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arxiv: 2506.03782 · v2 · submitted 2025-06-04 · ✦ hep-ph · hep-ex· hep-th· nucl-ex· nucl-th

Event Topology Classifiers at the Large Hadron Collider

Suraj Prasad , Sushanta Tripathy , Bhagyarathi Sahoo , Raghunath Sahoo This is my paper

Pith reviewed 2026-05-19 11:32 UTC · model grok-4.3

classification ✦ hep-ph hep-exhep-thnucl-exnucl-th
keywords event topologytransverse sphericitytransverse spherocityquark-gluon plasmahigh-multiplicity collisionsLHCproton-proton collisionsevent-shape observables
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The pith

Event topology classifiers such as transverse sphericity isolate QGP-like signals in high-multiplicity proton-proton collisions with reduced biases.

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

The paper reviews the development and application of event-shape observables at the LHC over five decades. It focuses on transverse sphericity, transverse spherocity, relative transverse activity classifier, and charged-particle flattenicity as tools to classify collision topologies. These observables are presented as a way to compare high-multiplicity proton-proton events with heavy-ion collisions while minimizing autocorrelation and selection biases. The infrared and collinear safety of the observables is highlighted for precision work on jets and heavy flavors. A reader would care because the review sets up methods for testing whether small systems can produce the same collective phenomena traditionally linked to large collision systems.

Core claim

Event classifiers are fundamental observables for probing event topology in hadronic and nuclear collisions. Recent measurements show high-multiplicity proton-proton collisions exhibit features similar to quark-gluon plasma formation previously thought possible only in heavy nucleus-nucleus collisions. To pinpoint the origin of these features with reduced biases and place all collision systems on equal footing, the paper summarizes the motivation, scope, and practical use of transverse sphericity, transverse spherocity, relative transverse activity classifier, and charged-particle flattenicity, integrating results from all major LHC experiments.

What carries the argument

Event topology classifiers (transverse sphericity, transverse spherocity, relative transverse activity classifier, and charged-particle flattenicity) that sort events according to the spatial distribution of final-state particles to separate different underlying physics processes.

If this is right

  • The classifiers allow direct comparison of proton-proton, proton-nucleus, and nucleus-nucleus data on the same footing.
  • Infrared and collinear safety supports cleaner extraction of jet and heavy-flavor observables across LHC energies.
  • Results can be used to prepare analysis strategies for Run 3, Run 4, and high-luminosity LHC data taking.

Where Pith is reading between the lines

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

  • If the classifiers prove robust, they could be tested for consistency across different center-of-mass energies in future collider runs.
  • Application of the same observables to lower-energy fixed-target data might reveal the energy threshold for the onset of the reported similarities.
  • Cross-checks between the four listed classifiers on identical datasets would quantify how much independent information each contributes.

Load-bearing premise

The assumption that high-multiplicity proton-proton collisions produce features genuinely similar to quark-gluon plasma formation and that these classifiers can isolate the similarity without adding new biases.

What would settle it

A controlled Monte Carlo study in which the classifiers return the same distribution for events with and without collective flow when the underlying generator is known to lack plasma-like behavior.

Figures

Figures reproduced from arXiv: 2506.03782 by Bhagyarathi Sahoo, Raghunath Sahoo, Suraj Prasad, Sushanta Tripathy.

