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REVIEW 3 major objections 4 minor 77 references

Measurement of jet track functions in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

T0 review · 3 major / 4 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read First measurement of jet track-function $r_q$ shows moments evolve as QCD predicts.

desk verdict First measurement of higher track-function moments; the RG-flow test is suggestive but has an unquantified flavor-fraction dependence. read the letter →

arxiv 2502.02062 v2 pith:SPUJCU6Q submitted 2025-02-04 hep-ex

ATLAS Collaboration This is my paper · ORCID
classification hep-ex
keywords jetsubstructuretrackfunctionschargedhadronfractionrenormalizationgroupevolutionunfoldingmachinelearningdijeteventsATLAS
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Quarks and gluons fragment into jets, and many jet-substructure measurements use only the charged tracks. Computing those observables requires track functions, which describe the fraction $r_q$ of a jet's transverse momentum carried by charged hadrons. This paper reports the first direct measurement of the $r_q$ distribution in dijet events from 140 fb$^{-1}$ of 13 TeV proton-proton collisions, and extracts its first six moments, whose higher orders have never been measured before. The scale evolution of these moments is compared with next-to-leading-logarithm predictions of the non-linear renormalization-group flow, and the data show good agreement, consistent with the cumulants flowing toward a fixed point as jet energy increases. If correct, the result supplies the missing non-perturbative input needed for precision track-based jet-substructure calculations.

What carries the argument

The central object is the track function $T_q(x)$, a universal non-perturbative function giving the probability that a fragmenting quark or gluon produces charged hadrons carrying transverse-momentum fraction $x$; the measured proxy is $r_q = p_T^{\mathrm{charged}}/p_T^{\mathrm{jet}}$. The argument is carried by the moments $E[X^n]$ of the $r_q$ distribution and their cumulants $\kappa_n$, since the non-linear renormalization-group evolution equations predict specific relationships between cumulants and products of lower-order ones, such as $\kappa_4$ versus $\kappa_2^2$. The machinery also includes iterative Bayesian unfolding with a response matrix built from the nominal Monte Carlo sample, plus a data-driven machine-learning correction, the OmniFold method, for binning artifacts in the moment extraction.

What would settle it

Repeat the measurement at higher jet $p_T$ or with a deliberately mis-modeled pixel-cluster-merging simulation: if the unfolded cumulant ratios move away from the next-to-leading-logarithm fixed-point predictions by more than the combined statistical and systematic uncertainties, the fixed-point interpretation would be falsified, while a null shift would confirm it.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is a first: direct, detector-unfolded access to $r_q$ and, in particular, to the higher moments $E[X^n]$ for $n=2$ through $6$ of the charged-track momentum fraction, which previously had no measured values. The paper argues these moments are not just numbers: the energy dependence of relationships between cumulants, such as $\kappa_4$ versus $\kappa_2^2$ and $\kappa_6$ versus $\kappa_3^2$, is set by the non-linear renormalization-group equations that govern correlations in hadronization. Comparing those relationships to next-to-leading-logarithm predictions, the paper finds good data-theory agreement and interprets the observed slowing of moment evolution at higher jet $p_T$ as evidence of flow toward a fixed point, with the caveat that convergence will be better tested at even higher momentum scales.

Load-bearing premise

The unfolded $r_q$ distributions assume that the detector simulation accurately reproduces track-reconstruction efficiency and momentum resolution inside dense jet cores, including the neural-network splitting of merged pixel clusters, so any residual simulation-data mismatch in track merging would propagate through the response matrix into the moments and the renormalization-group comparison.

Editorial extensions

If this is right

  • Universal track functions can now be extracted from data, removing a missing ingredient for next-to-leading-order and resummed calculations of track-based substructure observables.
  • The higher moments of $r_q$, previously unmeasured, are now known as functions of jet $p_T$ and pseudorapidity region, enabling direct comparisons with any future prediction.
  • The agreement between the measured cumulant flow and the next-to-leading-logarithm renormalization-group predictions constitutes a test of QCD beyond the single-hadron DGLAP framework.
  • The observation that moment evolution slows with increasing jet $p_T$ supports the picture of convergence toward a fixed point, with even higher scales expected to sharpen the test.
  • The statistical quark/gluon demixing provides separate moments for quark- and gluon-initiated jets, which the paper finds are systematically higher for quark-initiated jets.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the fixed-point flow is real, higher-$p_T$ data beyond 800 GeV should show the cumulant ratios flattening further; a deviation would indicate missing higher-order or hadronization effects.
  • The same data-driven binning-correction strategy could be applied to moments of other track-based observables, where Monte-Carlo-based corrections are currently used.
  • The measured track-function moments could serve as direct input for energy-energy correlator calculations on tracks, connecting this measurement to a different class of substructure observables.
  • The main place where a systematic error could mimic or mask the fixed-point signal is track reconstruction inside dense jet cores; quantifying pixel-cluster merging losses with a dedicated high-$p_T$ sample would test that assumption directly.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. This letter reports the first measurement of the charged-hadron transverse-momentum fraction r_q = p_T^charged/p_T^jet in dijet events using 140 fb^-1 of pp collisions at sqrt(s)=13 TeV recorded with the ATLAS detector. The r_q distributions are unfolded with Iterative Bayesian Unfolding, the first six moments are extracted with an OmniFold-based correction for binning artifacts, and the scale dependence of cumulant combinations is compared with a next-to-leading-logarithm RG-flow prediction. The paper claims good data-theory agreement and interprets this as evidence for the predicted non-linear renormalization group flow of track-function moments toward fixed-point values.

