pith. sign in

arxiv: 2606.11097 · v1 · pith:V63BJP3Vnew · submitted 2026-06-09 · 🌌 astro-ph.IM

A data-driven method for measuring corner-clipping probabilities in segmented particle detectors

Joaqu\'in de Jes\'us , Juan Manuel Figueira , Federico S\'anchez , Darko Veberi\v{c} This is my paper

Pith reviewed 2026-06-27 11:28 UTC · model grok-4.3

classification 🌌 astro-ph.IM
keywords corner-clipping probabilitysegmented particle detectorsdata-driven methodtiming resolutionPierre Auger Observatorymuon detectionair showersovercounting bias
0
0 comments X

The pith

A timing-based method measures corner-clipping probabilities directly from data in segmented detectors.

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

The paper develops a method to measure corner-clipping probabilities using only detector data. It leverages timing resolution to distinguish true single-particle events in neighbors from random coincidences, using non-neighboring elements as controls. When tested on simulations, it reproduces the true values with small errors, and a new analytical model parameterizes the results. This enables direct corrections in data analysis for more accurate particle counting in experiments like air shower observatories.

Core claim

The authors establish that a fully data-driven method, relying on nanosecond timing to statistically separate genuine corner-clipping events from random coincidences with non-neighboring elements as control, can measure the corner-clipping probability and reproduce its angular dependence with absolute deviations below 0.01 in simulations of the Underground Muon Detector.

What carries the argument

The statistical distinction of corner-clipping events using timing resolution and an intrinsic control sample from non-neighboring detection elements.

If this is right

  • The corner-clipping probability can be measured without Monte Carlo simulations, reducing modeling uncertainties.
  • Data-driven corrections can be incorporated into reconstruction algorithms for particle counting.
  • The analytical model allows parameterization incorporating detector geometry and minimum path length.
  • This leads to more accurate determination of the muonic component of extensive air showers.
  • The method applies to any segmented detector with sufficient timing resolution.

Where Pith is reading between the lines

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

  • Other experiments with segmented detectors could adopt this to improve their particle identification accuracy.
  • The method might enable on-the-fly corrections during data taking if timing is good enough.
  • It could be extended to measure other types of multi-hit probabilities in detectors.
  • This connects to improving muon flux measurements in cosmic ray studies.

Load-bearing premise

The approach relies on non-neighboring detection elements providing an accurate control sample for random coincidences and on the detector timing being fine enough to separate genuine events statistically.

What would settle it

A direct comparison between the data-driven probability measurement and the known true probability from detailed simulations or controlled tests, where the absolute difference exceeds 0.01 for some angles, would falsify the claim of accurate reproduction.

Figures

Figures reproduced from arXiv: 2606.11097 by Darko Veberi\v{c}, Federico S\'anchez, Joaqu\'in de Jes\'us, Juan Manuel Figueira.

