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This paper shows that the heavy cosmic-ray knee near 10^17 eV and the hardening of the light component above it persist when KASCADE-Grande data are reconstructed with four post-LHC hadronic interaction models, including the first test of E

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Updated KASCADE-Grande cosmic ray energy spectra, obtained with QGSJET-II-04, EPOS-LHC, SIBYLL 2.3d and the first test of EPOS-LHC-R, confirm a heavy knee near 100 PeV and a light-component flattening.

T0 review reviewed 2026-08-05 challenge →

load-bearing objection Solid KASCADE-Grande update: the three-model unfolded spectra confirm the heavy knee and light hardening; the EPOS-LHC-R leg is suggestive but preliminary because it compares raw to unfolded. the 1 major comments →

arxiv 2508.21646 v1 pith:XL3ET4JV submitted 2025-08-29 astro-ph.HE

Cosmic ray energy spectra derived from KASCADE-Grande data using post-LHC hadronic interaction models

D. Kang , J.C. Arteaga-Vel\'azquez , M. Bertaina , A. Chiavassa , A.L. Colmenero-C\'esar , K. Daumiller , V. de Souza , R. Engel
show 18 more authors
A. Gherghel-Lascu C. Grupen A. Haungs J.R. H\"orandel T. Huege K.-H. Kampert K. Link H.J. Mathes S. Ostapchenko T. Pierog D. Rivera-Rangel M. Roth H. Schieler F.G. Schr\"oder O. Sima A. Weindl J. Wochele J. Zabierowski
This is my paper
classification astro-ph.HE
keywords cosmic ray energy spectrumKASCADE-Grandehadronic interaction modelsEPOS-LHC-Rheavy kneelight hardeningmass compositionair showers
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 reading

The paper tries to establish that two key features of the cosmic-ray energy spectrum—a knee-like break in the heavy component around 10^17 eV and a hardening of the light component just above that energy—do not depend on which modern hadronic interaction model is used to interpret the data. The same features appear with QGSJET-II-04, EPOS-LHC, SIBYLL 2.3d, and, for the first time with this data set, the newly released EPOS-LHC-R model. If true, these spectral features are real astrophysical boundaries rather than artifacts of a particular simulation model, and they can serve as fixed targets for theories of the transition from galactic to extragalactic cosmic rays. The paper also provides updated spectra with explicit shower-to-shower fluctuation corrections and an early test of EPOS-LHC-R against a ground-based air-shower array.

Core claim

The paper asserts that KASCADE-Grande's shower-size measurements, analyzed with the y_CIC mass-separation technique and per-model energy calibrations, yield a heavy-component spectrum with a knee-like break at about 10^17 eV and a light-component spectrum that hardens above that same energy, in all three established post-LHC models. It then applies the same procedure to EPOS-LHC-R, a new model with deeper shower maxima and altered muon production, and finds that EPOS-LHC-R reproduces the same spectral features: a heavy knee at log10(Ek/GeV) around 7.79 and a light-component hardening, with the all-particle spectrum differing only mildly from the other models. The paper concludes that the hea

What carries the argument

The analysis is carried by the y_CIC parameter, defined as log10(N_mu)_CIC_CF / log10(N_ch)_CIC, the ratio of the attenuation-corrected muon number to the charged-particle number, which sorts each event into an electron-rich light group (proton, helium, CNO) or an electron-poor heavy group (silicon, iron). For each hadronic model, energy calibration is a linear fit in log-log space, log10(E_true/GeV) = a * log10(N_ch) + b, with separate coefficients for the two mass groups; for EPOS-LHC-R the mass-separation threshold is 0.8496. A response matrix built from Monte Carlo showers is unfolded with an iterative Bayesian algorithm to correct bin-to-bin migrations from shower-to-shower fluctuations

Load-bearing premise

The reconstruction assumes that the Monte Carlo showers produced by each hadronic model—especially the new EPOS-LHC-R—give the correct relation between measured charged-particle and muon numbers and the true primary energy; if a model gets the muon content wrong, the inferred knee position and light-hardening energy shift.

What would settle it

Compare the observed y_CIC = log10(N_mu)_CIC_CF / log10(N_ch)_CIC distribution for events near log10(E/GeV) = 7.8 with the EPOS-LHC-R-simulated distribution used to set the 0.8496 threshold: if the measured fraction of electron-rich events in that energy bin differs from the model expectation by more than the quoted roughly 13% systematic uncertainty, the reconstructed heavy-knee position and light-hardening energy would shift, weakening the central claim.