Figure 1
Figure 1. Figure 1: FIG. 1. Pictorial representation of multi-partonic interactions (MPI) in [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Pictorial representation of Color Reconnection (CR) [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Schematic showing different types of interactions in [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. A schematic representation of the correlation between [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Schematic representation of the Optical Glauber Model geometry, with transverse (a) and longitudinal (b) views. [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Self-normalised Charged-particle multiplicity distributions measured in mid (left panel) and forward (right panel) [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Distribution of number of multi-partonic interactions [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Correlation of mid (left panel) and forward (right panel) rapidity charged-particle multiplicity with number of MPI in [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Transverse sphericity distributions measured in [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Depiction of isotropic and jetty events based on the [PITH_FULL_IMAGE:figures/full_fig_p009_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Weighted and unweighted transverse spherocity distributions measured in [PITH_FULL_IMAGE:figures/full_fig_p010_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Correlation of [PITH_FULL_IMAGE:figures/full_fig_p011_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Correlation of [PITH_FULL_IMAGE:figures/full_fig_p012_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Depiction of different topological regions with re [PITH_FULL_IMAGE:figures/full_fig_p012_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16 [PITH_FULL_IMAGE:figures/full_fig_p013_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Distribution of [PITH_FULL_IMAGE:figures/full_fig_p014_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. Correlation of [PITH_FULL_IMAGE:figures/full_fig_p015_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19. charged-particle flattenicity distributions measured [PITH_FULL_IMAGE:figures/full_fig_p016_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: FIG. 20. Correlation of flattenicity with number of MPI [PITH_FULL_IMAGE:figures/full_fig_p016_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: FIG. 21. Depiction of thrust axis used as reference to study [PITH_FULL_IMAGE:figures/full_fig_p017_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: FIG. 22. The distribution of thrust [PITH_FULL_IMAGE:figures/full_fig_p018_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: FIG. 23. The first moment of the event shape variables thrust [PITH_FULL_IMAGE:figures/full_fig_p019_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: FIG. 24. Self-normalied yield of charged particles integrated [PITH_FULL_IMAGE:figures/full_fig_p021_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: FIG. 25. Transverse momentum distribution of charged pions for different slices of midrapidity (left panel) and forward [PITH_FULL_IMAGE:figures/full_fig_p022_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: FIG. 26. Correlation between [PITH_FULL_IMAGE:figures/full_fig_p023_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: FIG. 27. Top panel shows the transverse momentum distri [PITH_FULL_IMAGE:figures/full_fig_p023_27.png] view at source ↗
Figure 29
Figure 29. Figure 29: FIG. 29. Top panel shows the transverse momentum distribution of charged pions for different slices of [PITH_FULL_IMAGE:figures/full_fig_p024_29.png] view at source ↗
Figure 30
Figure 30. Figure 30: FIG. 30. Top panel shows the transverse momentum distribution of charged pions for different slices of [PITH_FULL_IMAGE:figures/full_fig_p025_30.png] view at source ↗
Figure 31
Figure 31. Figure 31: FIG. 31. Transverse momentum spectra of charged particles in toward, away, and transverse regions, from left to right for [PITH_FULL_IMAGE:figures/full_fig_p026_31.png] view at source ↗
Figure 32
Figure 32. Figure 32: FIG. 32. Transverse momentum spectra of pions in toward, away, and transverse regions, from left to right for different events [PITH_FULL_IMAGE:figures/full_fig_p027_32.png] view at source ↗
Figure 33
Figure 33. Figure 33: FIG. 33. Top panel shows the transverse momentum distri [PITH_FULL_IMAGE:figures/full_fig_p028_33.png] view at source ↗
Figure 34
Figure 34. Figure 34: FIG. 34. The upper panel shows the transverse momentum distribution of charged pions, kaons, protons, and charged hadrons, [PITH_FULL_IMAGE:figures/full_fig_p029_34.png] view at source ↗
Figure 35
Figure 35. Figure 35: FIG. 35. Mean transverse momentum of all charged and iden [PITH_FULL_IMAGE:figures/full_fig_p029_35.png] view at source ↗
Figure 36
Figure 36. Figure 36: FIG. 36. Mean transverse momentum of all charged and identified hadrons as a function of charged-particle multiplicity in [PITH_FULL_IMAGE:figures/full_fig_p030_36.png] view at source ↗
Figure 37
Figure 37. Figure 37: FIG. 37. Mean transverse momentum of all charged and iden [PITH_FULL_IMAGE:figures/full_fig_p030_37.png] view at source ↗
Figure 38
Figure 38. Figure 38: FIG. 38. Mean transverse momentum of all charged particles as a function of transverse sphericity ( [PITH_FULL_IMAGE:figures/full_fig_p031_38.png] view at source ↗
Figure 39
Figure 39. Figure 39: FIG. 39. Mean transverse momentum of all charged and identified hadrons as a function of [PITH_FULL_IMAGE:figures/full_fig_p031_39.png] view at source ↗
Figure 40