Figure 1
Figure 1. Figure 1: Schematic of a generic particle detector composed of a linear array of contiguous segments. The trajectory of an incident particle is shown with a magenta arrow. Its direction is characterized by the zenith angle, 𝜃 (blue), and the azimuthal angle, Δ𝜙 (green), measured with respect to the longitudinal axis of the segments. The illustrated event corresponds to a corner-clipping case, in which the particle i… view at source ↗
Figure 2
Figure 2. Figure 2: Schematic side view (cross-section) of two adjacent detector strips of height ℎ and width 𝑤, illustrating the geometric model for corner-clipping. A corner-clipping event is recorded only when an incident particle (µ) traverses a minimum path length 𝑑 in both strips. For a given zenith angle 𝜃, this requirement defines excluded regions of height 𝑥 at the upper and lower edges of the shared boundary, leavin… view at source ↗
Figure 3
Figure 3. Figure 3: Schematic of an Underground Muon Detector module. The module is segmented into 64 scintillator strips and is mechanically divided into two 32-strip sub-units. The incident particle trajectory is approximated by the shower axis (magenta), which is defined by the zenith angle, 𝜃 (blue), and the azimuthal angle, Δ𝜙 (green), relative to the longitudinal axis of the strips. probability, 𝑝cc, and whether it rema… view at source ↗
Figure 5
Figure 5. Figure 5: The observed fraction of neighboring pairs, 𝑝 obs neigh, in simulated events as a function of the absolute time difference, |Δ𝑡|. For large time differences (|Δ𝑡|/3.125 ns > 5), the fraction (open circles) reaches a constant asymptotic value. The average in this region yields 𝑝 obs 2µ = (6.6 ± 0.2) % (dashed line), consistent with the theoretically expected combinatorial probability 𝑝 exp 2µ = 6.25 % (dash… view at source ↗
Figure 6
Figure 6. Figure 6: Estimated numbers of corner-clipping events (𝑁ˆ cc, solid inverted triangles) and two-muon background events (𝑁ˆ 2µ, open triangles) as a function of the absolute time difference, |Δ𝑡|, obtained using the data￾driven method. For comparison, the true Monte-Carlo distributions of single-muon corner-clipping events (red hatched histogram) and two-muon events (grey filled histogram) are also shown. The close c… view at source ↗
Figure 7
Figure 7. Figure 7: The estimated corner-clipping probability, 𝑝ˆcc, obtained with the proposed data-driven method, is plotted against the true probability, 𝑝 true cc , from Monte-Carlo simulations. Each point represents a distinct bin in zenith and azimuth angle. The close alignment of the points with the identity line (dashed) demonstrates that the estimator accurately reproduces the true probability. statistical fluctuatio… view at source ↗
Figure 8
Figure 8. Figure 8: Estimated single-muon corner-clipping probability, 𝑝ˆcc, for UMD simulated data as a function of |sin(Δ𝜙)| for seven zenith-angle values (top) and as a function of 𝜃 for six Δ𝜙 bins (bottom). The dashed lines correspond to the global fit using the parameterization defined in Eq. (21). the corner-clipping probability reaches values up to ∼20 % for showers with zenith angles near 56◦ and trajectories transve… view at source ↗
Figure 9
Figure 9. Figure 9: Residuals of the global fit of the corner-clipping probability model to UMD simulated data, defined as the difference between the measured corner-clipping probability and the best-fit model from Eq. (21), shown as a function of |sin(Δ𝜙)| for different zenith angle bins. Residuals fluctuate around zero with absolute values below ∼0.01, indicating the high accuracy of the parameterization. geometric consider… view at source ↗
read the original abstract

The accuracy of particle counting in highly segmented detectors is limited by the corner-clipping effect, in which a single ionizing particle generates signals in adjacent detection elements. This phenomenon introduces a direction-dependent overcounting bias that distorts reconstructed observables and is commonly corrected using Monte-Carlo simulations, thereby inheriting modeling uncertainties. We present a fully data-driven method to directly measure the single-particle corner-clipping probability, exploiting the nanosecond timing resolution of modern detectors to statistically distinguish genuine corner-clipping events from random coincidences, with non-neighboring detection elements serving as an intrinsic control sample. The technique is validated using detailed simulations of the Underground Muon Detector of the Pierre Auger Observatory, reproducing the true angular dependence of the corner-clipping probability with absolute deviations below 0.01. To parameterize the results, we introduce a compact analytical model incorporating detector geometry, minimum detectable path length, and orientation-independent contributions. The proposed methodology and parameterization enable the direct incorporation of data-driven corner-clipping corrections into reconstruction algorithms, mitigating the overcounting bias and ultimately yielding a more accurate determination of the muonic component of extensive air showers. These developments are broadly applicable to any segmented detector with sufficient timing resolution, making them relevant to a wide range of experiments in high-energy and astroparticle physics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents a data-driven method to measure single-particle corner-clipping probabilities in segmented detectors. It exploits nanosecond timing resolution to statistically separate genuine corner-clipping events from random coincidences, using signals in non-neighboring elements as an intrinsic control sample. The technique is validated in detailed Monte Carlo simulations of the Pierre Auger Underground Muon Detector, reproducing the true angular dependence with absolute deviations below 0.01. An analytical parameterization incorporating detector geometry, minimum path length, and an orientation-independent term is introduced to facilitate incorporation into reconstruction algorithms for extensive air showers.

