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arxiv: 2606.05111 · v1 · pith:L2AZ7BNPnew · submitted 2026-06-03 · ✦ hep-ex

Software compensation of hadronic showers in the longitudinally segmented CRILIN Cherenkov crystal calorimeter

V. Ciccarella , E. Di Meco , R. Gargiulo , L. Sestini , I. Sarra This is my paper

Pith reviewed 2026-06-28 02:54 UTC · model grok-4.3

classification ✦ hep-ex
keywords software compensationhadronic showerscrystal calorimetergraph neural networkCRILINenergy resolutionPbF2Higgs factory
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The pith

A graph neural network corrects hadronic shower energy in the CRILIN PbF2 calorimeter to reduce its contribution to combined resolution to 1 GeV/E ⊕ 12%/√E ⊕ 2.5%.

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

Future electron-positron Higgs factories require precise jet energy measurements, yet homogeneous crystal calorimeters suffer from non-compensating response that degrades hadronic reconstruction. The paper investigates software compensation for the longitudinally segmented CRILIN calorimeter by correlating shower-shape observables with the invisible energy fraction in Geant4 pion simulations. Simple corrections from transverse RMS and longitudinal center-of-gravity already improve results, while a ParticleNet graph neural network using full 3D topology delivers substantially better performance. Under realistic downstream hadronic calorimeter assumptions, this brings the effective CRILIN term in the total resolution to approximately 1 GeV/E ⊕ 12%/√E[GeV] ⊕ 2.5%, showing that granular crystal designs can recover much of the lost information through software methods.

Core claim

Using Geant4 simulations of pion showers, shower-shape observables are strongly correlated with the fraction of deposited energy reconstructed in a CRILIN module. Simple event-by-event corrections based on the shower transverse RMS and longitudinal center-of-gravity already yield a substantial improvement in hadronic energy reconstruction. A ParticleNet Graph Neural Network exploiting the full three-dimensional shower topology achieves significantly improved performance with respect to simple energy sum reconstruction. Under realistic assumptions for the downstream hadronic calorimeter, the GNN-based reconstruction reduces the effective CRILIN contribution to the combined calorimetric resolu

What carries the argument

The ParticleNet Graph Neural Network that takes the full three-dimensional shower topology as input to predict event-by-event corrections for the invisible energy fraction in non-compensating PbF2 crystals.

If this is right

  • Event-by-event corrections using shower transverse RMS and longitudinal center-of-gravity already produce substantial gains over raw energy sum.
  • The GNN method outperforms the simple corrections and maintains good performance across the studied range of HCAL resolutions.
  • Highly granular crystal calorimeters can recover a large fraction of information lost to their non-compensating response via software techniques.
  • Such compensation makes crystal-based ECAL designs viable options for precision jet measurements at future collider experiments.

Where Pith is reading between the lines

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

  • The same topology-driven correction approach could be tested on other non-compensating homogeneous calorimeters.
  • Direct comparison of the GNN output against real beam-test data would be required before deployment in an experiment.
  • Further gains might come from combining the GNN with additional observables or with downstream HCAL information in a joint reconstruction.

Load-bearing premise

Geant4 simulations of pion showers in PbF2 crystals faithfully reproduce the real shower development and visible-energy fraction that would be observed in a physical CRILIN module.

What would settle it

A beam-test measurement of pion energy resolution in a real CRILIN prototype, after applying the trained GNN correction, that yields a combined ECAL+HCAL resolution significantly worse than the simulated 12%/√E level.

Figures

Figures reproduced from arXiv: 2606.05111 by E. Di Meco, I. Sarra, L. Sestini, R. Gargiulo, V. Ciccarella.