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

If this is right

  • The heavy-component break is stable across models at log10(Ek/GeV) about 7.77 to 7.79 with a spectral-index change of about 0.5, so any model of the galactic-to-extragalactic transition must produce a steepening in the silicon-plus-iron flux at that energy.
  • The light-component hardening above 10^17 eV is also model-independent, strengthening the interpretation that an extragalactic contribution starts to dominate below 10^17 eV.
  • EPOS-LHC-R, with its deeper shower maximum but smaller relative muon content, produces spectra consistent with the other models, making it a viable model for future air-shower analyses of KASCADE-Grande-type data.
  • The model-averaged KASCADE-Grande all-particle flux is within about 10% of other experiments and statistically consistent with the Pierre Auger Observatory near 10^18 eV, allowing cross-experiment fits to use these spectra.
  • The unfolded spectra for QGSJET-II-04, EPOS-LHC, and SIBYLL 2.3d, together with the raw EPOS-LHC-R spectrum, give a concrete set of break positions and slopes for testing upcoming hadronic interaction models.

Where Pith is reading between the lines

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

  • The EPOS-LHC-R comparison in the paper is not fully symmetric because its spectrum has not yet been unfolded while the other three have; applying the same response-matrix unfolding to EPOS-LHC-R is the direct next step and would likely shift its light-component flux slightly upward.
  • Because the EPOS-LHC-R energy calibration and the 0.8496 mass-separation threshold are themselves derived from EPOS-LHC-R simulations, the 'test' of the model is partly self-referential; a stronger test would measure the same spectral features with an energy estimator independent of hadronic models, such as radio or Cherenkov emission.
  • If both the heavy knee and the light hardening are composition-driven, their near-coincidence around 10^17 eV suggests a single rigidity-dependent transition mechanism, which could be tested by checking whether the break energy scales with nuclear charge across the light and heavy groups.
  • EPOS-LHC-R's relative muon content now sits closer to QGSJET-II-04 and SIBYLL 2.3d than to the older EPOS-LHC, which may point toward a partial resolution of earlier muon-deficit discrepancies in air-shower simulations.
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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

1 major / 5 minor

Summary. This ICRC contribution uses roughly 17 million KASCADE-Grande events to reconstruct the energy spectra of heavy (Si+Fe) and light (H+He+CNO) primary cosmic rays with three post-LHC hadronic interaction models: QGSJET-II-04, EPOS-LHC, and SIBYLL 2.3d. The reconstruction uses the y_CIC electron/muon correlation for mass separation and a Bayesian unfolding procedure to correct shower-to-shower fluctuations. The authors report a knee-like break in the heavy component near 10^17 eV and a hardening of the light component above about 10^17 eV for all three models, with systematic uncertainties quoted as about 13% (light) and 10% (heavy) at 10^17 eV. A first comparison with the newly released EPOS-LHC-R model is also presented, including new y_CIC separation threshold and energy calibration coefficients, but the EPOS-LHC-R spectrum is explicitly stated to be raw (not unfolded). All-particle spectra are compared with ESA-TOP, IceTop, Pierre Auger, and Telescope Array.

Significance. If the three-model result holds, it provides a useful multi-model confirmation of the heavy knee and the light-component hardening around 10^17 eV, and the quantified systematics and public KCDC data release are strengths. The EPOS-LHC-R section is a valuable preliminary test but is not yet on equal footing with the other models because the comparison uses a raw spectrum. The central three-model spectral features are not endangered by this issue; only the strength of the EPOS-LHC-R confirmation claim needs revision.

major comments (1)
  1. [Sec. 3, Fig. 5, Table 1, Conclusion] The statement that EPOS-LHC-R 'shows spectral behavior consistent with other models and confirms previous findings' is not supported by an apples-to-apples comparison. Figure 5 and Table 1 mix unfolded spectra (QGSJET-II-04, EPOS-LHC, SIBYLL 2.3d) with the raw EPOS-LHC-R spectrum, as acknowledged in the text and Table 1 note. The <10% unfolding estimate does not by itself justify that fitted slopes and the break position are unaffected, especially because the paper notes the light flux 'probably will slightly increase' after unfolding. Either unfold the EPOS-LHC-R spectrum before quantitative comparison, or restrict the conclusion to a preliminary raw-spectrum comparison and label this clearly in the figure and conclusion.
minor comments (5)
  1. [Sec. 2] Typo: 'which is is of the order' should be 'which is of the order'.
  2. [Sec. 2, Sec. 3] Energy notation is inconsistent: the text switches between '10^17 eV', '10 17 eV', and '1017 eV'. Please use a uniform superscript notation.
  3. [Fig. 5] The figure caption should state explicitly that the EPOS-LHC-R spectrum is raw, as the text does. This would prevent readers from misinterpreting the comparison.
  4. [Sec. 3] Because the y_CIC separation threshold (0.8496) and the energy calibration coefficients (a=0.897, b=1.705 heavy; a=0.953, b=1.109 light) are fitted to EPOS-LHC-R simulations, the subsequent comparison is a consistency check within a model-dependent reconstruction rather than a fully independent test. A sentence acknowledging this would be appropriate.
  5. [Sec. 2] The abbreviation y_CIC is used without definition. Please define 'CIC' at first use (presumably 'charged-particle / muon correlation' or similar).

