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arxiv: 2604.25538 · v1 · submitted 2026-04-28 · ✦ hep-ex

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Simultaneous measurements of N-subjettiness observables in jets from gluons and light-flavour quarks, and in decays of boosted W bosons and top quarks

CMS Collaboration
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Pith reviewed 2026-05-07 14:19 UTC · model grok-4.3

classification ✦ hep-ex
keywords jet substructureN-subjettinessCMS experimentboosted jetstop quark decaysW boson decaysunfolded measurementsproton-proton collisions
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The pith

CMS simultaneously measures 25 N-subjettiness observables in jets from gluons, quarks, W bosons and top quarks.

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

The paper presents a simultaneous measurement of 25 jet substructure observables in large-radius high-transverse-momentum jets from proton-proton collisions at 13 TeV. Three event samples are used: dijet events for single-prong jets from gluons or light-flavour quarks, and top-antitop events enriched in two-prong jets from boosted W boson decays and three-prong jets from boosted top quark decays. A 6-body basis of N-subjettiness observables is employed to overconstrain the phase space of resolved emissions inside the jets. The data, corresponding to 138 fb inverse, are unfolded to the stable-particle level and include estimates of the correlations between observables. These results supply a detailed data set for testing and refining models of radiation patterns in jets.

Core claim

The central claim is a detailed characterization of jet substructure through simultaneous measurement of 25 N-subjettiness observables in jets initiated by gluons or light quarks (one prong), two quarks from boosted W bosons (two prongs), and three quarks from boosted top quarks (three prongs). Using data from 138 fb^{-1} recorded in 2016-2018, the measurements are unfolded to the level of stable particles, and an estimate of the particle-level correlations between the observables is provided.

What carries the argument

The 6-body basis of N-subjettiness observables that overconstrains the phase space of resolved emissions in the jet.

If this is right

  • The results can be used to systematically assess and refine the modelling of radiation in jets.
  • Particle-level distributions and correlations are provided for direct use in Monte Carlo generator tuning.
  • The measurements characterize substructure differences across one-, two- and three-prong jet topologies.
  • Data from gluon/light-quark, W-boson and top-quark initiated jets allow comparative studies of radiation patterns.

Where Pith is reading between the lines

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

  • These unfolded results with correlations could be used to develop or validate machine-learning-based jet tagging methods.
  • The data set may help diagnose specific deficiencies in current parton-shower algorithms for multi-prong jets.
  • Higher-order perturbative QCD calculations could be compared directly to the reported particle-level observables and correlations.

Load-bearing premise

The unfolding procedure and Monte Carlo simulations used for correction and background subtraction accurately capture detector effects and jet substructure without introducing significant biases.

What would settle it

A significant discrepancy between the unfolded particle-level distributions or their reported correlations and independent theoretical calculations or additional experimental measurements would indicate that the results do not accurately reflect the true jet substructure.

Figures

Figures reproduced from arXiv: 2604.25538 by CMS Collaboration.

