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REVIEW 3 major objections 5 minor 127 references

Heavy charged relics that stop in Earth can be mined from water and rock and identified by mass spectrometry down to tiny dark-matter fractions.

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 →

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T0 review · grok-4.5

2026-07-14 15:03 UTC pith:KWMK7VGS

load-bearing objection Solid first map of CHAMP stopping depths plus a practical target/enrichment plan; the extreme f_X numbers are projections that hinge on O(1) retention and background rejection. the 3 major comments →

arxiv 2607.09845 v1 pith:KWMK7VGS submitted 2026-07-10 hep-ph astro-ph.COhep-ex

Searching for heavy charged relics in the Earth

Reza Ebadi , Peter W. Graham , Surjeet Rajendran , Erwin H. Tanin , Samuel S. Y. Wong This is my paper
classification hep-ph astro-ph.COhep-ex
keywords CHAMPsheavy charged particlesterrestrial accumulationgravitational enrichmentcentrifugal enrichmentmass spectrometrydark matter relicsstopping power
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 argues that galactic electrically charged massive particles (CHAMPs) raining onto Earth lose energy, stop at calculable depths, and can be recovered from monitored water or ice and from ancient geological samples. After multi-stage gravitational or centrifugal enrichment that concentrates them into gram-scale samples, mass spectrometry can distinguish their anomalous charge-to-mass ratios from ordinary heavy molecules. The method covers masses from roughly 1 TeV to 10^12 TeV and, under optimistic retention assumptions, can reach fractional dark-matter densities as low as 10^{-20}. Even a one-month pathfinder that processes only a liter of water with a single centrifuge (or a cubic meter without one) already probes new parameter space at the 10^{-10} level. The practical payoff is a scalable terrestrial search that is complementary to collider limits and to astrophysical bounds from neutron stars and white dwarfs.

Core claim

A local galactic population of heavy charged particles can be trapped in the Earth, concentrated from large volumes of water, ice or rock by gravitational settling or centrifugation, and identified by charge-to-mass spectrometry, yielding sensitivity to fractional dark-matter densities far below existing terrestrial bounds over masses 1–10^{12} TeV.

What carries the argument

The rock-equivalent stopping-depth distribution n_stop_X(z) (derived from Lindhard–Scharff energy loss integrated over a Maxwell–Boltzmann flux) that tells experimenters where CHAMPs accumulate and therefore which monitored or ancient samples to mine.

Load-bearing premise

The projected reach assumes that essentially every trapped CHAMP survives multi-stage enrichment and can be cleanly distinguished from heavy molecular backgrounds in a mass spectrometer.

What would settle it

A controlled pathfinder that processes one liter of water for one month (or one cubic meter without centrifugation) and reports either a clean null result at f_X ~ 10^{-10} or an unexplained excess mass/charge-to-mass signal that survives molecular-fragmentation cuts.

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

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 terrestrial search for galactic CHArged Massive Particles (CHAMPs) that stop and accumulate in Earth materials. It computes the distribution of first-stopping points for virialized CHAMPs under Lindhard–Scharff energy loss and an isotropic Maxwell–Boltzmann flux (Section II, Eqs. (4)–(8), Appendix A), estimates post-stopping Boltzmann equilibration and penetration in fluids (Appendix B), and identifies monitored water/ice, geological rocks, and ice cores as targets (Section III). Enrichment by multi-stage gravitational settling or centrifugation (Section IV, Appendix D) followed by mass-spectrometric identification is argued to yield sensitivity to f_X down to ~10^{-20} at low mass, with pathfinder experiments (liter-scale water + centrifuge, or m^3 without) already reaching ~10^{-10}. Projected reaches are summarized in Fig. 4 under the criterion N_sample_X ≳ 1 with O(1) end-to-end efficiency.

Significance. If the accumulation, enrichment, and identification chain can be realized at the assumed efficiency, the work would open a large, previously poorly constrained window for charged relics between collider and compact-object bounds, with a concrete pathfinder that already probes new parameter space. Strengths include a first-principles geometric stopping distribution (Appendix A), transparent order-of-magnitude equilibration and penetration criteria (Appendix B), and a staged experimental roadmap from pathfinder to ultimate reach. The proposal is falsifiable and complementary to existing astrophysical limits; even partial success would improve the robustness of terrestrial CHAMP searches relative to earlier water and rock analyses with poorly controlled histories.