Significance. If the result holds, it provides the first direct experimental constraint on the higher moments of track functions, which are needed for precision calculations of track-based jet substructure observables. The measurement is carried out with established ATLAS procedures: full detector simulation, multiple MC generators, a detailed systematic-uncertainty budget, and a data-driven binning correction. The central physics claim, however, rests on the RG-flow comparison, and the current presentation leaves a key model-dependence in that comparison unquantified. The paper is a useful and likely reproducible measurement, but its headline interpretation needs additional support before it can be accepted as a clean test of non-linear QCD evolution.

major comments (3)
  1. [Section 7, Figure 3] The NLL prediction is initialized using data in the lowest pT bin, as acknowledged in the text. This means the theory curve and the data share a point by construction, so the visual 'good data-theory agreement' is not an independent test of the absolute evolution. The paper should provide a quantitative comparison that excludes the initial condition, for example a chi-square over the flow increments between adjacent pT bins or a comparison of the slopes of the cumulant-pair curves, or it should explicitly limit the claim to the direction of flow. As written, the statement 'The results in Figures 3(a)-3(d) show good data-theory agreement' overstates the evidential value of the comparison.
  2. [Section 7, Figure 3; Appendix A] The inclusive r_q distribution is an admixture of quark- and gluon-initiated jets with pT- and rapidity-dependent flavor fractions, and the non-linear RG equations for track-function moments are flavor-specific and do not close under a weighted sum. The manuscript does not state whether the NLL prediction shown in Figure 3 evolves the inclusive mixture with an assumed fixed flavor composition or first demixes, evolves quark and gluon distributions separately, and then reconvolves. The quoted theory uncertainties include only scale variations, so the dependence on the MC-derived flavor fractions (e.g., Pythia8 vs Herwig7) is not quantified. Since Appendix A demonstrates that the collaboration has a demixing procedure, please specify the flavor treatment used for the Figure 3 prediction and add a flavor-fraction systematic to the theory band. Without this, the claimed agreement with the RG-flow prediction could be a consequence of the assumed quark/gluon mixture rather than a robust QCD test.
  3. [Section 7, Figure 3; Section 8] The conclusion that the data are 'consistent with the picture of flow towards a fixed point' is inferred from the qualitative observation that the moments evolve more slowly at higher pT. With only four pT bins and highly correlated cumulant pairs, this is a weak test. The paper should either provide a quantitative characterization of the flow, such as a fitted slope of the cumulant ratio versus log pT with its uncertainty, or temper the concluding claim. The data may well be consistent with a fixed point, but the current evidence is not sufficient to support the strength of the claim as stated.
minor comments (4)
  1. [Section 1] The sentence 'Experimentally, track functions can be determined from a measurement of the the transverse-momentum (pT) fraction' contains a duplicated 'the'.
  2. [Figure 3] The axis labels in Figure 3 are difficult to parse (for example, '2 2 ×10 3' and '3 2 ×10 5'); the caption should explicitly state which cumulant combination is plotted on each axis, e.g., κ4 vs κ2^2, κ5 vs κ2κ3, κ6 vs κ3^2, and κ6 vs κ2^3.
  3. [Section 8] The conclusion states 'an inclusive selections of dijet events'; this should read 'an inclusive selection of dijet events' or 'inclusive selections of dijet events'.
  4. [Section 5] The sentence 'Particle-level jets are reconstructed in MC generated events without detector simulation' is clear, but the preceding sentence about tracks uses 'the the' style phrasing; please proofread for similar duplicated articles throughout.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the ATLAS r_q measurement is self-contained, and the explicitly initial-condition-limited RG comparison is a legitimate external theory test.

full rationale

The paper's central deliverable is a detector-corrected measurement of the r_q distribution and its moments/cumulants, which is independent of the theory comparison. The unfolding uses a Pythia response matrix but is cross-checked with Sherpa and multiple generators, and the data-theory agreement in Figure 1 is not used to define the measured moments. The RG-flow comparison in Figure 3 explicitly uses the lowest-pT data as the initial condition, and the paper states that 'the direction of flow can be compared, but not each measurement individually.' This is a disclosed initial-value test, not a hidden fit: the evolution direction is determined by the cited NLL RG equations, not by the higher-pT data points being compared. The theory input comes from Ref. [20], whose author list overlaps with ATLAS coauthor I. Moult, but that cited result is a published, parameter-free QCD calculation whose assumptions do not include the measured higher-pT cumulants; the overlap alone does not make the comparison circular. The quark/gluon demixing in Appendix A uses Pythia flavor fractions and admits model dependence, but this does not feed back into the central inclusive measurement. No equation in the paper defines the measured quantity in terms of the predicted quantity by construction, and no fitted parameter is renamed as a prediction. The derivation chain is therefore self-contained; the main limitations are statistical/systematic and model-dependence concerns, not circularity.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The measurement itself introduces no free parameters, but the analysis choices for unfolding regularization and the appendix demixing rely on model inputs. The physics assumptions are standard QCD factorization and Monte Carlo modeling of hadronization and detector response.

