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REVIEW 4 major objections 5 minor 93 references

One self-supervised generative model, trained on real LHC collision data without channel labels or resonance masses, reproduces Standard Model structure across five decades of dilepton invariant mass and recovers the Weinberg angle and heav

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2026-08-01 21:14 UTC pith:TFPQYFN3

load-bearing objection Serious and unusually honest data-driven generator paper; the SM-structure claim is real but bounded by conditioned composition and supervised peaks. the 4 major comments →

arxiv 2607.16144 v1 pith:TFPQYFN3 submitted 2026-07-17 hep-ph cs.LGhep-ex

Learning Standard Model structure from LHC data with Riemannian flow matching

Midori Kato , Kevin A. Urqu\'ia-Calder\'on , Inar Timiryasov , Oleg Ruchayskiy This is my paper
classification hep-ph cs.LGhep-ex
keywords Standard Model structuregenerative modelflow matchingLHCATLAS Open Datadilepton resonancesWeinberg angleself-supervised learning
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.

This paper sets out to show that a single self-supervised generative model can internalise the structure of the Standard Model from roughly eight hundred million real proton–proton collisions, without being told the channel, the process, or any resonance mass. Trained only with the on-shell condition and the invariant-mass formula as physics priors, the model reproduces the opposite-sign same-flavour dilepton mass spectrum over five decades—with the J/ψ, ψ(2S), Υ, and Z peaks at their Particle Data Group positions—and yields a Drell–Yan forward–backward asymmetry from which the Weinberg angle comes out statistically compatible with the truth-sample fit in both muon and electron channels. It also closes on the W and top masses under the standard semileptonic reconstruction. The paper argues that these recoveries mean a substantial fraction of the Standard Model is learnable directly from recorded data, which would matter because it opens the way to data-driven event generators and anomaly searches that are not tied to a single simulation hypothesis. The evidence is paired on identical event composition: the generator receives the particle types, charges, missing transverse energy, and quality features as conditioning and generates only the kinematics.

Core claim

A single transformer-based Riemannian flow-matching generator, trained on the union of the two-lepton-to-four-lepton and single-lepton-plus-MET skims of the ATLAS Open Data 13 TeV release, recovers Standard Model structures across five orders of magnitude in invariant mass: the charmonium and bottomonium dilepton resonances and the Z peak appear at their PDG positions, the Drell–Yan forward–backward asymmetry preserves the leptonic weak mixing angle to within 0.3σ (dimuon) and 1.2σ (dielectron) of the truth-sample leading-order fit, and the reconstructed hadronic and leptonic top masses, hadronic W mass, and leptonic Z mass agree with truth under standard selections. No channel label or per-

What carries the argument

The central object is ShellFlow, a Riemannian conditional flow-matching model in which each particle’s momentum direction lives on a unit sphere and its energy (for leptons and photons) or boost-rapidity and log-mass (for taus and jets) live on flat charts, so that the on-shell relation E² = m² + |p|² holds by construction and no generated particle goes off shell. A dual-head transformer carries two objectives: the primary head regresses the flow-matching velocity field, while an auxiliary head supervises the log squared invariant mass of every K-tuple (K = 2, 3, 4) with a distribution-matching weight that amplifies under-produced mass regions—this is what lets narrow peaks like J/ψ and Υ em

Load-bearing premise

The claim that Standard Model structure is learnable from recorded data assumes the model is handed the event composition at sampling time—particle type, charge, missing transverse energy, and reconstruction features are conditioning inputs taken directly from validation events, so the generator only has to produce kinematics given the correct identities.

What would settle it

Swap or shuffle the composition conditioning among validation events (mismatching particle types, charges, and MET across events) and regenerate; if the J/ψ, Υ, and Z peaks, the Weinberg-angle value, and the top-mass closures persist, the physics is genuinely encoded in the kinematics—if they degrade or vanish, the model is largely transcribing structured conditioning rather than having learned the underlying relationships.