major comments (3)
  1. Section III, Eq. (11) and the surrounding text set the projected reach by requiring N_sample_X ≳ 1 with O(1) retention and background-free identification. Appendix D quotes ~90% retention for a six-stage 4 h_Boltz cut under ideal Boltzmann settling, but does not quantify wall adhesion when h_Boltz becomes microscopic (m_X ≳ 10^6–10^7 TeV), losses during rock/ice liquefaction, or residual multi-atom molecular backgrounds (proteins/viruses up to ~10^6 TeV) after fragmentation (Section IV.B). Because the numerical contours in Fig. 4 scale linearly with end-to-end efficiency, the paper should either (i) provide a conservative efficiency floor and re-draw the reach, or (ii) clearly demote the absolute f_X numbers to optimistic benchmarks and emphasize the qualitative strategy and pathfinder scaling.
  2. Section II.A and Appendix A neglect Earth’s gravity for v ≲ v_esc,⊕ and truncate the analysis at m_X ≲ 3×10^{12} TeV. For the high-mass end of Fig. 4 (rocks, ice cores) the stopped population is precisely the low-velocity tail; the paper should quantify how including gravitational focusing or the escape-speed cutoff would shift n_stop_X and the corresponding f_X contours, even if only by an O(1) factor, so that the claimed high-mass reach is not overstated.
  3. Section III.B adopts L_geo ~ 100 km for Gyr-scale geological smearing and takes N_rock_X = min(N_static, N_geo). This choice is highly conservative and largely determines the deep-rock curves in Fig. 4. The manuscript should either motivate L_geo with specific geological data for candidate sites or present a family of curves for a range of L_geo so that the reader can assess how sensitive the high-mass reach is to this free parameter.
minor comments (5)
  1. Fig. 4 caption and main text: the transition between centrifugal (V_exp = 10^5 m^3) and gravitational (V_exp = 4×10^7 m^3) enrichment is described as “smoothed over”; a short note on how the hybrid regime around m_X ~ 10^3 TeV is treated would improve reproducibility.
  2. Eq. (A1) and footnote a of Fig. 4: the Lindhard–Scharff normalization is taken from muon range data; a one-sentence comparison to alternative low-velocity stopping formulas would help readers judge systematic uncertainty on L_stop.
  3. Appendix C: the age–depth fit t_age(z) is given without uncertainty bands; even a brief statement of the fit residual relative to Ref. [95] would clarify the ice-core exposure integral.
  4. Typographical consistency: “form X” vs “for m_X”, and occasional missing spaces before units (e.g., “10 5 m3”) appear in several places; a light copy-edit pass would help.
  5. Section IV.B: CDMS mass reach is cited up to ~10^8 TeV; a short remark on how vertical geometry mitigates free-fall for still heavier particles would strengthen the identification discussion.

Circularity Check

1 steps flagged

Forward-looking experimental proposal; stopping distributions and enrichment factors are derived from standard inputs, not forced by fits or self-definition. Only minor non-load-bearing self-citation for centrifuge volume.

specific steps
  1. self citation load bearing [Sec. IV.A / App. D; low-mass V_exp choice in Fig. 4 caption]
    "Form X ≲10^3 TeV, gravitational enrichment becomes inefficient... we restrict the initial sample volume to smaller sizes (∼10^5 m^3), which can be processed directly using centrifugal enrichment, as detailed in Ref. [28]. ... Based on that analysis, we set the projected reach in the lower-mass regime (mX ≲10^3 TeV) by requiring N_X ≳1 within a 10^5 m^3 sample."

    The low-mass sample-volume ceiling (and thus part of the Fig. 4 contour for m_X ≲ 10^3 TeV) is taken from a prior paper with overlapping authors rather than re-derived here. This is a minor dependency: the central novelty (stopping-depth distribution, gravitational enrichment, rock/ice targets) does not rest on [28], and [28] is an independent analysis of centrifuges, not a self-definition of the present result. Not load-bearing for the main claim.

full rationale

The paper is a methods/proposal paper, not a claim that a fitted model predicts new data. The load-bearing physics chain is: Lindhard–Scharff dE/dx (A1) → L_stop (A2/4) → geometric n_stop_X for Maxwell–Boltzmann arrivals (A8/6) → Boltzmann height and equilibration timescales (10, App. B) → N_sample_X from chosen volumes/exposures (12–17) → sensitivity via N ≳ 1 (11). None of these steps defines the output in terms of itself or renames a fit as a prediction. Benchmark volumes (10^5 m^3 / 4×10^7 m^3 water, 1 m^3 rock, ice-core A_core×z_max) and t_exp are free experimental choices that set the plotted f_X contours; they do not circularly define the stopping physics. The ice-core age–depth fit (C1) is to external glaciological data [95], not to the CHAMP signal. The only mild self-citation is Ref. [28] (overlapping authors) for the claim that centrifugal enrichment can process ~10^5 m^3 and for mass-spectrometry review; gravitational enrichment (App. D) and the stopping-depth calculation are independent of that citation and carry the bulk of the new reach. No uniqueness theorem, no ansatz smuggled as theorem, no fitted CHAMP parameter re-sold as prediction. Score 1 for the minor non-load-bearing self-citation only.