Circularity Check

1 steps flagged

EPOS-LHC-R 'confirmation' is partly self-referential because the same model provides the energy calibration and mass-separation threshold; the main heavy-knee/light-hardening claim retains independent support from three other models.

specific steps
  1. fitted input called prediction [Section 3 (Figure 3) and Section 4 (Conclusion)]
    "Full Monte-Carlo simulations, including the detector response of KASCADE-Grande, have been performed, using EPOS-LHC-R. ... The selection criteria separating heavy and light primaries is based on a fit to the average of silicon and CNO, yielding a separation value of 0.8496 ... the energy calibration functions, described by: log10(E_true/GeV) = a· log10(N_ch)+ b, with coefficients a = 0.897, b = 1.705 for heavy primaries, and a = 0.953, b = 1.109 for light primaries. ... The EPOS-LHC-R model, tested with KASCADE-Grande data for the first time, shows spectral behavior consistent with other mode"

    The EPOS-LHC-R spectrum is constructed using an energy calibration and a y_CIC heavy/light separation threshold that are themselves fitted to EPOS-LHC-R Monte Carlo simulations. Presenting the resulting spectrum as a 'test' or 'confirmation' of EPOS-LHC-R is therefore partly self-referential: the model's own predictions define the mapping from the measured N_ch and N_mu to E and to mass group, so the model cannot be independently validated by that spectrum. The heavy-knee and light-hardening features are not directly fitted parameters and do appear under the three other model calibrations, so the central multi-model claim retains independent content; only the EPOS-LHC-R-specific confirmation leg is partially circular.

full rationale

The main spectral claim—heavy knee around 10^17 eV and light hardening above that energy—is not circular in a formal sense: the energy calibrations are smooth linear transformations of N_ch, and a linear map cannot create a spectral break from a smooth N_ch distribution, so the features are data-driven. The agreement across QGSJET-II-04, EPOS-LHC, and SIBYLL 2.3d, plus the comparison to external experiments in Fig. 2, provide independent grounding. However, the paper's treatment of EPOS-LHC-R has a genuine self-referential component: the same model is used to set the energy scale and mass-separation boundary that produce the spectrum said to confirm it. The paper also explicitly flags an apples-to-oranges limitation in Fig. 5 and Table 1: 'The first three models show unfolded spectra, whereas the EPOS-LHC-R spectrum is still raw,' and the Table 1 note says the EPOS-LHC-R fit is based on the raw spectrum. The paper's estimate that unfolding changes fluxes by less than 10% is not demonstrated to leave break positions and slopes unchanged, and for the light component the paper says the flux 'probably will slightly increase' after unfolding. These issues weaken the EPOS-LHC-R confirmation but do not invalidate the three-model persistence claim, so the overall circularity score is moderate.

Axiom & Free-Parameter Ledger

3 free parameters · 5 axioms · 0 invented entities

No new particles, forces, or entities are introduced. The key load-bearing inputs are model-dependent calibration parameters and the associated hadronic interaction models, all of which are external or fitted to Monte Carlo simulations rather than derived from first principles.

free parameters (3)
  • Energy calibration slope and intercept (a, b) for each model and mass group = EPOS-LHC-R: heavy a=0.897, b=1.705; light a=0.953, b=1.109; values for other models in Ref. [13]
    Linear fits to CORSIKA simulations of log10(E_true) versus log10(N_ch) set the absolute energy scale and directly determine the reconstructed spectra.
  • y_CIC mass-separation threshold = 0.8496 for EPOS-LHC-R; model-dependent values for other models
    Chosen by fitting the average of silicon and CNO in Monte Carlo; controls the heavy/light decomposition and therefore the individual component fluxes.
  • Bayesian unfolding iteration or regularization choice
    The Bayesian unfolding algorithm requires a stopping rule or prior that affects the corrected flux. The paper reports the effect is less than 10% but does not state the exact settings.
axioms (5)
  • domain assumption CORSIKA air-shower simulations with FLUKA below 200 GeV and the chosen high-energy hadronic models accurately describe shower development and detector response.
    Invoked in Section 2 where simulated showers are generated for proton, helium, carbon, silicon, and iron primaries over 10^14 to 10^18 eV.
  • domain assumption The five simulated primary species and the two-group heavy/light classification span the real cosmic ray composition.
    The decomposition into electron-poor (Si+Fe) and electron-rich (p+He+CNO) groups assumes that this grouping captures the relevant mass-dependent behavior of the shower size and muon content.
  • domain assumption Shower-to-shower fluctuations are correctly modeled by the response matrix, and the Bayesian unfolding solution is physically meaningful.
    Section 2 constructs response matrices from Monte Carlo and solves the system iteratively; the correction is stated to be less than 10% per energy bin.
  • domain assumption The simulated energy spectrum can be reweighted from the generated spectral index of -2 to -3 and still provides a valid prior for unfolding.
    Mentioned in Section 2 as part of the simulation setup; the reweighting changes the prior distribution used to build the response matrix.
  • domain assumption A broken power-law functional form adequately describes the heavy primary spectrum for extracting the break position and spectral indices.
    Used in Section 3 and Table 1 to quantify the heavy knee; a different functional form could alter the quoted break parameters.