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

If this is right

  • One trained network can serve as a data-driven event generator spanning sub-GeV to TeV invariant masses, the range the paper notes no single Monte Carlo sample covers.
  • The Weinberg-angle closure means the parity-violating structure of Drell–Yan events is recoverable from generated kinematics with no electroweak input.
  • The top and W mass closures imply internal features corresponding to top-like and W-like events exist in the latent representation, even though no such label was used in training.
  • The ablations show both physics priors are load-bearing: without the on-shell manifolds more than 99% of generated muons go off-shell and all narrow resonances disappear; without the K-body mass loss only a degraded Z peak remains.
  • The paper's own assessment attributes the absent ω/φ and Higgs peaks and the diluted hadronic cores to the present training horizon and rare-process statistics rather than to a structural limitation of the architecture.

Where Pith is reading between the lines

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

  • If the composition conditioning were released as a free variable—generating particle types, charges, and missing transverse energy jointly from noise—the paper's evidence would not directly support the learnability claim; a jointly-generative or chained variant is the natural stress test.
  • The failure pattern suggests a concrete next experiment: extending training beyond 30 epochs or reweighting toward rare selections should sharpen the hadronic top/W cores and may resurrect the H→4ℓ peak under quality cuts, since the current deficit is a rate problem rather than an absent internal feature.
  • Mechanistic interpretability could convert the recovered peaks into a physics probe: if a linear feature in the transformer activates selectively on Z→ℓℓ events, amplifying that feature at sampling time would sharpen the Z peak on demand and clarify what the network actually encodes.
  • The shallow deficit at η≈0 across all particle types is plausibly an artifact of the spherical chart parameterisation rather than detector physics; this is testable by reparameterising the direction chart with an equiareal embedding and checking whether the deficit persists on identical data.

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

4 major / 5 minor

Summary. ShellFlow is a Riemannian conditional flow matching transformer trained on ~8.2×10^8 ATLAS Open Data events. The model generates per-particle kinematics (pT, η, φ, E, m) on on-shell product manifolds, conditioned on the reconstructed event composition, charge, MET, and detector-quality features taken from validation events at sampling time. The authors report faithful single-particle marginals, OSSF dilepton spectra with J/ψ, ψ(2S), Υ, and Z peaks, a Drell–Yan A_FB closure giving sin^2θw compatible with the truth-sample LO fit, leading-dijet and three-body closures, and W/top mass peaks under a semileptonic ttbar reconstruction. The training uses a primary RCFM loss (Eq. 7) and an auxiliary K-body loss (Eqs. 17–18) that regresses predicted log m_K onto truth log m_K, reweighted by a truth-density KDE w* (Eq. 20). The paper explicitly labels the mass peaks as supervised in Table I and Sec. II D, and it reports quantitative failures (ω, φ, Higgs under quality cuts, hadronic core dilution). The conclusion nevertheless presents the model as having learned a substantial fraction of the Standard Model directly from data.

Significance. The empirical contribution is potentially significant: a compact 3M-parameter transformer fits the conditional kinematics of reconstructed LHC events across five decades of invariant mass using recorded data only, with a complete hyperparameter table, a four-way ablation, and unusually candid failure analysis. This is a useful step toward fast, data-driven event simulation and could support anomaly-detection applications. However, the headline claim that a self-supervised generator internalises Standard Model structure is not established by the evidence. The mass-peak positions are supervised through the auxiliary loss; the event composition, charges, MET, and quality variables are supplied as conditioning inputs; and the paper’s own Sec. IV D states that whether the network has learned physics or reproduced marginals through training statistics is not settled. As written, the paper demonstrates a well-characterised conditional generator with strong closure tests, not an unsupervised discovery of SM physics. The revision should reframe the central claim accordingly.

