Recognition: 2 theorem links
· Lean TheoremThe anti-k_t jet clustering algorithm
Pith reviewed 2026-05-13 00:43 UTC · model grok-4.3
The pith
The anti-k_t algorithm produces conical jets with equal active and passive areas while remaining infrared and collinear safe.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
The anti-k_t algorithm essentially behaves like an idealised cone algorithm, in that jets with only soft fragmentation are conical, active and passive areas are equal, the area anomalous dimensions are zero, the non-global logarithms are those of a rigid boundary and the Milan factor is universal. It provides a natural, fast, infrared and collinear safe replacement for the collinear unsafe plain iterative cone algorithm. None of these properties hold for existing sequential recombination algorithms, nor for cone algorithms with split-merge steps, such as SISCone.
What carries the argument
The anti-k_t distance measure, parametrised by a negative power of the transverse-momentum scale in the recombination criterion.
If this is right
- Jets remain conical even when soft particles are present.
- Jet-area calculations simplify because active and passive measures coincide.
- Resummation of large logarithms is eased by vanishing area anomalous dimensions.
- Non-global logarithms follow the same pattern as for a fixed cone boundary.
- Analyses can replace the plain iterative cone with a safe, fast equivalent.
Where Pith is reading between the lines
- This algorithm could reduce sensitivity of jet observables to soft underlying-event modeling in high-luminosity collider data.
- Phenomenologists might re-analyze older data sets that relied on iterative cones to check for shifts in extracted quantities.
- Further variants with other negative exponents could be explored to tune jet properties for specific measurements.
- The approach highlights how the sign of the power in the distance measure controls global versus local clustering behavior.
Load-bearing premise
The analytic properties derived from the negative-power distance measure continue to hold in realistic hadron-hadron collisions that include underlying event and multiple parton interactions.
What would settle it
Monte Carlo simulations that compare measured jet shapes and active versus passive areas for the anti-k_t algorithm against those of the plain iterative cone under controlled soft radiation, checking whether conicity and area equality are preserved.
read the original abstract
The k_t and Cambridge/Aachen inclusive jet finding algorithms for hadron-hadron collisions can be seen as belonging to a broader class of sequential recombination jet algorithms, parametrised by the power of the energy scale in the distance measure. We examine some properties of a new member of this class, for which the power is negative. This ``anti-k_t'' algorithm essentially behaves like an idealised cone algorithm, in that jets with only soft fragmentation are conical, active and passive areas are equal, the area anomalous dimensions are zero, the non-global logarithms are those of a rigid boundary and the Milan factor is universal. None of these properties hold for existing sequential recombination algorithms, nor for cone algorithms with split--merge steps, such as SISCone. They are however the identifying characteristics of the collinear unsafe plain ``iterative cone'' algorithm, for which the anti-k_t algorithm provides a natural, fast, infrared and collinear safe replacement.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript introduces the anti-k_t jet clustering algorithm as a sequential recombination method parametrized by a negative power in the distance measure. It derives that jets with only soft fragmentation are conical, that active and passive areas are equal, that area anomalous dimensions vanish, that non-global logarithms match those of a rigid boundary, and that the Milan factor is universal. These properties are presented as direct consequences of the distance measure, positioning the algorithm as a fast, infrared- and collinear-safe replacement for the plain iterative cone algorithm.
Significance. If the derived properties hold, the anti-k_t algorithm supplies a theoretically clean and computationally efficient tool for jet reconstruction that combines the intuitive geometry of idealised cone algorithms with the infrared/collinear safety of sequential recombination. The absence of free parameters or post-hoc fitting in the central derivations is a notable strength, providing a robust foundation for use in hadron-collider phenomenology.
minor comments (2)
- §2: the explicit form of the distance measure d_{ij} with negative power could be written out once more after the general parametrisation to aid readers comparing with the k_t and Cambridge/Aachen cases.
- Figure 2 (jet-area illustrations): the passive-area boundaries would be easier to interpret if the underlying hard partons were marked with distinct symbols.
Simulated Author's Rebuttal
We thank the referee for their careful reading of the manuscript and for recommending acceptance. The provided summary accurately reflects the central results on the properties of the anti-k_t algorithm.