Significance. If the method can be shown to work on real data, it would enable direct, simulation-independent corrections for overcounting bias in highly segmented detectors, improving accuracy in muonic component measurements of air showers. The timing-based statistical separation is a clever approach with potential applicability across other high-energy physics and astroparticle experiments that have sufficient timing resolution.

major comments (2)
  1. [Abstract and validation section] Abstract and validation section: The central claim that the method reproduces the true angular dependence with absolute deviations below 0.01 is load-bearing for the headline result, yet the manuscript provides no details on event selection, background subtraction procedure, or how statistical uncertainties are propagated in the simulation comparison. This absence prevents assessment of whether the reported agreement could be affected by analysis choices.
  2. [Method and control-sample description] Method and control-sample description: The assumption that non-neighboring detection elements furnish a valid control sample for random coincidences, and that timing resolution suffices to separate genuine corner-clipping events, is only verified inside the Monte Carlo where the modeled physics matches the simulation exactly. Any unmodeled real-detector effects (position-dependent efficiency, correlated noise, or timing jitter) would invalidate the subtraction without being detected by the reported test.
minor comments (2)
  1. [Analytical model section] Analytical model section: Clarify the status of the orientation-independent contribution—whether it is extracted directly from data or introduced as a free parameter—as this directly affects the strength of the 'fully data-driven' claim.
  2. [Method description] The manuscript would benefit from a brief statement on the minimum timing resolution required for the statistical separation to remain effective.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive comments, which highlight important aspects of clarity and scope. We address each major comment below and will revise the manuscript to strengthen the presentation while remaining within the scope of a simulation-based validation study.

read point-by-point responses

  1. Referee: [Abstract and validation section] Abstract and validation section: The central claim that the method reproduces the true angular dependence with absolute deviations below 0.01 is load-bearing for the headline result, yet the manuscript provides no details on event selection, background subtraction procedure, or how statistical uncertainties are propagated in the simulation comparison. This absence prevents assessment of whether the reported agreement could be affected by analysis choices.

    Authors: We agree that these procedural details are necessary for a complete evaluation. The original manuscript focused on the overall method and results but omitted explicit descriptions of event selection, the precise background subtraction using the non-neighboring control sample, and uncertainty propagation. In the revised manuscript we will add a dedicated subsection in the validation section covering these elements, including how the timing-based separation is implemented and how statistical errors are calculated for the deviation metric. revision: yes

  2. Referee: [Method and control-sample description] Method and control-sample description: The assumption that non-neighboring detection elements furnish a valid control sample for random coincidences, and that timing resolution suffices to separate genuine corner-clipping events, is only verified inside the Monte Carlo where the modeled physics matches the simulation exactly. Any unmodeled real-detector effects (position-dependent efficiency, correlated noise, or timing jitter) would invalidate the subtraction without being detected by the reported test.

    Authors: The referee correctly identifies that the validation is performed entirely within the Monte Carlo framework, where the detector model is self-consistent by construction. The method itself is formulated to be data-driven and relies on observable timing and spatial correlations that are intrinsic to the detector readout. We will revise the text to explicitly state the assumptions underlying the control-sample approach and to discuss how unmodeled effects could be diagnosed or mitigated when the method is applied to real data. A quantitative assessment of all possible real-detector systematics, however, requires experimental data that are not part of the present study. revision: partial

standing simulated objections not resolved
  • Demonstration that the method functions on actual experimental data, as the current work is restricted to Monte Carlo validation of the Pierre Auger Underground Muon Detector.