free parameters (2)
  • IBU iteration count = 2
    Chosen to minimize total uncertainty (Section 5); the unfolding result depends on this regularization choice.
  • Gluon fraction f_G = From Pythia 8 MC, varies with jet pT
    Used for quark/gluon demixing in Appendix A; model-dependent input with an assigned systematic uncertainty.
assumptions (4)
  • domain assumption Track functions are universal and obey QCD factorization in dijet events.
    Invoked in the Introduction to justify relating the measured r_q distribution to universal track functions.
  • domain assumption The Pythia8 A14 Monte Carlo provides an adequate prior for unfolding the data.
    The unfolding uses a response matrix from Pythia8; the systematic uncertainty covers differences to Sherpa, but the method relies on MC modeling of the detector-level distribution.
  • domain assumption The detector simulation, including the neural-network pixel-cluster splitting, accurately models track reconstruction in dense jet cores.
    Section 4 describes the mitigation of track merging in dense cores; biases here would shift the unfolded r_q distributions.
  • domain assumption The NLL renormalization-group evolution of track-function moments from Ref. [20] is correct.
    Used in Section 7 for the theory comparison; the paper takes the calculation from the literature rather than deriving it.

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Cite this review

Pith. "Pith review of Measurement of jet track functions in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector." pith.science (2026). https://pith.science/paper/SPUJCU6Q

@misc{pith2026250202062,
  author       = {Pith},
  title        = {Pith review of: Measurement of jet track functions in $pp$ collisions at $\sqrts=13$ TeV with the ATLAS detector},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SPUJCU6Q}},
  note         = {Machine review of arXiv:2502.02062}
}
abstract

Measurements of jet substructure are key to probing the energy frontier at colliders, and many of them use track-based observables which take advantage of the angular precision of tracking detectors. Theoretical calculations of track-based observables require `track functions', which characterize the transverse momentum fraction $r_q$ carried by charged hadrons from a fragmenting quark or gluon. This letter presents a direct measurement of $r_q$ distributions in dijet events from the 140 fb$^{-1}$ of proton--proton collisions at $\sqrt{s}=13$ TeV recorded with the ATLAS detector. The data are corrected for detector effects using machine-learning methods. The scale evolution of the moments of the $r_q$ distribution is sensitive to non-linear renormalization group evolution equations of QCD, and is compared with analytic predictions. When incorporated into future theoretical calculations, these results will enable a precision program of theory-data comparison for track-based jet substructure observables.

Figures

Figures reproduced from arXiv: 2502.02062 by the authors.

Figure 1
Figure 1. The unfolded central (a) and forward (b) normalized differential cross-sections as a function of 𝑟𝑞 for data compared to predictions from several MC generators. The grey uncertainty band shows the combined statistical and systematic uncertainties on the measurement. The bottom panel shows the breakdown of the uncertainties grouped by their sources. In particular, the ‘Exp. Conditions’ group includes uncertainties re… view at source ↗
Figure 2
Figure 2. The first six moments of the unfolded (a) central and (b) forward 𝑟𝑞 distributions in jet 𝑝T bins. The grey uncertainty band shows the combined statistical and systematic uncertainties on the measurement. 7 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Non-trivial RG flow relationship between higher-order cumulants and products of lower-order ones coming from the non-linearity of the track function evolution. The relationship between (a) 𝜅4 and 𝜅 2 2 , (b) 𝜅5 and 𝜅2𝜅3, (c) 𝜅6 and 𝜅 3 2 , and (d) 𝜅6 and 𝜅 2 3 are shown for different bins of the particle-level jet 𝑝T. The ellipses correspond to the 68% confidence regions based on the combined statistical and systema… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: The gluon fraction obtained from the nominal Pythia 8 MC event sample for the more forward and more central of the two dijets as a function of the jet 𝑝T. The cross markers do not include uncertainties in this plot. The demixed quark and gluon interpretation of 𝑟𝑞 are s…
Figure 5
Figure 5. Figure 5: The demixed (a, c) gluon and (b, d) quark interpretation of the unfolded 𝑟𝑞 cross-sections for (a, b) 300 GeV < 𝑝T < 400 GeV, and (c, d) 600 GeV < 𝑝T < 800 GeV for data compared to predictions from several MC generators. The grey uncertainty band shows the combined sta…
Figure 6
Figure 6. Figure 6: The first six moments of the demixed (a) gluon and (b) quark 𝑟𝑞 distributions in jet 𝑝T bins. The uncertainty bands show the combined statistical and systematic uncertainties on the measurement. References [1] A. J. Larkoski, I. Moult, and B. Nachman, Jet substructure …

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Reference graph

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