Circularity Check
No significant circularity identified
full rationale
The paper introduces the anti-k_t algorithm by selecting a negative power in the sequential recombination distance measure (a direct generalization of k_t and Cambridge/Aachen). The listed properties—conical jets for soft fragmentation, equality of active and passive areas, vanishing area anomalous dimensions, rigid-boundary non-global logarithms, and universal Milan factor—are derived as analytic consequences of that choice for parton-level configurations. These follow from the definition without reduction to fitted parameters, self-citation chains, or renaming of prior results. IRC safety is inherited from the sequential recombination class by construction, which is standard and externally verifiable. No load-bearing step collapses to an input by definition; the derivation remains self-contained.
Axiom & Free-Parameter Ledger
axioms (2)
- domain assumption Sequential recombination jet algorithms are parametrized by the power of the energy scale in the distance measure
- domain assumption Infrared and collinear safety are required for perturbative QCD calculations
Forward citations
Cited by 36 Pith papers
-
Search for single vector-like quark production in opposite-sign dilepton final states in proton-proton collisions at $\sqrt{s}$ = 13 TeV
No excess observed in search for vector-like top quark T to tH in opposite-sign dilepton final states; 95% CL upper limits on sigma times BR range from 2.0 pb at 600 GeV to 0.1 pb at 1000 GeV.
-
Energy Correlators Within Jets in Transversely Polarized Proton-Proton Collisions at $\sqrt{s} = 200$ GeV
First measurement of energy correlators in jets from transversely polarized pp collisions at 200 GeV shows sizable spin asymmetries for pions that provide sensitivity to nucleon transversity with reduced fragmentation...
-
Probing Boosted Light Scalars in the Type-I 2HDM
Boosted light scalars decaying to b b-bar in Type-I 2HDM can be tagged as double-b fat-jets and used with SM gauge bosons to probe heavy scalars up to 540 GeV at the HL-LHC for masses 30-70 GeV.
-
Precision Cell Resampling with a Relative and Resonant Aware Metric
A resonance-sensitive metric using relative transverse momenta allows cell resampling to reduce negative weights in NLO W+2jets samples while preserving resonance predictions with high accuracy.
-
Physics inspired quantum algorithm for QCD splitting functions
A modular two-qubit quantum circuit is constructed to encode the concurrence of helicity entanglement in pure-gluon splitting, with parameters calibrated to LHC jet data so that composed circuits reproduce experimenta...
-
Measurement of jet photoproduction in ultra-peripheral Pb+Pb collisions without nuclear breakup at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV with the ATLAS detector
First measurement of γ+IP→jets cross-sections in 0n0n ultra-peripheral Pb+Pb collisions at 5.02 TeV, achieved by statistically separating photon-pomeron, photon-photon, and peripheral photonuclear contributions via te...
-
Quantum-Inspired Tensor Network Autoencoders for Anomaly Detection: A MERA-Based Approach
A MERA-based autoencoder supplies a locality-aware hierarchical inductive bias that improves reconstruction-based anomaly detection for collider jets, with disentanglers providing benefit at strong compression bottlenecks.
-
Many Wrongs Make a Right: Leveraging Biased Simulations Towards Unbiased Parameter Inference
Template-Adapted Mixture Model uses many biased simulations for data-driven estimates of signal and background distributions, yielding unbiased signal fraction estimates with well-calibrated uncertainties.
-
The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations
MadGraph5_aMC@NLO automates tree-level, NLO, shower-matched, and merged cross-section computations for collider processes in a unified flexible framework.
-
NLO QCD and parton-shower effects for Higgs-boson production in association with a hard photon via vector-boson fusion
NLO QCD plus parton-shower matched implementation for VBF Higgs plus photon production, with studies showing small shower effects on Higgs observables and larger effects on sub-leading jets.
-
SMEFT everywhere: a NLO study of $\boldsymbol{pp \to t\bar{t}H}$ with decaying tops
NLO QCD corrections to pp to ttbar H in the di-lepton channel with SMEFT operators included in both production and top-quark decays.
-
Composite top partners in exotic colour representations
Colour-sextet top partners in composite Higgs models are excluded up to 2-2.5 TeV by current LHC data via top-rich decays, with HL-LHC reach near 3 TeV.
-
Observation of impact parameter dependent modifications of nuclear parton distributions in photonuclear Pb+Pb collisions at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV with the ATLAS detector
ATLAS reports a 6 sigma observation that nuclear parton distribution modifications in photonuclear Pb+Pb collisions depend on impact parameter, shown by differing cross-section shapes versus x+ with and without forwar...
-
How Invisible: Regressing The Key Model Parameter for Semi-visible Jet Searches
A regression model reconstructs the key parameter r_inv for semi-visible jets at higher precision than prior analytical methods and may unify s- and t-channel production searches.