Axiom & Free-Parameter Ledger

4 free parameters · 4 axioms · 0 invented entities

The central reach claim rests on a short list of standard astrophysical and nuclear-physics inputs plus a handful of benchmark experimental parameters chosen by hand. No new particles or forces are invented; CHAMPs are taken from the existing literature. The free parameters are the exposure volumes, times, and geological-smearing lengths that set the numerical contours in Fig. 4.

free parameters (4)
  • V_exp (monitored water/ice) = 10^5 m^3 / 4e7 m^3
    Benchmark volumes 10^5 m^3 (centrifugal) and 4×10^7 m^3 (gravitational) chosen to set the low-mass reach; not derived from first principles.
  • t_exp = 10 yr
    Exposure time of 10 yr for monitored samples; free experimental choice.
  • L_geo = ~100 km
    Geological smearing length ~100 km assumed for Gyr-old rocks; conservative but hand-chosen.
  • V_rock / A_core = 1 m^3 / 0.01 m^2
    Fiducial rock volume 1 m^3 and ice-core area 10^{-2} m^2 set the ancient-sample reach.
axioms (4)
  • domain assumption Local CHAMP density is a free fraction f_X of the standard DM density with isotropic Maxwell–Boltzmann velocities of dispersion 10^{-3}c, neglecting magnetic deflection and Earth’s boost for the bulk of the flux.
    Stated in Section II.A; underpins the entire flux and stopping calculation.
  • domain assumption Energy loss of slow CHAMPs is given by the Lindhard–Scharff formula extrapolated from muon data (Eq. (A1)).
    Appendix A.1; determines L_stop and therefore the depth distribution.
  • ad hoc to paper After neutralization, CHAMPs reach a Boltzmann distribution on the timescales of Appendix B and can be retained with O(1) efficiency through multi-stage enrichment.
    Section III and Appendix D; required for the N_sample_X ≳ 1 sensitivity criterion.
  • domain assumption Earth is modeled as a uniform-density sphere of 2.5 g cm^{-3} with a 4 m rock-equivalent atmosphere; only depths ≲1 km are accessible.
    Section II.B; simplifies geometry while remaining adequate for shallow targets.

pith-pipeline@v1.1.0-grok45 · 33637 in / 3140 out tokens · 34416 ms · 2026-07-14T15:03:45.369595+00:00 · methodology

0 comments
read the original abstract

We propose a method for detecting an ambient density of heavy, electrically-charged particles. Such particles would impact the Earth, lose energy in terrestrial matter, and become trapped. We study the accumulation of these rare particles in multiple target materials that provide large exposure, such as water and geological rocks. We discuss strategies for concentrating the particles by centrifugation or gravitational settling, along with particle identification using mass spectrometry. This method enables the discovery of charged relics with masses $1-10^{12}\,{\rm TeV}$ comprising a tiny fraction of the local dark matter density, reaching down to $f_X\sim 10^{-20}$ at the lowest masses. A pathfinder experiment using only a liter of water and one centrifuge (or $\sim \text{m}^3$ and no centrifuge) operating for a month can already reach $f_X\sim 10^{-10}$ and probe new parameter space.

Figures

Figures reproduced from arXiv: 2607.09845 by Erwin H. Tanin, Peter W. Graham, Reza Ebadi, Samuel S. Y. Wong, Surjeet Rajendran.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustration of the proposed experimental strategy. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The typical stopping length [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: , we show n stop X /fX as a function of z for ∆t = 5 Gyr and mX = 105 , 107 , 109 , 1011 TeV. The general trend is that as the mass mX increases, the incoming flux de￾creases as ΦX ∝ m−1 X , while the typical X particles pen￾etrate deeper into the Earth; this results in a smaller number density at shallow depths, but a distribution that reaches larger penetration depths. In the limit of z,L¯ stop ≪ R⊕, the… view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Projected sensitivity of our proposed searches to singly charged CHAMPs [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. CHAMP stopping geometry. The [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Boltzmann equilibration timescale in water with [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Benchmark ice-core depth-age relation, fitted from [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗

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Reference graph

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