major comments (4)
  1. [§III C, Eqs. (17)–(20); Table I] The K-body auxiliary loss directly supervises the invariant-mass axis: Eq. (17)–(18) regress log m_K^pred onto log m_truth^K for every 2/3/4-tuple, and w* in Eq. (20) is constructed from the truth-density KDE p_truth(log m). The resonance positions in Fig. 4 are therefore fits to truth mass labels, not emergent placements. Table I correctly marks these rows as ‘aux. mass density,’ and Sec. II D states that peak placement is ‘a fidelity claim rather than an emergence one.’ This contradicts the abstract’s ‘told nothing else’ and the Fig. 4 caption’s ‘None of these masses was supplied to the model.’ The manuscript should state explicitly that the mass axis is supervised, and that only the angular/joint structural closures are unsupervised.
  2. [§III D; §IV C] The generator produces only particle kinematics; the particle type, charge, MET, b-tag scores, isolation variables, and remaining reconstruction features are conditioning inputs taken from validation events at sampling time. Thus all truth-vs-generated comparisons are paired on identical composition, and the model never proposes which particles an event contains, nor assigns identities to misreconstructed objects, nor predicts MET. The conclusion’s claim that ‘a substantial fraction of the Standard Model is learnable directly from recorded collision data’ is broader than the evidence, which concerns p(kinematics | composition). The paper’s own Sec. IV C lists these as systematic limitations. The title, abstract, and conclusion should be qualified to ‘conditional kinematics given the reconstructed composition,’ or the model should be extended to generate composition jointly.
  3. [§II E; §IV D] The forward-backward asymmetry and the other ‘no-loss’ observables are deterministic functionals of the conditional kinematics that Eq. (7) is trained to match. Their closure is therefore a measure of how well the model fits the training distribution, not evidence of an independently discovered physical law. Sec. II E states that A_FB is ‘the cleanest case of structure the model can only have learned from the joint event kinematics,’ but the primary RCFM loss already targets the joint kinematics through per-particle velocity regression. Moreover, Sec. IV D explicitly says that whether the network has learned the physics or only reproduced marginals is ‘not settled.’ To support the stronger claim, the paper would need intervention tests, representation analyses, or a model that generates composition jointly. As it stands, the principal result should be framed as fit fidelity with possible
  4. [§II H, Table III] The heavy-particle mass closures are weaker than the abstract implies. For the hadronic top and hadronic W, the generated samples cannot be fitted with a free-shape DSCB; the paper fixes the resolution and tail parameters to the truth fit and floats only normalisation, position, and background (Sec. II H). The generated core yields are 9% (hadronic top) and 23% (hadronic W) below truth, and the distributions are 10–18% broader. Thus the ‘W and top-quark mass’ claims rest on template-fit positions rather than on independently reconstructed resonant cores. This is acknowledged in the body, but the abstract and conclusion overstate the closure. Please report the free-fit failure in the abstract-level summary and temper the wording.
minor comments (5)
  1. [Fig. 4 caption] ‘None of these masses was supplied to the model’ is inaccurate given Eq. (17)–(18). Suggest rewording to ‘no per-process mass labels were used; the K-body auxiliary loss provides log m_truth^K as a global supervision channel.’
  2. [Eq. (19)–(20); Table VIII] The KDE bandwidth h=0.01 is a hyperparameter of the distribution-matching weight but does not appear in Table VIII. Please add it to the loss hyperparameter list.
  3. [Table VI] The variant name ‘shellFlow’ appears lowercase in Table VI while the model is named ShellFlow elsewhere. Unify the notation.
  4. [Sec. II I, Fig. 9] The Higgs failure after quality cuts is visually severe (W1=62.5, SKL=1.16). The text mentions it, but this quantitative degradation should be stated in Sec. II I or in the conclusion, since it is one of the paper’s main negative results.
  5. [Sec. I] The term ‘self-supervised’ is used before the conditioning structure is described. Since the model is trained on a regression objective with truth mass labels in the auxiliary loss, define what ‘self-supervised’ means relative to the conditioning and supervision channels early in the paper.

Circularity Check

1 steps flagged

Mass-peak recoveries are supervised fits via the K-body auxiliary loss; full event composition is conditioned, not generated.

specific steps
  1. fitted input called prediction [Sec. II D, Fig. 4; Sec. III C, Eqs. (17)-(18); Table I]
    "The K=2 branch of the auxiliary loss (Sec. III C) supervises log m_ℓℓ directly, so peak placement is a fidelity claim rather than an emergence one. ... Δpos_I = log m_pred_K(I) − log m_truth_K(I)."