Circularity Check

0 steps flagged

No circularity: data-driven measurement validated externally against simulation truth; analytical model is post-hoc parameterization.

full rationale

The paper's core claim is a data-driven extraction of corner-clipping probability using timing and non-neighboring control samples, validated by direct comparison to known truth in Monte Carlo (deviations <0.01). The subsequent analytical model is introduced only to parameterize those measured results and incorporates geometry and path-length terms as inputs, not as a self-referential loop that forces the reported angular dependence. No step reduces a prediction to a fitted parameter by construction, no self-citation chain is load-bearing for the central result, and the derivation remains self-contained against the external simulation benchmark. This is the expected non-finding for a methods paper whose primary output is an empirical extraction rather than a closed-form derivation.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that timing resolution permits statistical isolation of corner-clipping and that non-neighboring segments form an unbiased control; the analytical model introduces at least one free parameter (orientation-independent contribution) whose value is not derived from first principles.

free parameters (1)
  • orientation-independent contribution
    Term included in the compact analytical model to parameterize results beyond geometry and minimum path length.
axioms (1)
  • domain assumption Non-neighboring detection elements provide an intrinsic control sample for random coincidences
    Invoked to separate genuine corner-clipping from accidental overlaps via timing.

pith-pipeline@v0.9.1-grok · 5775 in / 1359 out tokens · 22690 ms · 2026-06-27T11:28:51.727902+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

31 extracted references · 30 canonical work pages

  1. [1]

    Chiba et al., Akeno Giant Air Shower Array (AGASA) cov- ering 100 km2 area

    N. Chiba et al., Akeno Giant Air Shower Array (AGASA) cov- ering 100 km2 area. Nucl. Instrum. Methods A311, 338 (1992). https://doi.org/10.1016/0168-9002(92)90882-5

    work page doi:10.1016/0168-9002(92)90882-5 1992

  2. [2]

    A.Borioneetal.,Alargeairshowerarraytosearchforastrophysical sources emitting gamma-rays with energies>10 14 eV. Nucl. Instrum.MethodsA346,329(1994).https://doi.org/10.1016/0168- 9002(94)90722-6

    work page doi:10.1016/0168- 1994

  3. [3]

    Hayashida et al., Muons ( ≥ 1 GeV) in large extensive air showers of energies between1016.5 eV and 1019.5 eV ob- served at Akeno

    N. Hayashida et al., Muons ( ≥ 1 GeV) in large extensive air showers of energies between1016.5 eV and 1019.5 eV ob- served at Akeno. J. Phys. G: Nucl. Part. Phys.21, 1101 (1995). https://doi.org/10.1088/0954-3899/21/8/008

    work page doi:10.1088/0954-3899/21/8/008 1995

  4. [4]

    Glasmacher et al., The cosmic ray composition be- tween 1014 and 1016 eV

    M. Glasmacher et al., The cosmic ray composition be- tween 1014 and 1016 eV. Astropart. Phys.12, 1 (1999). https://doi.org/10.1016/S0927-6505(99)00076-6

    work page doi:10.1016/s0927-6505(99)00076-6 1999

  5. [5]

    JINST11, P02012 (2016)

    Pierre Auger Collaboration, Prototype muon detectors for the AMIGA component of the Pierre Auger Observatory. JINST11, P02012 (2016). https://doi.org/10.1088/1748-0221/11/02/P02012

    work page doi:10.1088/1748-0221/11/02/p02012 2016

  6. [6]

    A. D. Supanitsky et al., Underground muon counters as a tool for composition analyses. Astropart. Phys.29, 461 (2008). https://doi.org/10.1016/j.astropartphys.2008.05.003

    work page doi:10.1016/j.astropartphys.2008.05.003 2008

  7. [7]

    Ravignani, A

    D. Ravignani, A. D. Supanitsky, A new method for re- constructing the muon lateral distribution with an array of segmented counters. Astropart. Phys.65, 1 (2015). https://doi.org/10.1016/j.astropartphys.2014.11.007

    work page doi:10.1016/j.astropartphys.2014.11.007 2015

  8. [8]

    A. D. Supanitsky, Estimation of the number of muons with muon counters. Astropart. Phys.127, 102535 (2021). https://doi.org/10.1016/j.astropartphys.2020.102535

    work page doi:10.1016/j.astropartphys.2020.102535 2021

  9. [9]

    Gesualdi, A

    F. Gesualdi, A. D. Supanitsky, Estimation of the number of counts onaparticlecounterdetectorwithfulltimeresolution.Eur.Phys.J. C82, 925 (2022). https://doi.org/10.1140/epjc/s10052-022-10895- 9

    work page doi:10.1140/epjc/s10052-022-10895- 2022

  10. [10]

