0311189

    arXiv

  15. [23]

    Jaeckel and A

    J. Jaeckel and A. Ringwald, Annu. Rev. Nucl. Part. Sci. 6 0, 405-437 (2010)

    2010

  16. [24]

    Davidson, B

    S. Davidson, B. Campbell and D. Bailey, Phys. Rev. D 43, 2 314 (1991) 7 Acknowledgements 9

    1991

  17. [25]

    Prinz et al., SLAC Collaboration, Phys

    A. Prinz et al., SLAC Collaboration, Phys. Rev. Lett. 81 , 1175 (1998) arXiv: hep-ex/9804008

    1998 arXiv

  18. [26]

    Essig, T

    R. Essig, T. Volansky, and T.T. Yu, Phys. Rev. D 96, 04301 7 (2017)

    2017

  19. [27]

    Liu and T

    H. Liu and T. R. Slatyer, Phys. Rev. D 98, 023501 (2018)

    2018

  20. [28]

    Mitsui et al., Phys

    T. Mitsui et al., Phys. Rev. Lett. 70, 2265 (1993)

    1993

  21. [29]

    Lundeen, F.M

    S.R. Lundeen, F.M. Pipkin, Phys. Rev. Lett. 46, 232 (198 1)

  22. [30]

    Xu, JHEP 09, 055 (2022) arXiv: 2207.00178

    Y. Xu, JHEP 09, 055 (2022) arXiv: 2207.00178

    2022 arXiv

  23. [31]

    Xu, JHEP (2024) arXiv: 2405.00060

    Y. Xu, JHEP (2024) arXiv: 2405.00060

    2024 arXiv

  24. [32]

    M.Yu.Khlopov, V.M.Chechetkin, Sov. J. Part. Nucl 18, 2 67-288 (1987)

    1987

  25. [33]

    D. J. H. Chung, E. W.Kolb, and A.Riotto, Phys.Rev.Lett. 81, 4048, (1998) arXiv: hep-ph/9805473

    1998 arXiv

  26. [34]

    D. J. H. Chung, E. W.Kolb, and A.Riotto, Phys.Rev. D59, 0 23501 (1998) arXiv: hep-ph/9802238

    1998 arXiv

  27. [35]

    Kuzmin and I

    V. Kuzmin and I. Tkachev, JETP Lett. 68, 271¨C275 (1998) arXiv: hep- ph/9802304

    1998

  28. [36]

    E. W. Kolb, D. J. Chung, and A. Riotto, WIMPzillas!, hep- ph/9810361

  29. [37]

    D. J. H. Chung, E. W. Kolb, A. Riotto, and I. I. Tkachev, Ph ys. Rev. D 62, 043508 (2000) arXiv: hep-ph/9910437

    2000 arXiv

  30. [38]

    D. J. H. Chung, P. Crotty, E. W. Kolb, and A. Riotto„ Phys. Rev. D 64, 043503 (2001) arXiv: hep-ph/0104100

    2001 arXiv

  31. [39]

    E. W. Kolb, A. Starobinsky, and I. Tkachev, JCAP 0707, 00 5 (2007) arXiv: hep-th/0702143

    2007 arXiv

  32. [40]

    L.Covi, M.Grefe, A.Ibarra and D.Tran, JCAP 1004, 017 (2 010) arXiv: 0912.3521

    arXiv

  33. [41]

    T.Yanagid a Phys

    B.Feldstein, A.Kusenko, S.Matsumoto and T. T.Yanagid a Phys. Rev. D 88, 015004 (2013) arXiv: 1303.7320

    2013 arXiv

  34. [42]

    M. A. Fedderke, E. W. Kolb, and M. Wyman, Phys. Rev. D 91, 0 63505 (2015) arXiv:1409.1584

    2015 arXiv

  35. [43]

    Aloisio, S

    R. Aloisio, S. Matarrese and A. V. Olinto, JCAP, 1508, 02 4 (2015), arXiv: 1504.01319

    2015 arXiv

  36. [44]

    Peres, JCAP, 1211, 034 (20 12) arXiv:1205.5281

    A.Esmaili, A.Ibarra and O.L. Peres, JCAP, 1211, 034 (20 12) arXiv:1205.5281

    arXiv

  37. [45]

