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REVIEW 2 major objections 6 minor 102 references

Daily Earth-shielding modulation can disentangle sub-GeV dark matter's nuclear and electron couplings.

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2026-08-01 09:50 UTC pith:EJ7ZLYGB

load-bearing objection A solid two-interaction framework that makes a real case for daily Earth-shielding modulation as a discriminator of DM-electron vs DM-nucleon couplings, with an unquantified annual-velocity approximation that should be tested before the projections are trusted. the 2 major comments →

arxiv 2607.20620 v1 pith:EJ7ZLYGB submitted 2026-07-22 hep-ph astro-ph.HEhep-ex

Dark Matter Weather: Probing Sub-GeV Interactions with Earth-Shielding Modulation

Tetiana Kozynets , Rebecca Leane , Juri Smirnov This is my paper
classification hep-ph astro-ph.HEhep-ex PACS 95.35.+d
keywords dark matterdaily modulationEarth shieldingsub-GeVDM–electron scatteringDM–nucleon scatteringliquid argonliquid xenon
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.

The paper aims to turn the Earth itself into part of a dark-matter detector: as the planet rotates, an underground detector samples dark matter arriving through different thicknesses of rock, so the observed rate acquires a predictable daily cycle. The authors show that in models where dark matter scatters off both nuclei and electrons, this cycle is controlled by the DM–nucleon cross section while the overall ionization rate is set by the DM–electron cross section. That separation means the daily modulation's shape carries information a rate-only search misses. They introduce a statistical test based on the integrated difference between background and signal isoangle distributions, and show projected sensitivities in argon and xenon that are competitive with Migdal searches — up to about an order of magnitude beyond DAMIC-M in specific mass windows. If right, this gives low-threshold liquid-noble experiments a new validation and discrimination handle.

Core claim

The central claim is that Earth attenuation and detector ionization are governed by different couplings of the same dark-matter particle, so the time-dependent signal separates them. The spin-independent DM–nucleon cross section sets the daily isoangle modulation pattern through Earth scattering, while the DM–electron cross section sets the overall ionization yield; a shape-based statistic (the integrated absolute CDF distance in isoangle space) combined with the ionization spectrum can therefore measure the nuclear cross section even when only electron recoils are detected. The paper demonstrates this for liquid argon and liquid xenon, and illustrates the method with a case study using 653

What carries the argument

The central object is the isoangle Θ, the angle between the detector's position vector and the apparent dark-matter wind; detectors at equal Θ receive the same attenuated flux. The framework separates two cross sections: the spin-independent DM–nucleon cross section controls the Θ-dependent attenuation and hence the daily modulation shape, while the DM–electron cross section controls the overall ionization signal. The statistical engine is D_isoang, the integrated absolute difference between the background-only and signal-plus-background cumulative isoangle distributions (a one-dimensional Wasserstein distance), which is robust to isolated fluctuations and can be combined with the ionization

Load-bearing premise

The analysis fixes the Earth's orbital velocity to its March 9 value for both the signal model and the event timestamps; over a full year the daily modulation curve shifts phase with the seasons, so a long exposure sees a smeared shape that the projections do not account for.

What would settle it

Take one year of timestamped events from a low-threshold liquid-noble detector, bin them by the true day-by-day seasonally varying isoangle, and compare the observed daily modulation phase and amplitude against the fixed-March-9 prediction; if the phase shifts measurably across the year, the paper's fixed-velocity projections are optimistic, and if it does not, the approximation holds.

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

If this is right

  • A daily modulation with the predicted phase, shape, target dependence, and site dependence would be difficult for most detector backgrounds to mimic, giving a validation handle on any sub-GeV candidate.
  • The isoangle shape test can place 90% C.L. limits on the DM–nucleon cross section using only electron-recoil ionization data, complementary to Migdal-based atomic-ionization searches.
  • Because Northern and Southern Hemisphere detectors sample different isoangle ranges, comparing sites sharpens the interpretation of any signal.
  • The method is ready for tonne-scale liquid-noble exposures, which can accumulate the required statistics in days to months.
  • In light-mediator models, screening and forward-peaked scattering suppress the daily modulation at fixed reference cross section, so the effect primarily probes contact interactions at the quoted cross sections.

Where Pith is reading between the lines

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

  • The paper fixes the Earth's orbital velocity to a single date; a natural extension would model the full seasonal drift of the isoangle curve, letting a combined daily-plus-annual analysis use the complete time morphology rather than a smeared daily average.
  • The same two-cross-section logic should transfer to semiconductor or scintillator targets, where different ionization thresholds would probe different mass windows and provide cross-material consistency checks.
  • The D_isoang statistic is a Wasserstein-1 distance; higher-order Wasserstein metrics or harmonic decompositions of the isoangle PDF might capture subtler shape information that the integrated CDF difference averages out.
  • The separation between rate and shape could also be used as a diagnostic after a candidate excess appears: a rate-only excess with no daily shape distortion would point toward pure DM–electron coupling, whereas a distorted shape would indicate significant Earth attenuation.