Figure 1
Figure 1. Figure 1: Geant4 CRILIN module representation embedding all the final [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Top: distribution of the ratio between number of emitted Cherenkov [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Correlation between Ereco/Etrue and shower RMS for a simulated pion sample with uniform energies from 5 to 100 GeV, with a linear fit super￾imposed. smeared with a Gaussian fluctuation corresponding to a rela￾tive resolution of 25%/ √ E[GeV], yielding a variable E 25%/ √ E HCAL , mimicking the behaviour of a compensating or dual-readout HCAL with energy resolution dominated by the stochastic term and only … view at source ↗
Figure 3
Figure 3. Figure 3: Three event displays for simulated pion showers in the CRILIN [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Distribution of (Ecorr + E 25%/ √ E HCAL )/Ebeam for a combined CRILIN and HCAL system, with and without the RMS-based correction, for a simulated pion sample. The resolutions (σ) quoted in the plot is corresponding to the case with corrections applied. 20 30 40 50 60 70 80 90 100 [GeV] EBEAM 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 BEAM / E reco E σ Resolution with/without RMS-based correcti… view at source ↗
Figure 6
Figure 6. Figure 6: Energy resolution for a combined CRILIN and HCAL system, as a [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Correlation between reconstructed energy and longitudinal center-of [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Energy resolution for a simulated pion sample with respect to beam [PITH_FULL_IMAGE:figures/full_fig_p006_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Distributions of Ereco/Ebeam − 1 for two beam energy intervals with a simulated pion sample, i.e. 20-25 GeV and 75-80 GeV, fitted with a Double Crystal Ball function. The resolution (σ 68) corresponding to the central 68% quantile interval is evaluated. 20 30 40 50 60 70 80 90 100 [GeV] EBEAM 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 BEAM / E reco E σ No cuts, 25%/ E HCAL smearing, 0.2 p.e./Me… view at source ↗
Figure 10
Figure 10. Figure 10: Energy resolution as a function of beam energy, before and after [PITH_FULL_IMAGE:figures/full_fig_p007_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: Contribution of CRILIN after GNN reconstruction within the com [PITH_FULL_IMAGE:figures/full_fig_p008_12.png] view at source ↗
read the original abstract

Future electron-positron Higgs factories require excellent jet energy resolution to perform precision measurements of Higgs boson couplings to quarks and gluons. Although homogeneous crystal calorimeters provide remarkable electromagnetic energy resolution, their strongly non-compensating response makes hadronic energy reconstruction particularly challenging. In this work, software compensation techniques are investigated for CRILIN, a longitudinally segmented Cherenkov crystal electromagnetic calorimeter based on PbF$_2$ crystals. Using Geant4 simulations of pion showers, it is shown that shower-shape observables are strongly correlated with the fraction of deposited energy reconstructed in a CRILIN module. Simple event-by-event corrections based on the shower transverse RMS and longitudinal center-of-gravity already yield a substantial improvement in hadronic energy reconstruction. A ParticleNet Graph Neural Network exploiting the full three-dimensional shower topology achieves significantly improved performance with respect to simple energy sum reconstruction. Under realistic assumptions for the downstream hadronic calorimeter, the GNN-based reconstruction reduces the effective CRILIN contribution to the combined calorimetric resolution to approximately $(1 ~\mathrm{GeV}/E \, \oplus \, 12\%/\sqrt{E[\mathrm{GeV}]}\,\oplus\,2.5\%)$, therefore preserving an excellent combined ECAL+HCAL performance. The dependence of the result on the assumed HCAL resolution is also studied and found to be limited within the range considered. These results show that highly granular crystal calorimeters can recover a large fraction of the information lost because of their non-compensating response through software-based compensation techniques, achieving an excellent energy resolution on hadrons in a combined ECAL+HCAL system, making them promising options for future collider experiments.

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 / 1 minor

Summary. The paper investigates software compensation for hadronic showers in the longitudinally segmented CRILIN PbF2 Cherenkov crystal calorimeter using Geant4 simulations of pion showers. It shows that simple corrections based on transverse RMS and longitudinal center-of-gravity improve reconstruction, while a ParticleNet GNN exploiting 3D shower topology achieves better performance. Under assumed downstream HCAL parameters, the GNN reduces the effective CRILIN contribution to combined resolution to approximately (1 GeV/E ⊕ 12%/√E[GeV] ⊕ 2.5%), with limited dependence on the HCAL resolution assumption.