Figure 40. Figure 40: FIG. 40. Average transverse momentum ( [PITH_FULL_IMAGE:figures/full_fig_p032_40.png] view at source ↗
Figure 41
Figure 41. Figure 41: FIG. 41. Mean transverse momentum of all charged and identified hadrons as a function of [PITH_FULL_IMAGE:figures/full_fig_p033_41.png] view at source ↗
Figure 42
Figure 42. Figure 42: FIG. 42. Average transverse momentum ( [PITH_FULL_IMAGE:figures/full_fig_p034_42.png] view at source ↗
Figure 43
Figure 43. Figure 43: FIG. 43. Mean transverse momentum of all charged and iden [PITH_FULL_IMAGE:figures/full_fig_p034_43.png] view at source ↗
Figure 44
Figure 44. Figure 44: FIG. 44 [PITH_FULL_IMAGE:figures/full_fig_p035_44.png] view at source ↗
Figure 45
Figure 45. Figure 45: FIG. 45 [PITH_FULL_IMAGE:figures/full_fig_p036_45.png] view at source ↗
Figure 46
Figure 46. Figure 46: FIG. 46 [PITH_FULL_IMAGE:figures/full_fig_p036_46.png] view at source ↗
Figure 47
Figure 47. Figure 47: FIG. 47 [PITH_FULL_IMAGE:figures/full_fig_p037_47.png] view at source ↗
Figure 48
Figure 48. Figure 48: FIG. 48 [PITH_FULL_IMAGE:figures/full_fig_p037_48.png] view at source ↗
Figure 49
Figure 49. Figure 49: FIG. 49. Ratio of particle yield to pions as a function of unweighted transverse spherocity in high multiplicity events based [PITH_FULL_IMAGE:figures/full_fig_p038_49.png] view at source ↗
Figure 50
Figure 50. Figure 50: FIG. 50 [PITH_FULL_IMAGE:figures/full_fig_p038_50.png] view at source ↗
Figure 51
Figure 51. Figure 51: FIG. 51 [PITH_FULL_IMAGE:figures/full_fig_p039_51.png] view at source ↗
Figure 52
Figure 52. Figure 52: FIG. 52 [PITH_FULL_IMAGE:figures/full_fig_p040_52.png] view at source ↗
Figure 53
Figure 53. Figure 53: FIG. 53 [PITH_FULL_IMAGE:figures/full_fig_p041_53.png] view at source ↗
Figure 54
Figure 54. Figure 54: FIG. 54 [PITH_FULL_IMAGE:figures/full_fig_p042_54.png] view at source ↗
Figure 55
Figure 55. Figure 55: FIG. 55 [PITH_FULL_IMAGE:figures/full_fig_p043_55.png] view at source ↗
Figure 56
Figure 56. Figure 56: FIG. 56 [PITH_FULL_IMAGE:figures/full_fig_p044_56.png] view at source ↗
Figure 57
Figure 57. Figure 57: FIG. 57 [PITH_FULL_IMAGE:figures/full_fig_p045_57.png] view at source ↗
Figure 58
Figure 58. Figure 58: FIG. 58 [PITH_FULL_IMAGE:figures/full_fig_p046_58.png] view at source ↗
Figure 59
Figure 59. Figure 59: FIG. 59 [PITH_FULL_IMAGE:figures/full_fig_p047_59.png] view at source ↗
Figure 60
Figure 60. Figure 60: FIG. 60 [PITH_FULL_IMAGE:figures/full_fig_p048_60.png] view at source ↗
Figure 61
Figure 61. Figure 61: FIG. 61 [PITH_FULL_IMAGE:figures/full_fig_p049_61.png] view at source ↗
Figure 62
Figure 62. Figure 62: FIG. 62 [PITH_FULL_IMAGE:figures/full_fig_p050_62.png] view at source ↗
Figure 63
Figure 63. Figure 63: FIG. 63 [PITH_FULL_IMAGE:figures/full_fig_p051_63.png] view at source ↗
Figure 64
Figure 64. Figure 64: FIG. 64 [PITH_FULL_IMAGE:figures/full_fig_p052_64.png] view at source ↗
Figure 65
Figure 65. Figure 65: FIG. 65. Elliptic flow ( [PITH_FULL_IMAGE:figures/full_fig_p052_65.png] view at source ↗
Figure 66
Figure 66. Figure 66: FIG. 66. The azimuthal associated yield for the long-range region 1.6 [PITH_FULL_IMAGE:figures/full_fig_p053_66.png] view at source ↗
Figure 67
Figure 67. Figure 67: FIG. 67 [PITH_FULL_IMAGE:figures/full_fig_p053_67.png] view at source ↗
Figure 68
Figure 68. Figure 68: FIG. 68 [PITH_FULL_IMAGE:figures/full_fig_p054_68.png] view at source ↗
Figure 69
Figure 69. Figure 69: FIG. 69. Top panel [PITH_FULL_IMAGE:figures/full_fig_p055_69.png] view at source ↗
Figure 70
Figure 70. Figure 70: FIG. 70. Transverse momentum space correlation ( [PITH_FULL_IMAGE:figures/full_fig_p056_70.png] view at source ↗
Figure 71
Figure 71. Figure 71: FIG. 71. Two-particle azimuthal correlation function for dif [PITH_FULL_IMAGE:figures/full_fig_p056_71.png] view at source ↗
Figure 72
Figure 72. Figure 72: FIG. 72. Elliptic (top) and triangular (bottom) flow as a function of transverse momentum in (40-50)% centrality for different [PITH_FULL_IMAGE:figures/full_fig_p057_72.png] view at source ↗
Figure 73
Figure 73. Figure 73: FIG. 73. Elliptic (top) and triangular (bottom) flow as a function of centrality for different spherocity selections in Pb–Pb [PITH_FULL_IMAGE:figures/full_fig_p057_73.png] view at source ↗
Figure 74
Figure 74. Figure 74: FIG. 74 [PITH_FULL_IMAGE:figures/full_fig_p058_74.png] view at source ↗
Figure 75
Figure 75. Figure 75: FIG. 75. Transverse spherocity and collision centrality dependence of symmetry plane correlations using Gaussian Estimator [PITH_FULL_IMAGE:figures/full_fig_p058_75.png] view at source ↗
Figure 76
Figure 76. Figure 76: FIG. 76. Transverse spherocity dependence of kinetic freeze [PITH_FULL_IMAGE:figures/full_fig_p059_76.png] view at source ↗
Figure 77
Figure 77. Figure 77: FIG. 77. Azimuthal dependence of two-particle correlation function ( [PITH_FULL_IMAGE:figures/full_fig_p060_77.png] view at source ↗
Figure 78
Figure 78. Figure 78: FIG. 78 [PITH_FULL_IMAGE:figures/full_fig_p061_78.png] view at source ↗
Figure 79
Figure 79. Figure 79: FIG. 79. Ratio of [PITH_FULL_IMAGE:figures/full_fig_p062_79.png] view at source ↗
Figure 80
Figure 80. Figure 80: FIG. 80. Correlation matrix showing the values of the cor [PITH_FULL_IMAGE:figures/full_fig_p062_80.png] view at source ↗
Figure 81
Figure 81. Figure 81: FIG. 81. (Top) Evolution of mean-absolute error (∆ [PITH_FULL_IMAGE:figures/full_fig_p063_81.png] view at source ↗
Figure 82
Figure 82. Figure 82: FIG. 82. Predicted spherocity distribution from the GBDT model (red) compared to the true spherocity distribution from [PITH_FULL_IMAGE:figures/full_fig_p063_82.png] view at source ↗
read the original abstract