    The headline resonance peaks (J/ψ, ψ(2S), Υ, Z at PDG positions) are produced by an auxiliary loss whose per-tuple residual regresses the generated log invariant mass directly onto the truth log invariant mass from training events, reweighted by a KDE of the truth mass density (w*, Eq. (20)). The peak positions are therefore supervised fits, and the Fig. 4 caption's statement that 'None of these masses was supplied to the model' is contradicted by the m_truth target in Eq. (18). Table I itself records the Supervision of these rows as 'aux. mass density'. The same holds for the W and top closures, also marked 'aux. mass density' in Table I.

full rationale

The strongest concrete form of the paper's claim — the OSSF dilepton resonances appearing at PDG positions — is, by the paper's own equations, a supervised reproduction rather than an emergent prediction. Equation (18) regresses log m_pred onto log m_truth for every 2/3/4-tuple, and Eq. (20) reweights this loss with a truth-density KDE; Sec. II D explicitly says 'peak placement is a fidelity claim rather than an emergence one,' and Table I lists 'aux. mass density' as the supervision channel. This is pattern 2: a fitted input presented as recovery. The paper's honest 'Supervision' column and its Sec. IV D admission ('Whether the network has learned this physics or has only reproduced the marginals through correlations in the training statistics is not settled') reduce the score somewhat, but do not remove the by-construction fit of the headline masses. Separately, composition conditioning (Sec. III D: 'The model generates only the particle kinematics (pT, η, φ, E, m). The particle type, charge, MET, and the remaining reconstruction features are conditioning inputs, taken at sampling time directly from the validation events.') means all SM-structure closures are for p(kinematics | truth composition), so the 'single self-supervised generator internalises SM relationships from recorded data alone' claim is narrower than stated; this is a scope reduction rather than a hidden equivalencing of the angular/EW closures. The Weinberg-angle and inter-particle closures are not directly supervised and are genuine (if conditioned) fidelity tests, which is why the paper retains independent content and the score is 6 rather than 8-10. There are no load-bearing self-citations or imported uniqueness theorems.

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 0 invented entities

No new physics entities are postulated; the model introduces architecture and supervision choices, not new particles or forces. The ledger records the hand-chosen and data-derived constants behind the headline results, and the axioms record that the strongest 'emergence' claims (masses) are produced by a designed supervision channel (Eqs. 17–20), while the genuinely unsupervised claims (Weinberg angle, angular correlations) rest on the conditioning and reconstruction assumptions listed above.

free parameters (5)
  • Distribution-matching weight hyperparameters α, k, η (Eq. 20) = α=1.0, k=5, η=1/3 (w*_max=3)
    Hand-chosen loss-shaping constants (Table VIII) that make the auxiliary loss resolve narrow resonance peaks; central to the mass-peak result, with no stated selection procedure or sensitivity scan.
  • Per-type reference scales E_ref,k and m_floor,k (Table IV) = Not quoted in text
    Estimated on the training set; the log-energy normalization compresses the sub-GeV regime, which the authors themselves connect to the ω/φ failure (Sec. IV C).
  • Per-type normalization means and stds (Eq. 13) = Not quoted in text
    Measured on the training set to rescale chart coordinates; standard per-coordinate rescaling but data-derived.
  • Loss constants: Huber δ, gate t_gate, quality floor q_cfm_floor = δ=1, t_gate=0.99, q_cfm_floor=0.5
    Hand-chosen (Table VIII); modulate gradient weighting of object quality and of late-flow-time mass supervision.
  • Per-type detector quality cuts and sigmoid slopes (Table VII) = e.g., isolation cut 0.15, slope 10; |d0/σ| cut 3.0, slope 1
    Fixed per-type constants chosen to mirror ATLAS analysis cuts; enter the per-particle loss weight q_eff (Eq. 16).
axioms (6)
  • standard math Riemannian flow matching: geodesic interpolants and conditional velocity regression share gradients with the intractable marginal regression (Chen & Lipman).
    The entire training objective Eq. (7) depends on this theorem; invoked from Ref. 58 without proof.
  • standard math Closed-form spherical exp/log/slerp maps on S² (Eq. 9), with linear-interpolation fallback near Ω→0.
    Used for all direction coordinates; the fallback at parallel directions is a numerical patch that is not proven to preserve the flow-matching gradient identity.
  • domain assumption Reconstructed ATLAS objects faithfully stand in for the underlying final-state particles.
    The model trains and evaluates on reconstruction-level Open Data; Sec. IV C concedes 'a particle mislabelled by the reconstruction is generated as its assigned type'.
  • domain assumption Event composition, charges, MET, and per-object detector features are supplied as ground truth at generation time.
    Sec. III D: conditioning is 'taken at sampling time directly from the validation events'; all comparisons are paired on identical composition.
  • domain assumption The joint-sample selections (2-to-4 lepton + 1LMET30 skims, N_particles ≤ 8) define the operative meaning of 'complete events'.
    Sec. III D and Sec. IV C: event-level completeness claims are implicitly conditioned on the multiplicity cut, and the physics scope is set by the two skims.
  • ad hoc to paper The K-body auxiliary loss with truth-density weight w* injects the invariant-mass distribution without biasing the unsupervised angular observables.
    Eqs. (17)–(20); the ablation (Table VI) shows both priors are needed, but the independence of w*'s effect on angular observables rests on the authors' argument, not on a control with matched loss weight and no mass target.