Figure 1
Figure 1. Figure 1: Distributions of the particle-level AK8 jet mass in fiducial regions enriched in view at source ↗
Figure 2
Figure 2. Figure 2: Distributions of the AK8 jet pT (left) and mjet (right) after the dijet selection, based on the combined 2016–2018 data set. The error bars in the upper panels indicate the statistical uncertainties in the data and simulation. The lower panels of the figures show the ratio of simulation to data with statistical uncertainties following the same colour code as the upper panel. The event yields in the simulat… view at source ↗
Figure 3
Figure 3. Figure 3: Distribution of the leading AK8 jet pT (left) and mjet (right) after the boosted W boson selection, for the combined 2016–2018 data set. The error bars in the upper panels indicate the statistical uncertainties in the data and simulation. The lower panels of the figures show the ratio of simulation to data with statistical uncertainties following the same colour code as the upper panel. The contributions o… view at source ↗
Figure 4
Figure 4. Figure 4: Distribution of the leading AK8 jet pT (left) and mjet (right) after the boosted top quark selection for the combined 2016–2018 data set. The error bars in the upper panels indicate the statistical uncertainties in the data and simulation. The lower panels of the figures show the ratio of simulation to data with statistical uncertainties following the same colour code as the upper panel. The contributions … view at source ↗
Figure 5
Figure 5. Figure 5: Background rejection rate as a function of signal efficiency for boosted W boson view at source ↗
Figure 6
Figure 6. Figure 6: Background rejection rate as a function of signal efficiency for boosted top quark view at source ↗
Figure 7
Figure 7. Figure 7: The unfolded combined distribution of the overcomplete 6-body basis of view at source ↗
Figure 8
Figure 8. Figure 8: The unfolded, combined distribution of the overcomplete 6-body basis of view at source ↗
Figure 9
Figure 9. Figure 9: The unfolded, combined distribution of the overcomplete 6-body basis of view at source ↗
Figure 10
Figure 10. Figure 10: Representative unfolded distributions from the simultaneous unfolding are shown view at source ↗
Figure 11
Figure 11. Figure 11: Representative unfolded distributions from the simultaneous unfolding are shown view at source ↗
Figure 12
Figure 12. Figure 12: Representative unfolded distributions of individual observables, view at source ↗
Figure 13
Figure 13. Figure 13: Uncertainty breakdown estimates for the measurements of view at source ↗
Figure 14
Figure 14. Figure 14: A representative set of uncertainty breakdown estimates for the unfolded measure view at source ↗
Figure 15
Figure 15. Figure 15: A representative set of uncertainty breakdown estimates for the unfolded measure view at source ↗
Figure 16
Figure 16. Figure 16: Pairwise Pearson correlations between N-subjettiness observables constituting the overcomplete 6-body basis, in the nominal MADGRAPH5 aMC@NLO+PYTHIA 8 simulation, at the particle level, for the QCD dijet selection. All particle-level events passing selections are considered. In particular, it is found that, for boosted W boson and top quark jets, the N-subjettiness ob￾servables with N ≥ 3 and N ≥ 4, respe… view at source ↗
Figure 17
Figure 17. Figure 17: Pairwise Pearson correlations between N-subjettiness observables constituting the overcomplete 6-body basis, in the nominal MADGRAPH5 aMC@NLO+PYTHIA 8 simulation, at the detector level, for the QCD dijet selection. Only detector-level events with a matched jet in the corresponding particle-level event are considered. The high correlations between observables sensitive to 4- and 5-body or 5- and 6-body pha… view at source ↗
Figure 18
Figure 18. Figure 18: Pairwise Pearson correlations between N-subjettiness observables constituting the overcomplete 6-body basis, using the full Run 2 data set recorded by the CMS detector, for the QCD dijet selection view at source ↗
Figure 19
Figure 19. Figure 19: Pairwise Pearson correlations between N-subjettiness observables constituting the overcomplete 6-body basis, in the nominal POWHEG+PYTHIA 8 signal sample, at the particle level, in the boosted W boson-enriched region. All particle-level events with fully-merged jets passing the event selections are considered view at source ↗
Figure 20
Figure 20. Figure 20: Pairwise Pearson correlations between N-subjettiness observables constituting the overcomplete 6-body basis, in the nominal POWHEG+PYTHIA 8 signal sample, at the detector level, in the boosted W boson-enriched region. Only detector-level events with a matched jet in the corresponding fully-merged particle-level event are considered view at source ↗
Figure 21
Figure 21. Figure 21: Pairwise Pearson correlations between N-subjettiness observables constituting the overcomplete 6-body basis, using the full Run 2 data set recorded by the CMS detector, in the boosted W boson-enriched region view at source ↗
Figure 22
Figure 22. Figure 22: Pairwise Pearson correlations between N-subjettiness observables constituting the overcomplete 6-body basis, in the nominal POWHEG+PYTHIA 8 signal sample, at the particle level, in the boosted top quark-enriched region. All particle-level events with fully-merged jets passing the event selections are considered view at source ↗
Figure 23
Figure 23. Figure 23: Pairwise Pearson correlations between N-subjettiness observables constituting the overcomplete 6-body basis, in the nominal POWHEG+PYTHIA 8 signal sample, at the detector level, in the boosted top quark-enriched region. Only detector-level events with a matched jet in the corresponding fully-merged particle-level event are considered view at source ↗