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

2 major / 6 minor

Summary. The paper studies daily modulation of sub-GeV dark-matter signals caused by DM–nucleus scattering inside the Earth, in a scenario where DM also scatters off electrons in the detector. Using DaMaSCUS to obtain the Earth-modified speed distribution f(v|Θ) and density ρ(Θ) for a grid of (mχ, σ_SI_χn), and DarkArt for atomic ionization form factors, it computes the Θ-dependent ionization rates in argon and xenon targets through Eq. (11). It introduces a location-dependent isoangle exposure w(Θ) (Eq. 13) and a shape statistic D_isoang (Eq. 20) that quantifies the daily-modulation shape, with p-values calibrated by Poisson pseudoexperiments and a CL_s procedure. It presents projected 90% C.L. exclusions on σ_SI_χn for 1–10 tonne-month argon/xenon at LNGS/SUPL and for XENONnT/LZ-like exposures, claiming sensitivity competitive with or up to an order of magnitude better than Migdal searches in certain mass windows. It also applies the framework to DarkSide-50 by combining spectral and isoangle-shape constraints, assuming no observed daily modulation because public timestamps are unavailable. The analysis fixes the Earth’s orbital velocity to its March 9 value (Eq. 9) for both signal modeling and timestamp-to-Θ mapping.

Significance. The proposed two-interaction interpretation is conceptually novel and, if the projected sensitivity is correct, practically valuable: it turns Earth shielding into a diagnostic for interaction structure rather than a nuisance rate correction, and it explicitly incorporates the location-dependent isoangle exposure, which previous work did not include. Strengths of the paper are the parameter-free signal model for fixed input cross sections, the use of public DaMaSCUS and DarkArt outputs, the standard CL_s calibration with Poisson pseudoexperiments, and the explicit model benchmarks (heavy dark photon and U(1)_B × U(1)_L). The DarkSide-50 case study is honest about the lack of public timing information. The main caveat is that the annual-variation approximation is unquantified and could affect exactly the long-exposure projections that support the headline comparison with Migdal searches.

major comments (2)
  1. [Sec. II.A, Eq. (9); Figs. 5, 13–15] The fixed March-9 orbital velocity is load-bearing for the claimed sensitivity. The text acknowledges that the resulting Θ(t) “does not capture the full seasonal dependence,” but no bias estimate is given. Fig. 5 shows that switching to the true September velocity (thin dashed vs thick dashed) shifts the daily Θ(t) curve by an amount that is not small compared with the modulation features, and for XENONnT-like exposures (94 tm ≈ 16 months) or LZ-like exposures (50 tm ≈ 7 months) a single fixed mapping will smear the predicted daily phase. Since D_isoang and the CL_s contours in Figs. 13–15 are computed entirely under this fixed mapping, the projected reach—including the claimed order-of-magnitude improvement over DAMIC-M—could be degraded precisely in the long-exposure regime. Please recompute with the full time-dependent v_orb(t), or provide a quantitative seasonal-smearing estimate (e.
  2. [Sec. II.B, Figs. 6–8] The rate-shape input to D_isoang is built from 6° DaMaSCUS bins smoothed with a four-parameter tanh (or parabolic) fit. The entire CL_s calculation uses these fitted interpolators, but no closure test is shown for the full (mχ, σ_SI_χn) grid used in the projections; Fig. 8 demonstrates only a single representative mass, mχ = 40 MeV, at two cross sections. If the analytic parameterization is inaccurate in some region of the grid, the predicted isoangle shape—and hence the projected exclusions—could be biased. Please add a closure test comparing the interpolated Θ shapes to the direct DaMaSCUS outputs for a few points spanning the contours in Figs. 13–15, or propagate the Monte Carlo outputs directly through the statistical analysis.
minor comments (6)
  1. [Sec. VI] Typo: “side-real modulation” should be “sidereal modulation”.
  2. [Fig. 12 caption] The labels p_sb and p_b in the bottom-center panel are not defined in the caption; please define them or refer explicitly to Eqs. (23)–(25).
  3. [Fig. 5 caption] The legend notation “v⊙⊕(t) v⊙⊕(Mar9)” is garbled; please clarify which curves correspond to the fixed March-9 velocity and which to the season-dependent velocity.
  4. [Table I] Please state the provenance of the argon N_e=1 and N_e=2 background rates more explicitly. In particular, the argon N_e=1 rate is extrapolated from DarkSide-50 data via the spurious-electron model of Eq. (B3); the caption should say so and give the associated uncertainty, since these rates directly set the projected reach in Figs. 13–14.
  5. [Sec. IV.A, Eq. (27)] The conversion σ_SI_χn = σ_χp (Z/A)^2 with Z/A = 0.5 for all terrestrial nuclei is an approximation. A brief comment on the spread in Z/A over realistic Earth composition (e.g., Fe has Z/A ≈ 0.46) and its effect on the σ_SI_χn normalization would help interpret the contours.
  6. [Fig. 9 caption] Please note in the caption that w(Θ) is computed with the fixed March-9 velocity of Eq. (9); this is important because the exposure density itself becomes season-dependent in a full treatment.