pith-pipeline@v1.3.0-alltime-deepseek · 41502 in / 23334 out tokens · 191642 ms · 2026-08-01T21:14:21.522841+00:00 · methodology

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read the original abstract

In this work we demonstrate that a single transformer-based generative model can capture Standard Model structure spanning five decades of invariant mass, from the sub-GeV regime to the TeV continuum, a range that no single Monte Carlo sample covers. To achieve this we design \textsc{ShellFlow}, a Riemannian conditional flow matching model that, given the recorded event composition, generates each particle on its on-shell manifold. Its only physics priors are the on-shell condition and the invariant-mass formula. The model is trained on $\sim 10^{9}$ real $pp$ collision events from the ATLAS Open Data 13~TeV release and told nothing else. From a single training run, the model learns to reproduce all of the following: intra-particle kinematics, the dilepton resonances ($J/\psi$, $\Upsilon$, $Z$) at their PDG positions, the leptonic Weinberg angle, the $W$ and top-quark masses, and inter-particle correlations that enter no training objective. A substantial fraction of the Standard Model is thus learnable directly from recorded collision data.

Figures

Figures reproduced from arXiv: 2607.16144 by Inar Timiryasov, Kevin A. Urqu\'ia-Calder\'on, Midori Kato, Oleg Ruchayskiy.