    V. V. K. Covilakam, A. D. Supanitsky, D. Ravignani, Recon- struction of air shower muon lateral distribution functions using integrator and binary modes of underground muon detectors. Eur. Phys. J. C83, 1157 (2023). https://doi.org/10.1140/epjc/s10052- 023-12344-7

    work page doi:10.1140/epjc/s10052- 2023

  11. [11]

    M. Scornavacche et al., Effect of the knock-on electrons in the calorimetric mode of an underground muon detector, in Proceedings of 7th International Symposium on Ultra High Energy Cosmic Rays. PoS(UHECR2024)484, 116 (2025). https://doi.org/10.22323/1.484.0116

    work page doi:10.22323/1.484.0116 2025

  12. [12]

    Pierre Auger Collaboration, Direct measurement of the muonic content of extensive air showers between2×10 17 and 2×10 18 eV at the Pierre Auger Observatory. Eur. Phys. J. C80, 751 (2020). https://doi.org/10.1140/epjc/s10052-020-8055-y

    work page doi:10.1140/epjc/s10052-020-8055-y 2020

  13. [13]

    J. M. Figueira for the Pierre Auger Collaboration, An improved reconstruction method for the AMIGA detectors, inProceedings of 35th International Cosmic Ray Conference. PoS(ICRC2017) 301, 396 (2017). https://doi.org/10.22323/1.301.0396

    work page doi:10.22323/1.301.0396 2017

  14. [14]

    M. Scornavacche for the Pierre Auger Collaboration, Muon count- ing with the underground muon detector of the Pierre Auger Observatory, inProceedings of 6th International Symposium on Ultra High Energy Cosmic Rays.EPJWebConf.283,06012(2023). https://doi.org/10.1051/epjconf/202328306012

    work page doi:10.1051/epjconf/202328306012 2023

  15. [15]

    https://doi.org/10.22323/1.484.0077

    J.deJesúsforthePierreAugerCollaboration,Improvedcalibration methods and reconstruction of the Underground Muon Detector of the Pierre Auger Observatory, inProceedings of 7th International Symposium on Ultra High Energy Cosmic Rays.PoS(UHECR2024) 484, 077 (2025). https://doi.org/10.22323/1.484.0077

    work page doi:10.22323/1.484.0077 2025

  16. [16]

    Pierre Auger Collaboration, The Pierre Auger cosmic ray Observatory. Nucl. Instrum. Methods A798, 172 (2015). https://doi.org/10.1016/j.nima.2015.06.058

    work page doi:10.1016/j.nima.2015.06.058 2015

  17. [17]

    Pierre Auger Collaboration, Constraining models for the origin of ultra-high-energy cosmic rays with a novel combined analysis of arrival directions, spectrum, and composition data measured at the Pierre Auger Observatory. J. Cosmol. Astropart. Phys.01, 022 (2024). https://doi.org/10.1088/1475-7516/2024/01/022

    work page doi:10.1088/1475-7516/2024/01/022 2024

  18. [18]

    PierreAugerCollaboration,Searchforadiffusefluxofphotonswith energiesabovetensofPeVatthePierreAugerObservatory.J.Cos- mol.Astropart.Phys.05,061(2025).https://doi.org/10.1088/1475- 7516/2025/05/061

    work page doi:10.1088/1475- 2025

  19. [19]

    Pierre Auger Collaboration, The Pierre Auger Obser- vatory open data. Eur. Phys. J. C85, 70 (2025). https://doi.org/10.1140/epjc/s10052-024-13560-5

    work page doi:10.1140/epjc/s10052-024-13560-5 2025

  20. [20]

    https://doi.org/10.1088/1748-0221/16/04/P04003

    Pierre Auger Collaboration, Calibration of the underground muon detectorofthePierreAugerObservatory.JINST16,P04003(2021). https://doi.org/10.1088/1748-0221/16/04/P04003

    work page doi:10.1088/1748-0221/16/04/p04003 2021

  21. [21]