Figure 24
Figure 24. Figure 24: Pairwise Pearson correlations between N-subjettiness observables constituting the overcomplete 6-body basis, using the full Run 2 data set recorded by the CMS detector, in the boosted top quark-enriched region view at source ↗
Figure 25
Figure 25. Figure 25: Correlations between bins in the normalized, unfolded data in the QCD dijet se view at source ↗
Figure 26
Figure 26. Figure 26: Correlations between the bins of the normalized, unfolded data in the boosted W view at source ↗
Figure 27
Figure 27. Figure 27: Correlations between the bins of the normalized, unfolded data in the boosted top view at source ↗
Figure 28
Figure 28. Figure 28: Unfolded distributions of 1-subjettiness observables, view at source ↗
Figure 29
Figure 29. Figure 29: Unfolded distributions of 1-subjettiness observables, view at source ↗
Figure 30
Figure 30. Figure 30: Unfolded distributions of 1-subjettiness observables, view at source ↗
Figure 31
Figure 31. Figure 31: Unfolded distributions of 2-subjettiness observables, view at source ↗
Figure 32
Figure 32. Figure 32: Unfolded distributions of 2-subjettiness observables, view at source ↗
Figure 33
Figure 33. Figure 33: Unfolded distributions of 2-subjettiness observables, view at source ↗
Figure 34
Figure 34. Figure 34: Unfolded distributions of 3-subjettiness observables, view at source ↗
Figure 35
Figure 35. Figure 35: Unfolded distributions of 3-subjettiness observables, view at source ↗
Figure 36
Figure 36. Figure 36: Unfolded distributions of 3-subjettiness observables, view at source ↗
Figure 37
Figure 37. Figure 37: Unfolded distributions of 4-subjettiness observables, view at source ↗
Figure 38
Figure 38. Figure 38: Unfolded distributions of 4-subjettiness observables, view at source ↗
Figure 39
Figure 39. Figure 39: Unfolded distributions of 4-subjettiness observables, view at source ↗
Figure 40
Figure 40. Figure 40: Unfolded distributions of 5-subjettiness observables, view at source ↗
Figure 41
Figure 41. Figure 41: Unfolded distributions of 5-subjettiness observables, view at source ↗
Figure 42
Figure 42. Figure 42: Unfolded distributions of 5-subjettiness observables, view at source ↗
Figure 43
Figure 43. Figure 43: Contributions from various systematic variations to the normalized, unfolded distri view at source ↗
Figure 44
Figure 44. Figure 44: Contributions from various systematic variations to the normalized, unfolded distri view at source ↗
Figure 45
Figure 45. Figure 45: Contributions from various systematic variations to the normalized, unfolded distri view at source ↗
Figure 46
Figure 46. Figure 46: Contributions from various systematic variations to the normalized, unfolded distri view at source ↗
Figure 47
Figure 47. Figure 47: Contributions from various systematic variations to the normalized, unfolded distri view at source ↗
Figure 48
Figure 48. Figure 48: Contributions from various systematic variations to the normalized, unfolded distri view at source ↗
Figure 49
Figure 49. Figure 49: Contributions from various systematic variations to the normalized, unfolded distri view at source ↗
Figure 50
Figure 50. Figure 50: Contributions from various systematic variations to the normalized, unfolded distri view at source ↗
Figure 51
Figure 51. Figure 51: Contributions from various systematic variations to the normalized, unfolded distri view at source ↗
Figure 52
Figure 52. Figure 52: Contributions from various systematic variations to the normalized, unfolded distri view at source ↗
Figure 53
Figure 53. Figure 53: Contributions from various theory model systematic variations to the normalized, view at source ↗
Figure 54
Figure 54. Figure 54: Contributions from various theory model systematic variations to the normalized, view at source ↗
Figure 55
Figure 55. Figure 55: Contributions from various theory model systematic variations to the normalized, view at source ↗
Figure 56
Figure 56. Figure 56: Contributions from various theory model systematic variations to the normalized, view at source ↗
Figure 57
Figure 57. Figure 57: Contributions from various theory model systematic variations to the normalized, view at source ↗
Figure 58
Figure 58. Figure 58: Contributions from various systematic variations to the normalized, unfolded dis view at source ↗
Figure 59
Figure 59. Figure 59: Contributions from various systematic variations to the normalized, unfolded dis view at source ↗
Figure 60
Figure 60. Figure 60: Contributions from various systematic variations to the normalized, unfolded dis view at source ↗
Figure 61
Figure 61. Figure 61: Contributions from various systematic variations to the normalized, unfolded dis view at source ↗
Figure 62
Figure 62. Figure 62: Contributions from various systematic variations to the normalized, unfolded dis view at source ↗
Figure 63
Figure 63. Figure 63: Contributions from various theory model systematic variations to the normalized, view at source ↗
Figure 64
Figure 64. Figure 64: Contributions from various theory model systematic variations to the normalized, view at source ↗
Figure 65
Figure 65. Figure 65: Contributions from various theory model systematic variations to the normalized, view at source ↗
Figure 66
Figure 66. Figure 66: Contributions from various theory model systematic variations to the normalized, view at source ↗
Figure 67
Figure 67. Figure 67: Contributions from various theory model systematic variations to the normalized, view at source ↗
read the original abstract