Circularity Check

0 steps flagged

No significant circularity: the signal model and statistical calibration are self-contained, and the paper's acknowledged approximations are modeling limitations, not circular reductions.

full rationale

The central derivation chain is self-contained. Given (mχ, σ̄e, σ_SI_χn), the ionization rates follow from Eq. (11) using public DaMaSCUS outputs for f(v|Θ) and ρχ(Θ) and DarkArt RHF form factors; no parameter is fitted to the quantity being predicted. The D_isoang shape statistic (Eq. 20) is a distance between background-only and signal-plus-background isoangle CDFs, and its p-value is calibrated with Poisson pseudoexperiments under stated hypotheses (Eqs. 21-25), so the exclusion contours in Figs. 13-15 are not forced by construction. The DarkSide-50 case study is explicitly illustrative: timestamps are unavailable, and the paper assumes an Asimov background-only isoangle distribution (Sec. V.A), while the fitted SE background parameters (Eq. B5) are a background model, not a DM prediction. The only author self-citations (Refs. [56,57] for DM-electron scattering and Ref. [100] for an anomaly-free baryon model in Appendix A) are not load-bearing for the modulation formalism. The paper's own limitation statement, that fixing v_⊙⊕ to March 9 in Eq. (9) 'does not capture the full seasonal dependence,' is an acknowledged modeling approximation and a potential systematic bias in the reach estimates, but it is not a circular reduction of the predictions to their inputs.

Axiom & Free-Parameter Ledger

6 free parameters · 10 axioms · 0 invented entities

The central signal model is loaded from prior literature and public simulation tools (DaMaSCUS v1.1, DarkArt v0.1.0); the halo, interaction-model, and Earth-composition inputs are standard or explicitly flagged. The only numbers fitted in this paper are DarkSide-50 background parameters and rate-interpolator smoothing coefficients; they are not part of the physics claim. No new particles, forces, or conserved quantities are introduced: the U(1)_D dark photon (Eqs. A1–A7) and gauged U(1)_B⊗U(1)_L mediators (Eqs. A8–A15) are cited prior constructions used only to motivate correlated vs independent (σ̄e, σ_SI_χn) benchmarks.