-
A new approach to long-lived particle detection at hadron colliders: the $\textsf{DELIGHT-SHIELD}$ concept
DELIGHT-SHIELD uses a dedicated shield followed by tracking to suppress hadronic and electromagnetic backgrounds by up to seven orders of magnitude, reaching branching ratio sensitivity of O(10^{-9}) for h to phi phi ...
-
Measurement of jet quenching in O+O collisions at $\sqrt{s_\mathrm{NN}}=200$ GeV by the STAR experiment at RHIC
STAR reports 20% suppression of recoiling hadrons and jets in high-event-activity O+O collisions at 200 GeV, with a measured 0.7 GeV/c pT shift for large-radius jets, providing evidence for jet quenching in small systems.
-
Dijet invariant mass of charged-particle jets in pp and p-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV
The first measurement of charged-particle dijet invariant mass spectra shows no significant nuclear modification in p-Pb collisions at low masses.
-
Search for pair production of additional neutral scalars within the Inert Doublet Model in a final state with two electrons or two muons in proton-proton collisions at $\sqrt{s}$ = 13 TeV and 13.6 TeV
No significant excess found; new exclusion limits reach m_H = 108 GeV for m_H - m_A = 78 GeV in the Inert Doublet Model.
-
Time-dependent signals of new physics at the LHC
Incorporating timing information from time-dependent new physics signals can improve LHC search sensitivity by up to a factor of two compared to standard time-invariant analyses.
-
Explainable AI for Jet Tagging: A Comparative Study of GNNExplainer, GNNShap, and GradCAM for Jet Tagging in the Lund Jet Plane
Explainability techniques applied to LundNet show that assigned node importance correlates with classical jet substructure observables such as N-subjettiness ratios and energy correlation functions, with shifts across...
-
Kitchen Sink Anomaly Detection
A combined kitchen sink observable set of Energy Flow Polynomials and subjettiness variables outperforms standard baselines in sensitivity to a wide range of resonant signals, with new public benchmarks released and a...
-
Quantum Tomography and Entanglement in Semi-Leptonic $h\to VV^*$ Decays at Higher Orders
Semi-leptonic h to VV* decays retain an effective two-qutrit description for quantum tomography and entanglement after including finite fermion masses and NLO corrections.
-
Logarithmic EW corrections at two-loop
Implementation of NNLO EW NLL corrections in OpenLoops for massless fermions and transversely polarized vector bosons, validated against analytic results and applied to representative LHC processes.
-
LHC signatures of a light pseudoscalar in a flipped two-Higgs scenario: the usefulness of boosted $b{\bar b}$ pairs
Boosted di-b-jet tagging plus BDT analysis yields 5-10 sigma significance for a light pseudoscalar in flipped 2HDM with 3 ab^{-1} including 10% systematics.
-
DELPHES 3, A modular framework for fast simulation of a generic collider experiment
DELPHES 3 delivers a modular fast-simulation framework with particle-flow and pile-up features for reconstructing physics objects in collider detector studies.
-
Constraints on anomalous Higgs boson couplings to vector bosons and fermions using the $\gamma\gamma$ final state in proton-proton collisions at $\sqrt{s}$ = 13 TeV
Updated constraints from the full Run 2 dataset show no evidence for anomalous Higgs couplings in gluon fusion, vector boson fusion, and associated production modes decaying to two photons.
-
Search for charginos and neutralinos with $B-L$ $R$-parity violating decays in $\sqrt{s}=13$ TeV and $13.6$ TeV $pp$ collisions with the ATLAS detector
No evidence for charginos and neutralinos in R-parity violating Higgs-decay channels; masses 150-1100 GeV excluded at 95% CL assuming equal lepton branching fractions.
-
Phenomenology of electroweak spin-1 resonances
Composite Higgs models with SU(2)_L × SU(2)_R predict spin-1 resonances mixing with electroweak bosons that remain viable at the LHC down to masses of about 1.5 TeV.
-
Search for quantum black holes in lepton+jet final states using proton-proton collisions at $\sqrt{s}=13.6$ TeV with the ATLAS detector
No significant excess of high-mass lepton+jet events is observed in 164 fb^{-1} of 13.6 TeV pp collisions, setting 95% CL upper limits on quantum black hole production cross-section times branching ratio that reach a ...
-
Sensitivity to top-quark FCNC interactions at future muon colliders
A 10 TeV muon collider with 10 ab^{-1} could reach O(10^{-3}) sensitivity on top-quark FCNC couplings, improving current ATLAS/CMS bounds by more than an order of magnitude.