Figure 1
Figure 1. Figure 1: Muon kinematics. Muon intra-particle marginals in collider coordinates (pT , η, ϕ, E): truth compared with the generated distribution. Selection: all reconstructed muons in the validation sample. The agreement metrics W1, SKL, and BC are defined at the start of Sec. II. The corresponding marginals for the other five reconstructed object types are collected in App. A. reaching the smallest numerical values … view at source ↗
Figure 2
Figure 2. Figure 2: Transverse momentum conservation. Event-level pT closure on the joint sample: signed components PpT ,x+E miss x and PpT ,y + E miss y , plus the signed magnitude residual |p vis T | − E miss T , truth vs. generated. The signed components close at zero. The asymmetric magnitude bump on the negative side is carried by the 1LMET30 component, whose E miss T selection and unstored soft activity make E miss T ex… view at source ↗
Figure 3
Figure 3. Figure 3: Inter-particle kinematics. Inter-particle observables that enter neither the primary flow-matching loss nor the auxiliary K-body loss and have no dedicated conditioning channel: the OSSF cone distance ∆Rℓℓ, the dilepton-to-MET azimuthal opening ∆ϕ(ℓℓ, MET), the transverse mass mT of Eq. (1), the scalar transverse-momentum sum HT , and the leading and sub-leading lepton pT , all defined in the text. Truth (… view at source ↗
Figure 4
Figure 4. Figure 4: Main result: OSSF dilepton invariant-mass spectrum, truth (validation set) vs. generated, across five decades in mℓℓ, with zooms on the four resonance regions. The J/ψ(1S) and ψ(2S) appear as two distinct peaks at their PDG positions, the bottomonium family Υ(1S, 2S, 3S) forms a single composite peak, and the Z at ≈ 91.2 GeV rises above the falling Drell– Yan continuum. None of these masses was supplied to… view at source ↗
Figure 5
Figure 5. Figure 5: Dilepton resonances and angular relations. Joint distribution of the OSSF dilepton invariant mass and the azimuthal opening angle, displayed as a 3 × 3 grid (rows: J/ψ family, Υ family, Z peak, each restricted to a mass window centred on the resonance; columns: truth, generated, σ contours). The third column overlays the 1σ, 2σ, and 3σ isocontours of the truth (solid) and generated (dashed) distributions. … view at source ↗
Figure 6
Figure 6. Figure 6: Weinberg angle extraction. Forward–backward asymmetry AFB(mℓℓ) in six bins of dilepton rapidity |Yℓℓ|, on truth (validation set) and on generated samples. In each panel the points are the measured asymmetry (truth in black, generated in orange), the curves are the LO Drell–Yan template evaluated at the best-fit sin2 θw of the corresponding sample (truth solid, generated dashed), and the strip below each pa… view at source ↗
Figure 7
Figure 7. Figure 7: Dijet kinematics. Joint distribution of the leading-dijet invariant mass mjj and average pseudorapidity ¯η = (η1+η2)/2, truth (validation set) vs. generated. In all panels the two observables are built from the two leading jets of events with at least two reconstructed jets, and the triangular envelope is the kinematic constraint x1, x2 ≤ 1 on the parton momentum fractions. Left: truth. Middle: generated. … view at source ↗
Figure 8
Figure 8. Figure 8: Heavy-particle masses. Reconstructed-mass closures for the top quark, the W, and the Z, truth (validation) vs. generated. In every panel the truth peak is fit with a free-shape DSCB on a linear background, the generated peak with a truth-shape DSCB template in which only the normalisation, position, and background float (see text), and the lower sub￾panel shows the bin-by-bin generated-to-truth ratio. Top-… view at source ↗
Figure 9
Figure 9. Figure 9: Higgs in the four-lepton invariant-mass spectrum. Four-lepton invariant-mass spectrum m4ℓ in the H → ZZ∗ → 4ℓ golden channel, truth (validation) vs. generated, at the two selection stages defined in the text. The lower sub-panels show the bin-by-bin generated-to-truth ratio. Left: kinematic stage (∼ 2.3 × 104 events per sample). The generator reproduces the continuum shape with a moderate excess in the 150… view at source ↗
Figure 10
Figure 10. Figure 10: Embedding-layer architecture. Raw inputs (top row, grey, outside the model) are lifted into the four conditioning streams of the transformer backbone: a per-particle token h, a per-particle adaLN-Zero modulation signal cond, a global time token temb, and K MET cross-attention tokens. The diffusion state zt on the chart of Sec. III B is the only stream that is fed into the type-conditional two-path linear … view at source ↗
Figure 11