free parameters (6)
  • R_SE (spurious-electron background normalization) = 4.07 (kg^-1 day^-1)
    Fitted to the DarkSide-50 ionization spectrum in App. B (Eq. B5); used in the DS-50 spectral and combined constraints.
  • p_SE (spurious-electron pile-up probability) = 0.21
    Fitted to DarkSide-50 data (Eq. B5); shapes the low-N_e background that the DS-50 modulation and spectral analyses rely on.
  • F_SE (Gaussian width scale for SE reconstruction) = 1.37
    Fitted to DarkSide-50 data (Eq. B5); enters the SE background model in Eq. (B2).
  • Radiogenic background pulls σ_39Ar, σ_85Kr, σ_PMT = 0.17, 0.10, 0.23
    Fitted to DarkSide-50 data (Eq. B6); normalization pulls on 39Ar, 85Kr, and PMT backgrounds.
  • 15% bin-to-bin uncorrelated background systematic = 0.15
    Hand-chosen uncertainty assigned to the total DS-50 background model (Sec. V.A); directly controls the spectral p-values and combined constraints.
  • Rate-interpolator coefficients (4-parameter tanh or parabolic) = not quoted
    Fitted to DaMaSCUS-derived rates to build (mχ, σ_SI_χn) rate interpolators (Sec. II.B, Fig. 8); smoothing of MC output, with ad hoc switch between parameterizations.
axioms (10)
  • domain assumption Standard Halo Model: unattenuated DM is an isotropic truncated Maxwell–Boltzmann distribution with v0=238 km/s, vesc=544 km/s, ρ=0.3 GeV/cm^3 (Eqs. 1–7).
    The unattenuated input to all Earth-scattering calculations; if the local halo has non-Maxwellian structure, the predicted isoangle shapes shift.
  • domain assumption Heavy-mediator (contact) interaction is the default for the signal grid; light mediators are deferred to Appendix C.
    App. C shows light-mediator modulation is strongly suppressed at fixed reference cross sections; the numerical reach claimed in Secs. IV–V is contact-interaction-specific.
  • ad hoc to paper DaMaSCUS Earth composition assumes Z/A = 0.5 for all terrestrial nuclei, used to convert σ_χp to σ_SI_χn via Eq. (27).
    A modeling simplification of the Earth-composition profile; real Earth Z/A varies around 0.46–0.50, so this introduces a few-percent-level O(1) uncertainty in the attenuation scale.
  • ad hoc to paper Fixed orbital velocity v⊙⊕(March 9); annual variation of the Earth's orbital velocity is neglected (Eq. 9).
    Load-bearing for the t→Θ mapping and signal shape over year-long exposures; the paper flags it but does not quantify the bias.
  • domain assumption DaMaSCUS v1.1 correctly simulates Earth propagation (free-nucleus scattering, energy loss, deflection) for sub-GeV DM.
    The inherited MC framework from Refs. [25, 62–67] is used as a black box; the paper does not validate it against independent simulations.
  • domain assumption Roothaan–Hartree–Fock non-relativistic orbitals and ionization form factors (DarkArt) with the listed binding energies; spin-orbit splitting neglected.
    Standard treatment from Refs. [34, 79, 80]; the paper notes the neglected relativistic sub-dominant effects.
  • domain assumption Ionization yield models: argon continuous N_e (Refs. [78, 82]), xenon integer-N_e probability mass function (Refs. [79, 83]).
    The conversion of electron-recoil energy to observed N_e relies on published yield models; errors here directly shift the predicted spectra.
  • standard math Poisson property: for a Poisson process, total event count and the isoangle distribution are statistically independent (used for Fisher's combination, Eq. 29).
    Standard conditional-Poisson/multinomial fact; correctly applied in Sec. V.B.
  • standard math CLs prescription and Poisson pseudoexperiment calibration of p-values (Sec. III.C).
    K_b and K_sb distributions are self-calibrated under the tested hypotheses; a standard likelihood-free test construction.
  • domain assumption Background model for DS-50: spurious electrons (Eq. B3), 39Ar, 85Kr, PMT components with published uncertainties (Ref. [82]).
    The DS-50 constraints inherit the fidelity of this background decomposition; subdominant components (cryostat radioactivity) are neglected.

pith-pipeline@v1.3.0-alltime-deepseek · 23028 in / 29536 out tokens · 241694 ms · 2026-08-01T09:50:01.548954+00:00 · methodology

0 comments
read the original abstract

Daily modulation from Earth shielding provides a powerful search handle for sub-GeV dark matter (DM) in low-threshold experiments. We use this effect as a probe of interaction structure in scenarios where DM couples to both electrons and nuclei. Nuclear scattering in the Earth alters the incident DM flux, while electron scattering produces the observable ionization signal, so the total rate and modulation pattern encode different aspects of the underlying interactions. We develop this two-interaction framework for argon and xenon targets and introduce a new statistical analysis that tests the modulation shape, including the location-dependent exposure of underground detectors to different Earth-crossing trajectories, alone and in combination with the ionization spectrum. We demonstrate the method for liquid-noble detectors at underground sites SURF (USA), LNGS (Italy), and SUPL (Australia), and apply it to DarkSide-50 data as a concrete case study. Our results show that Earth-scattering modulation can help disentangle electron and nuclear DM interactions and provide a validation handle for low-threshold liquid-noble searches.

Figures

Figures reproduced from arXiv: 2607.20620 by Juri Smirnov, Rebecca Leane, Tetiana Kozynets.

Figure 1
Figure 1. Figure 1: FIG. 1. Illustration of spin-independent DM–nucleus scatter [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Mean free path [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: illustrates how intraterrestrial scattering also [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Evolution of the isoangle Θ throughout the day at [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. DM-induced argon ionization spectra, [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p005_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Argon and xenon ionization rates at [PITH_FULL_IMAGE:figures/full_fig_p006_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Daily isoangle exposure densities [PITH_FULL_IMAGE:figures/full_fig_p007_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Comparison of the background-only and signal-plus [PITH_FULL_IMAGE:figures/full_fig_p008_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Distributions of the isoangle shape statistic [PITH_FULL_IMAGE:figures/full_fig_p009_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Projected 90% C.L. exclusion limits on [PITH_FULL_IMAGE:figures/full_fig_p010_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p011_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Projected 90% C.L. exclusion limits on [PITH_FULL_IMAGE:figures/full_fig_p012_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Illustrative 90% C.L. exclusions of selected ( [PITH_FULL_IMAGE:figures/full_fig_p014_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Illustrative 90% C.L. constraints on [PITH_FULL_IMAGE:figures/full_fig_p014_17.png] view at source ↗

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