    Abraham, et al., The Pierre Auger Collaboration, Phy s

    J. Abraham, et al., The Pierre Auger Collaboration, Phy s. Lett. B 685, 239- 246 (2010) arXiv: 1002.1975

    2010 arXiv

  38. [46]

    K.Murase and J.F.Beacom, JCAP 1210, 043 (2012) arXiv:1 206.2595

    2012

  39. [47]

    C.Rott, K.Kohri and S.C.Park, Phys. Rev. D 92, 023529 (2 015) arXiv:1408.4575 7 Acknowledgements 10

    arXiv

  40. [48]

    M.Kachelriess, O.E.Kalashev and M.Yu.Kuznetsov, Phy s. Rev. D 98, 083016 (2018) arXiv: 1805.04500

    2018 arXiv

  41. [49]

    Y.Bai, R.Lu and J.Salvado, JHEP, 01, 161 (2016) arXiv:1 311.5864

    2016

  42. [50]

    A.Bhattacharya, R.Gandhi and A.Gupta, JCAP 1503, 027, (2015) arXiv:1407.3280

    2015 arXiv

  43. [51]

    Block, L

    M.M. Block, L. Durand and P. Ha, Phys. Rev. D89, 094027 (2 014) arXiv: 1404.4530

    arXiv

  44. [52]

    Martin M.Block, Phuoc Ha, Douglas W.McKay, Phys. Rev. D 82, 077302 (2010) arXiv: 1008.4555

    2010 arXiv

  45. [53]

    Mastrodicasa on behalf of the Pierre Auger Collabora tion, Proceedings of the 37th International Cosmic Ray Conference, Berlin, Ge rmany, 12-23 July 2021, 324

    M. Mastrodicasa on behalf of the Pierre Auger Collabora tion, Proceedings of the 37th International Cosmic Ray Conference, Berlin, Ge rmany, 12-23 July 2021, 324

    2021

  46. [54]

    Bellido, et al., the Pierre Auger Collaboration, P roceedings of the 29th International Cosmic Ray Conference, Pune, India, 3-10 Aug ust 2005, 101-106, arXiv: astro-ph/0507103

    J.A. Bellido, et al., the Pierre Auger Collaboration, P roceedings of the 29th International Cosmic Ray Conference, Pune, India, 3-10 Aug ust 2005, 101-106, arXiv: astro-ph/0507103

    2005 arXiv

  47. [55]

    Abreu, et al., the Pierre Auger Collaboration, Astro particle Physics, 34, 368-381 (2011) arXiv: 1010.6162

    P. Abreu, et al., the Pierre Auger Collaboration, Astro particle Physics, 34, 368-381 (2011) arXiv: 1010.6162

    2011 arXiv

  48. [56]

    Gonzalez for the Pierre Auger Collaboration, PoS( ICRC2023)288, Pro- ceedings of the 38th International Cosmic Ray Conference, N agoya, Japan, 26 July - 3 August, 2023, 288

    J.M. Gonzalez for the Pierre Auger Collaboration, PoS( ICRC2023)288, Pro- ceedings of the 38th International Cosmic Ray Conference, N agoya, Japan, 26 July - 3 August, 2023, 288

    2023

  49. [57]

    Vogel and J

    H. Vogel and J. Redondo, JCAP, 1402, 029 (2014) arXiv: 13 11.2600

    2014

  50. [58]

    N.Aghanim, et al., Planck Cobbaboration, A&A 641, A6 (2 020) arXiv:1807.06209

    arXiv

  51. [59]

    Y. Xu, J. Lan and W. Gao, Phys. Lett. B 859, 139127, 2024

    2024

  52. [60]

    Dolgov, S.L

    A.D. Dolgov, S.L. Dubovsky, G.I. Rubtsov and I.I. Tkach ev, Phys. Rev. D 88, 117701 (2013) arXiv: 1310.2376

    2013 arXiv

  53. [61]

    Bes t fit

    S. Abe, et al., Eur. Phys. J. C 83, 1028 (2023) arXiv: 2311 .12656 7 Acknowledgements 11 /s49/s56/s46/s48 /s49/s56/s46/s53 /s49/s57/s46/s48 /s49/s57/s46/s53 /s50/s48/s46/s48 /s50/s48/s46/s53 /s49/s48 /s51 /s55 /s49/s48 /s51 /s56 /s49/s56/s46/s48 /s49/s56/s46/s53 /s49/s57/s46/s...

    2023

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.