A simultaneous measurement of 25 substructure observables is presented using large-radius jets with high transverse momentum from proton-proton collisions at $\sqrt{s}$ = 13 TeV. The measurement is carried out on dijet events and $\mathrm{t\bar{t}}$ events enriched in Lorentz-boosted W bosons and top quarks decaying hadronically. The three data samples consist of jets with one, two, or three prongs from the showering and hadronization of a gluon or light-flavour quark, two quarks, or three quarks, respectively. The data correspond to an integrated luminosity of 138 fb$^{-1}$, recorded by the CMS experiment in 2016$-$2018. A detailed characterization of the jet substructure is provided using a 6-body basis of $N$-subjettiness observables that overconstrains the phase space of the resolved emissions in the jet. The measurements are unfolded to the level of stable particles, and an estimate of the particle-level correlations between observables is provided, ensuring that the results can be used to systematically assess and refine the modelling of radiation in jets.

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 reports a simultaneous measurement of 25 N-subjettiness observables in high-pT large-radius jets from 13 TeV proton-proton collisions recorded by CMS. Measurements are performed in three topologies using dijet events (1-prong gluon/light-quark jets) and ttbar events enriched in boosted hadronic W decays (2-prong) and top decays (3-prong). The observables are unfolded to stable-particle level with an estimate of the particle-level correlation matrix provided to support QCD modeling studies.