    M. A. Scornavacche for the Pierre Auger Collaboration, Muon signal charge in the Underground Muon Detec- tor of AugerPrime, inProceedings of 39th International Cosmic Ray Conference. PoS(ICRC2025)501, 389 (2025). https://doi.org/10.22323/1.501.0389 12 J. de Jesús et al.: A data-driven method for measuring corner-clipping probabilities in segmented particl...

    work page doi:10.22323/1.501.0389 2025

  22. [22]

    JINST15, P10021 (2020)

    PierreAugerCollaboration,Reconstructionofeventsrecordedwith the surface detector of the Pierre Auger Observatory. JINST15, P10021 (2020). https://doi.org/10.1088/1748-0221/15/10/P10021

    work page doi:10.1088/1748-0221/15/10/p10021 2020

  23. [23]

    Pierre Auger Collaboration, The energy spectrum of cosmic rays beyondtheturn-downaround 1017 eVasmeasuredwiththesurface detector of the Pierre Auger Observatory. Eur. Phys. J. C81, 966 (2021). https://doi.org/10.1140/epjc/s10052-021-09700-w

    work page doi:10.1140/epjc/s10052-021-09700-w 2021

  24. [24]

    JINST20, P08002 (2025)

    Pierre Auger Collaboration, The scintillator surface detector of the Pierre Auger Observatory. JINST20, P08002 (2025). https://doi.org/10.1088/1748-0221/20/08/P08002

    work page doi:10.1088/1748-0221/20/08/p08002 2025

  25. [25]

    Heck et al., CORSIKA: A Monte Carlo code to simulate extensiveairshowers.Tech.Rep.FZKA6019,Forschungszentrum Karlsruhe (1998)

    D. Heck et al., CORSIKA: A Monte Carlo code to simulate extensiveairshowers.Tech.Rep.FZKA6019,Forschungszentrum Karlsruhe (1998). https://www.iap.kit.edu/corsika/70.php

    1998

  26. [26]

    EPOS LHC: Test of collective hadronization with data measured at the CERN Large Hadron Collider.Phys

    T. Pierog et al., EPOS LHC: Test of collective hadronization with data measured at the CERN Large Hadron Collider. Phys. Rev. C 92, 034906 (2015). https://doi.org/10.1103/PhysRevC.92.034906

    work page doi:10.1103/physrevc.92.034906 2015

  27. [27]

    Agostinelli et al., Geant4 – a simulation toolkit

    S. Agostinelli et al., Geant4 – a simulation toolkit. Nucl. In- strum. Methods A506, 250 (2003). https://doi.org/10.1016/S0168- 9002(03)01368-8

    work page doi:10.1016/s0168- 2003

  28. [28]

    M Botti, F

    A. M Botti, F. Sánchez, M. Roth, A. Etchegoyen, Development and validation of the signal simulation for the underground muon detectorofthePierreAugerObservatory.JINST16,P07059(2021). https://doi.org/10.1088/1748-0221/16/07/P07059

    work page doi:10.1088/1748-0221/16/07/p07059 2021

  29. [29]

    Argiro et al., The Offline software framework of the Pierre Auger Observatory

    S. Argiro et al., The Offline software framework of the Pierre Auger Observatory. Nucl. Instrum. Methods A580, 1485 (2007). https://doi.org/10.1016/j.nima.2007.07.010

    work page doi:10.1016/j.nima.2007.07.010 2007

  30. [30]

    Efron, Bootstrap methods: Another look at the jackknife, The Annals of Statistics 7 (1) (1979) 1–26.doi:10.1214/aos/1176344552

    B. Efron, Bootstrap methods: Another look at the jackknife. Ann. Statist.7, 1 (1979). https://doi.org/10.1214/aos/1176344552

    work page doi:10.1214/aos/1176344552 1979

  31. [31]

    Kulesa et al., Sampling distributions and the bootstrap

    A. Kulesa et al., Sampling distributions and the bootstrap. Nat. Methods12, 477 (2015). https://doi.org/10.1038/nmeth.3414

    work page doi:10.1038/nmeth.3414 2015