Significance. If the Geant4 modeling of PbF2 pion showers and visible-energy fractions holds, the work demonstrates that highly granular crystal calorimeters can recover substantial hadronic information via software compensation, preserving good combined ECAL+HCAL jet resolution for Higgs-factory physics. The GNN approach on full shower topology and the explicit study of HCAL dependence are positive elements; the simulation-only nature means the result is a proof-of-principle rather than a validated performance claim.

major comments (2)
  1. [Abstract] Abstract and simulation study: the quoted combined resolution (1 GeV/E ⊕ 12%/√E[GeV] ⊕ 2.5%) is obtained by training and evaluating the GNN exclusively on the same Geant4 pion-shower sample and then combining its output with an externally assumed HCAL term. While not forced by construction, this makes the central performance number sensitive to any mismatch between simulated and real shower shapes, e/h ratios, or visible-energy fractions in PbF2; no beam-test anchors or alternative physics-list comparisons are reported.
  2. [Methods] Methods (Geant4 setup): the mapping from deposited to reconstructed energy depends on the simulated longitudinal/transverse profiles and neutron-capture modeling. Because the GNN corrections are derived from these profiles, any systematic discrepancy with real PbF2 response (e.g., scintillation vs. Cherenkov yields) directly propagates into the claimed compensation gain and the final resolution formula.
minor comments (1)
  1. [Results] The dependence of the result on the assumed HCAL resolution is stated to be limited, but the specific range of HCAL parameters explored and the quantitative variation in the combined resolution should be shown in a dedicated figure or table for clarity.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive comments and positive assessment of the significance of the work. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract and simulation study: the quoted combined resolution (1 GeV/E ⊕ 12%/√E[GeV] ⊕ 2.5%) is obtained by training and evaluating the GNN exclusively on the same Geant4 pion-shower sample and then combining its output with an externally assumed HCAL term. While not forced by construction, this makes the central performance number sensitive to any mismatch between simulated and real shower shapes, e/h ratios, or visible-energy fractions in PbF2; no beam-test anchors or alternative physics-list comparisons are reported.

    Authors: The manuscript is presented throughout as a Geant4 simulation study of a conceptual calorimeter design, with the quoted resolution derived under those specific modeling assumptions and the stated HCAL parameters. Training and evaluation on the same sample is standard for assessing the potential of a reconstruction technique in simulation. We agree that real-data performance would depend on how accurately the simulation reproduces actual shower development and visible energy fractions in PbF2. We will add explicit wording in the abstract and conclusions to reinforce that the result is simulation-based and constitutes a proof-of-principle. No beam-test anchors exist for this design, and alternative physics lists were not compared because the focus is the compensation method rather than a full simulation validation. revision: partial

  2. Referee: [Methods] Methods (Geant4 setup): the mapping from deposited to reconstructed energy depends on the simulated longitudinal/transverse profiles and neutron-capture modeling. Because the GNN corrections are derived from these profiles, any systematic discrepancy with real PbF2 response (e.g., scintillation vs. Cherenkov yields) directly propagates into the claimed compensation gain and the final resolution formula.

    Authors: This dependence is inherent to any simulation-derived compensation technique. The Geant4 setup models Cherenkov photon production explicitly in PbF2, and the GNN exploits the resulting 3D topology. We will add a short paragraph in the methods section discussing the principal modeling assumptions (e.g., neutron capture and e/h ratio) and their potential influence on the reported gains. A quantitative sensitivity study to alternative physics lists or parameter variations lies beyond the present scope but is a natural direction for follow-up work once beam-test data become available. revision: partial

standing simulated objections not resolved
  • Provision of beam-test anchors or real-data validation, as the study is based entirely on Geant4 simulations of a conceptual design for which no experimental data exist.

Circularity Check

0 steps flagged

No significant circularity; simulation-derived performance is not forced by construction

full rationale

The paper derives its resolution claims directly from Geant4 pion-shower simulations in PbF2, with a GNN trained on shower-shape observables to correct visible energy. The quoted combined resolution formula explicitly adds an externally assumed HCAL term and studies its variation; this is a transparent modeling step rather than a self-referential definition. No load-bearing self-citations, uniqueness theorems, or ansatzes imported from prior author work appear. The GNN output is a trained correction, not a fitted input renamed as prediction. The result is therefore self-contained within the stated simulation framework and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central performance claim rests on the fidelity of Geant4 modeling of hadronic showers in PbF2 and on the choice of realistic HCAL resolution parameters; no free parameters are explicitly fitted in the abstract beyond the GNN training itself.

axioms (1)
  • domain assumption Geant4 accurately models the visible energy fraction and shower topology for pions in PbF2 crystals
    All quantitative results are derived from these simulations.

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