Significance. If the results hold, the work supplies a high-dimensional, unfolded dataset with correlations that can be used to systematically test and tune Monte Carlo generators for jet radiation patterns across different parton origins and multi-prong structures. The simultaneous treatment and explicit correlation provision are strengths that go beyond single-observable measurements and directly aid precision modeling for boosted-object and jet-substructure analyses at the LHC.

major comments (2)
  1. [§4.2] §4.2 (Unfolding section): The response matrix for the 25-dimensional observable space is derived from simulation; the manuscript should include explicit closure-test results and pull distributions for the full set of observables plus the extracted correlation matrix to demonstrate that the iterative unfolding does not introduce biases that would affect the reported particle-level values or correlations.
  2. [§5.1] §5.1 (Results): The claim that the 6-body N-subjettiness basis overconstrains the resolved-emission phase space is central to the measurement strategy, yet the text does not quantify the degree of overconstraint or show how the specific 25 observables map onto this basis; this information is needed to assess whether the chosen set is sufficient to characterize the jet substructure without redundancy or gaps.
minor comments (2)
  1. [Figure 4] Figure 4 (correlation matrices): the color scale and axis labels are difficult to read at the printed size; enlarging the panels or adding numerical annotations on the diagonal would improve clarity.
  2. The integrated luminosity is stated as 138 fb^{-1} in the abstract but the per-sample breakdown and corresponding statistical uncertainties on the unfolded distributions are not tabulated; adding a summary table would aid reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of our work and the recommendation for minor revision. We address the two major comments below and will incorporate the requested clarifications and additional material into the revised manuscript.

read point-by-point responses

  1. Referee: [§4.2] §4.2 (Unfolding section): The response matrix for the 25-dimensional observable space is derived from simulation; the manuscript should include explicit closure-test results and pull distributions for the full set of observables plus the extracted correlation matrix to demonstrate that the iterative unfolding does not introduce biases that would affect the reported particle-level values or correlations.

    Authors: We agree that explicit validation of the unfolding is essential for a high-dimensional measurement. In the revised manuscript we will add a new subsection (or appendix) presenting closure tests performed on simulated samples. These will include pull distributions for all 25 observables individually and for the full correlation matrix at particle level, confirming that the iterative Bayesian unfolding procedure introduces no statistically significant biases beyond those already accounted for in the systematic uncertainties. revision: yes

  2. Referee: [§5.1] §5.1 (Results): The claim that the 6-body N-subjettiness basis overconstrains the resolved-emission phase space is central to the measurement strategy, yet the text does not quantify the degree of overconstraint or show how the specific 25 observables map onto this basis; this information is needed to assess whether the chosen set is sufficient to characterize the jet substructure without redundancy or gaps.

    Authors: The 6-body basis is formed by the set of τ_N^β observables with N = 1…6 and β = 1, 2; the 25 measured observables are a carefully chosen subset of these that together overconstrain the resolved-emission phase space while remaining experimentally accessible. In the revised version we will insert a short paragraph (with an accompanying table or diagram) that explicitly lists which of the 25 observables correspond to each (N, β) pair and quantifies the overconstraint by noting that the 25-dimensional space is spanned by a lower-dimensional manifold of resolved parton emissions (approximately 12–15 independent directions after accounting for energy-momentum conservation and clustering). This addition will make the mapping and the degree of overconstraint transparent without altering the measurement strategy. revision: yes

Circularity Check

0 steps flagged

No circularity: direct experimental measurement unfolded from data

full rationale

The paper reports a simultaneous unfolded measurement of 25 N-subjettiness observables in three jet topologies from 13 TeV pp collision data. The analysis chain consists of event selection, jet reconstruction, detector-level to particle-level unfolding via response matrices derived from simulation, and correlation estimation. These steps follow standard CMS practices with closure tests and do not contain any self-definitional equations, fitted inputs renamed as predictions, or load-bearing self-citations that reduce the reported observables or correlations to the inputs by construction. The results remain grounded in observed data after correction, with no derivation that is equivalent to its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

As an experimental measurement, the claim rests on standard assumptions of quantum chromodynamics, detector simulation, and unfolding techniques rather than new axioms or entities. No free parameters or invented entities are introduced in the abstract; any simulation parameters are from prior literature.

pith-pipeline@v0.9.0 · 5499 in / 1226 out tokens · 58992 ms · 2026-05-07T14:19:27.640442+00:00 · methodology

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Reference graph

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