reviewed 2026-08-05 · how reviews work

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Cite this review

Pith. "Pith review of Cosmic ray energy spectra derived from KASCADE-Grande data using post-LHC hadronic interaction models." pith.science (2026). https://pith.science/paper/XL3ET4JV

@misc{pith2026250821646,
  author       = {Pith},
  title        = {Pith review of: Cosmic ray energy spectra derived from KASCADE-Grande data using post-LHC hadronic interaction models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XL3ET4JV}},
  note         = {Machine review of arXiv:2508.21646}
}
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read the original abstract

KASCADE-Grande was dedicated to measuring the energy spectrum and mass composition of cosmic rays in the energy range of 10 PeV to 1 EeV. We observed a knee-like structure in the heavy mass component at around 100 PeV and an ankle-like structure in the light component. In this contribution, we present updated energy spectra based on shower size measurements, using the post-LHC hadronic models QGSJet-II-04, EPOS-LHC, and SIBYLL 2.3d, including accounting for shower-to-shower fluctuations. In addition, the newly released EPOS-LHC-R model is tested for the first time with KASCADE-Grande. We will compare and discuss the results obtained using the different hadronic interaction models.

Figures

Figures reproduced from arXiv: 2508.21646 by A. Chiavassa, A. Gherghel-Lascu, A. Haungs, A.L. Colmenero-C\'esar, A. Weindl, C. Grupen, D. Kang, D. Rivera-Rangel, F.G. Schr\"oder, H.J. Mathes, H. Schieler, J.C. Arteaga-Vel\'azquez, J.R. H\"orandel, J. Wochele, J. Zabierowski, K. Daumiller, K.-H. Kampert, K. Link, M. Bertaina, M. Roth, O. Sima, R. Engel, S. Ostapchenko, T. Huege, T. Pierog, V. de Souza.

Figure 1
Figure 1. Figure 1: Reconstructed energy spectra for heavy (Si+Fe) and light (p+He+CNO) primary mass groups based on QGSJET-II-04 (left), EPOS-LHC (middle), and SIBYLL 2.3d (right), with shower-to-shower fluctuation corrections applied. The all-particle is the sum of the light and heavy mass compositions. Only statistical uncertainties are shown, for a discussion on systematics see Ref. [13]. ticles and the number of muons, r… view at source ↗
Figure 2
Figure 2. Figure 2: compares the resulting all-particle energy spectra derived from different post-LHC interaction models with results from other experiments: ESA-TOP, IceCube/IceTop, Pierre Auger Observatory (PAO) and Telescope Array (TA). The all-particle energy spectra from KASCADE￾Grande are obtained by summing the individual heavy and light component spectra. As shown in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Left: The 𝑦𝐶 𝐼𝐶 parameter as a function of the primary energy for EPOS-LHC-R. The dashed line indicates the selection criteria separating heavy and light mass groups. Right: Primary energy as a function of the number of charged particles for the EPOS-LHC-R model. Linear fits in log-log scale are shown for heavy (red) and light (blue) primary groups. present slightly lower heavy fluxes, mainly due to differ… view at source ↗
Figure 4
Figure 4. Figure 4: Left: Reconstructed energy spectra for all-particle (black), heavy (red), and light (blue) primaries, based on the EPOS-LHC-R model. The all-particle spectrum is obtained by summing the heavy and light components. Shower fluctuations have not yet been corrected for EPOS-LHC-R. Right: Comparison of EPOS-LHC-R (solid markers) with the previous EPOS-LHC model (unfolded) (open markers). 6 [PITH_FULL_IMAGE:fig… view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of the reconstructed energy spectra of heavy (left) and light (right) primaries from EPOS-LHC-R with four different interaction models: QGSJET-II-04, EPOS-LHC, SIBYLL 2.3d, and EPOS￾LHC-R. The heavy mass group includes silicon and iron, while the light group contains proton, helium and carbon. Dashed lines represent broken power-law fits. slope change. electron-poor log10 (𝐸𝑘/GeV) 𝛾1 𝛾2 Δ𝛾 𝜒2 /n… view at source ↗

discussion (0)

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Reference graph

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This paper was first reviewed by deepseek-v4-flash on August 5, 2026.