Event classifiers are the most fundamental observables to probe the event topology of hadronic and nuclear collisions at relativistic energies. Over the last five decades, significant progress has been made to establish suitable event classifiers to probe different physics processes occurring in elementary $e^{+}e^{-}$ to heavy-ion collisions in a broad range of center of mass energies. One of the major motivations to revisit event classifiers at the Large Hadron Collider (LHC) originates from the recent measurements of high multiplicity proton-proton collisions, which have revealed that these small collision systems exhibit features similar to the formation of quark-gluon plasma (QGP), traditionally believed to be only achievable in heavy nucleus-nucleus collisions at ultra-relativistic energies. To pinpoint the origin of these QGP-like phenomena with substantially reduced autocorrelation and selection biases, and to bring all collision systems on equal footing, along with charged-particle multiplicity, lately several event topology classifiers such as transverse sphericity, transverse spherocity, relative transverse activity classifier, and charged-particle flattenicity have been used extensively in experiments as well as in the phenomenological front. In addition, the infrared and collinear safety of event-shape observables makes them ideal for precision studies of jets and heavy-flavors at the LHC. In this review article, we summarise the motivation, scope, and practical use of these event-shape observables. The discussion integrates results and insights from all major LHC experiments, setting the stage for precision investigations for Run 3, Run 4, and future high luminosity upgrades of the LHC.