-
Probing Heavy Neutral Higgs Bosons via Single Vector-Like Bottom Quark Production at the HL-LHC
XGBoost multivariate analysis extends the 5-sigma discovery reach for singly produced vector-like bottom quarks decaying via heavy neutral Higgs bosons to 1.6 TeV at the HL-LHC with 3 ab^{-1}.
-
Machine Learning Study on Single Production of a Singlet Vector-like Lepton at the Large Hadron Collider
XGBoost machine learning improves discrimination in LHC searches for singlet vector-like leptons, yielding projected 2σ mass exclusion limits of 620 GeV (three-lepton) and 490 GeV (four-lepton) at 14 TeV with 3000 fb^{-1}.
-
Open LHC Monte Carlo Event Generation
A review of initiatives to make LHC Monte Carlo event generations available as open data to minimize redundant simulations and resource use.
-
Track and Vertex Reconstruction with the ATLAS Inner Detector
ATLAS Inner Detector track and vertex reconstruction maintains high efficiency, good resolution, and low fake rates for up to 80 simultaneous proton-proton interactions in Run 2 and Run 3 data and simulations.
-
FastJet user manual
FastJet is a C++ package providing implementations of sequential recombination jet algorithms, cone algorithms via plugins, jet substructure tools, and pileup estimation for pp and e+e- collisions.
- Looking inside jets: an introduction to jet substructure and boosted-object phenomenology
Reference graph
Works this paper leans on
-
[1]
Successive Combination Jet Algorithm For Hadron Collisions
S. Catani, Y. L. Dokshitzer, M. H. Seymour and B. R. Webber , Nucl. Phys. B 406 (1993) 187 and refs. therein; S. D. Ellis and D. E. Soper, Phys. Rev. D 48 (1993) 3160 [hep-ph/9305266]
work page Pith review arXiv 1993
-
[2]
Y. L. Dokshitzer, G. D. Leder, S. Moretti and B. R. Webber, JHEP 9708, 001 (1997) [hep-ph/9707323]; M. Wobisch and T. Wengler, hep-ph/99072 80
work page Pith review arXiv 1997
- [3]
-
[4]
M. Cacciari, G. P. Salam and G. Soyez, JHEP 0804 (2008) 005 [arXiv:0802.1188]
work page Pith review arXiv 2008
- [5]
-
[6]
CMS physics: Technical design repor t
G. L. Bayatian et al. [CMS Collaboration], “CMS physics: Technical design repor t.”
-
[7]
T. Sjostrand et al. , Comput. Phys. Commun. 135 (2001) 238 [hep-ph/0010017]; T. Sjostrand et al. , hep-ph/0308153
- [8]
-
[9]
Resummation of non-global QCD observables
M. Dasgupta and G. P. Salam, Phys. Lett. B 512, 323 (2001) [arXiv:hep-ph/0104277]
work page Pith review arXiv 2001
-
[10]
M. Dasgupta and G. P. Salam, JHEP 0203 (2002) 017 [arXiv:hep-ph/0203009]
-
[11]
C. F. Berger, T. Kucs and G. Sterman, Phys. Rev. D 68 (2003) 014012 [arXiv:hep-ph/0303051]
work page Pith review arXiv 2003
-
[12]
A. Banfi, G. Marchesini and G. Smye, JHEP 0208 (2002) 006 [arXiv:hep-ph/0206076]
work page Pith review arXiv 2002
- [13]
-
[14]
A. Banfi and M. Dasgupta, JHEP 0401 (2004) 027 [arXiv:hep-ph/0312108]; Y. Delenda, R. Ap- pleby, M. Dasgupta and A. Banfi, JHEP 0612 (2006) 044 [arXiv:hep-ph/0610242]
- [15]
-
[16]
M. Dasgupta, L. Magnea and G. Smye, JHEP 9911 (1999) 025 [arXiv:hep-ph/9911316]
- [17]
- [18]
-
[19]
Dispelling the N^3 myth for the Kt jet-finder
M. Cacciari and G. P. Salam, Phys. Lett. B 641 (2006) 57 [arXiv:hep-ph/0512210]
work page Pith review arXiv 2006
-
[20]
A. Fabri et al. , Softw. Pract. Exper. 30 (2000) 1167; J.-D. Boissonnat et al. , Comp. Geom. 22 (2001) 5
work page 2000
-
[21]
M. Cacciari, G. P. Salam and G. Soyez, http://www.lpthe.jussieu.fr/~salam/fastjet
- [22]
- [23]
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.