Figure 11. Figure 11: Model backbone. A stack of L adaLN-Zero DiT blocks operates on the per-particle token stream h produced by the embedding layer of [PITH_FULL_IMAGE:figures/full_fig_p019_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Ablation: OSSF dilepton spectra of the four variants in the format of [PITH_FULL_IMAGE:figures/full_fig_p022_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Electron kinematics. Electron intra-particle marginals (pT , η, ϕ, E). Truth (validation set) vs. generated. Same conventions as [PITH_FULL_IMAGE:figures/full_fig_p024_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Photon kinematics. Photon intra-particle marginals (pT , η, ϕ, E). Truth (validation set) vs. generated. Same conventions as [PITH_FULL_IMAGE:figures/full_fig_p024_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Hadronic-τ kinematics. Hadronic-τ intra-particle marginals (pT , η, ϕ, E, m). The reconstructed mass m is included because τhad uses the massive chart R × S 2 × R (Table V). Truth vs. generated; same conventions as [PITH_FULL_IMAGE:figures/full_fig_p025_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Small-R jet kinematics. Small-R jet intra-particle marginals (pT , η, ϕ, E, m). The reconstructed mass m is included because jets use the massive chart R × S 2 × R (Table V). Truth vs. generated; same conventions as [PITH_FULL_IMAGE:figures/full_fig_p025_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Large-R jet kinematics. Large-R jet intra-particle marginals (pT , η, ϕ, E, m). The reconstructed mass m is included because large-R jets use the massive chart R × S 2 × R (Table V). Truth vs. generated; same conventions as [PITH_FULL_IMAGE:figures/full_fig_p026_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Electron Cartesian components. Electron Cartesian marginals (px, py, pz). Truth vs. generated [PITH_FULL_IMAGE:figures/full_fig_p026_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Muon Cartesian components. Muon Cartesian marginals (px, py, pz). Truth vs. generated. 0 1 2 3 4 5 Events ×104 W1 = 2.92 SKL = 0.00319 BC = 0.0304 px Truth Gen 0 1 2 3 4 5 Events ×104 W1 = 2.76 SKL = 0.00309 BC = 0.03 py Truth Gen 0 1 2 3 4 5 6 7 Events ×10 4 W1 = 3.09 SKL = 0.00176 BC = 0.0275 pz Truth Gen −100 0 100 px [GeV] 0.7 0.8 0.9 1.0 1.1 Gen / Truth −100 0 100 py [GeV] 0.7 0.8 0.9 1.0 1.1 Gen / T… view at source ↗
Figure 20
Figure 20. Figure 20: Photon Cartesian components. Photon Cartesian marginals (px, py, pz). Truth vs. generated [PITH_FULL_IMAGE:figures/full_fig_p027_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Hadronic-τ Cartesian components. Hadronic-τ Cartesian marginals (px, py, pz). Truth vs. generated. 0 1 2 3 4 5 Events ×106 W1 = 2.4 SKL = 0.00254 BC = 0.0274 px Truth Gen 0 1 2 3 4 5 Events ×106 W1 = 2.4 SKL = 0.0028 BC = 0.029 py Truth Gen 0 1 2 3 4 5 6 Events ×10 6 W1 = 0.809 SKL = 2.57e-05 BC = 0.00259 pz Truth Gen −100 0 100 px [GeV] 0.9 1.0 1.1 Gen / Truth −100 0 100 py [GeV] 0.9 1.0 1.1 Gen / Truth … view at source ↗
Figure 22
Figure 22. Figure 22: Small-R jet Cartesian components. Small-R jet Cartesian marginals (px, py, pz). Truth vs. generated [PITH_FULL_IMAGE:figures/full_fig_p028_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Large-R jet Cartesian components. Large-R jet Cartesian marginals (px, py, pz). Truth vs. generated. Appendix C: Forward-process noising of the dilepton spectrum This appendix documents how the OSSF dilepton invariant-mass distribution degrades under the CFM for￾ward noising process at a sequence of flow times t ∈ {1, 0.99, 0.95, 0.9, 0.8, 0.5, 0.3, 0.1}, where the noising follows xt = t xdata + (1 − t) z… view at source ↗
Figure 24
Figure 24. Figure 24: CFM forward noising of the dimuon spectrum. Truth OSSF dimuon invariant-mass spectrum after application of the CFM forward noising xt = t xdata + (1 − t) z at flow times t ∈ {1, 0.99, 0.95, 0.9, 0.8, 0.5, 0.3, 0.1} (clean → noisy). The narrow light-quarkonium peaks ω and ϕ and the ψ(2S) are washed into the continuum already at t ≈ 0.99; the J/ψ(1S) and Υ families follow by t ≈ 0.9; below t ≈ 0.8 only the … view at source ↗
Figure 25
Figure 25. Figure 25: Three-particle kinematics. Three-particle invariant masses and system pT spectra, truth vs. generated (log-log). The lower sub-panel of each pair shows the bin-by-bin generated-to-truth ratio. Eight combinations are shown: mℓℓℓ, mγℓℓ, mℓℓj , mjjj , mℓjj , and the corresponding system pT distributions. The hadronic top peak at mjjj ≈ 173 GeV emerges above the multijet QCD continuum [PITH_FULL_IMAGE:figure… view at source ↗

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Reference graph

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