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

0 major / 2 minor

Summary. This review summarizes the motivation, scope, and LHC results for event topology classifiers (transverse sphericity, transverse spherocity, relative transverse activity classifier, and charged-particle flattenicity) in high-multiplicity proton-proton collisions. The central claim is that these observables help isolate QGP-like features with reduced autocorrelation and selection biases relative to multiplicity alone, drawing on existing experimental and phenomenological literature from all major LHC experiments while noting the infrared/collinear safety of the relevant observables.

Significance. If the citations are accurate and representative, the review provides a useful compilation of results and motivations for these classifiers, serving as a reference for precision studies in Run 3, Run 4, and high-luminosity LHC upgrades. It explicitly credits the infrared and collinear safety properties and the integration of multi-experiment data as strengths for jet and heavy-flavor analyses.

minor comments (2)
  1. Abstract, motivation paragraph: the phrasing 'substantially reduced autocorrelation and selection biases' is repeated from the reader's strongest claim but would benefit from a single concrete example (e.g., a cited LHC measurement) to illustrate the reduction relative to multiplicity-only selections.
  2. The manuscript correctly frames the infrared/collinear safety discussion as background rather than a new result; however, a brief table comparing safety properties across the four listed classifiers would improve clarity for readers new to the topic.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the positive assessment of its scope and utility as a reference for LHC studies in Runs 3 and 4. The recommendation for minor revision is noted. No specific major comments were enumerated in the report, so we have no individual points requiring detailed rebuttal at this stage. We will perform a minor revision to ensure all citations remain accurate and representative, as flagged in the significance statement, and to incorporate any editorial suggestions.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

This is a review article summarizing motivation, scope, and existing LHC results for event topology classifiers such as transverse sphericity and spherocity. No new derivations, equations, or fitted parameters are introduced that could reduce to the paper's own inputs by construction. All central claims draw on external experimental and phenomenological literature from multiple independent sources, rendering the content self-contained against external benchmarks with no load-bearing self-citation chains or self-definitional steps.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

As a review article the paper introduces no new free parameters, axioms, or invented entities; it aggregates previously published definitions and measurements of event classifiers.

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