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REVIEW 3 major objections 4 minor 85 references

Secondary Lund jet plane as a gluon enriched sample

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The subleading jet of a collinear, asymmetric dijet pair is gluon-initiated about 90% of the time, making its primary Lund plane density a practical proxy for the gluon-rich secondary Lund plane.

desk verdict A simple, credible new route to gluon-enriched jet samples; the 90% purity rests on solid LO work and an indirect but decent MC consistency check. read the letter →

arxiv 2412.14247 v1 pith:SDLBFVPY submitted 2024-12-18 hep-ph hep-exnucl-th

Cristian Baldenegro , Alba Soto-Ontoso , Gregory Soyez This is my paper · ORCID
classification hep-phhep-exnucl-th
keywords gluonjetsLundjetplanesecondarydijetselectionsubstructurequark-gluondiscriminationLHCpartonshowertuning
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

The paper proposes a phase-space selection at the LHC that produces a gluon-enriched sample of jets without taggers or statistical demixing: take a dijet pair with a hard leading jet ($p_t>700$ GeV), a much softer subleading jet ($150

What carries the argument

The central object is the secondary Lund plane density $\rho_s$: the density of emissions obtained by recursively declustering the softer subjet of the primary Cambridge/Aachen declustering, plotted in $(\ln k_t,\ln 1/\Delta)$. Its power comes from the QCD soft singularity, which makes the soft branch of an asymmetric splitting usually a gluon, so $\rho_s$ is dominated by colour factor $C_A$. The dijet selection turns this abstract plane into a measurable object: the subleading jet of a collinear, asymmetric pair is treated as the secondary plane, so its primary Lund plane density, computed with the standard anti-$k_t$ reclustering, is the observable.

What would settle it

Measure the parton flavour of the subleading jet with a quark/gluon discriminator on real LHC data in exactly the fiducial region $p_{t,\mathrm{lead}}>700$ GeV, $150<p_{t,\mathrm{sublead}}<200$ GeV, and $1<\Delta R<1.2$: if the gluon fraction comes out well below 90%, or if the measured subleading-jet Lund plane density deviates from the primary Lund plane of $gg\to gg$ gluon jets by more than the claimed 10% in any $(\ln k_t,\ln 1/\Delta)$ bin, the equivalence breaks.

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Extended reading notes

Core claim

The central claim is that the secondary Lund plane, the set of emissions off the softer branch of the primary splitting, is a gluon-dominated object, and that a simple dijet selection makes it experimentally accessible. At leading order the secondary emission's colour factor is $C_A$ whenever the split is $q\to qg$ with a soft gluon or $g\to gg$, while the $g\to q\bar q$ channel is suppressed because it lacks a soft singularity. With $p_{t,\mathrm{lead}}>700$ GeV, $150<p_{t,\mathrm{sublead}}<200$ GeV, and $1<\Delta R<1.2$, the subleading anti-$k_t$ jet is "practically equivalent" to the secondary Lund plane and is gluon-initiated in about 90% of cases, for both quark- and gluon-initiated events. The gluon purity is resilient to the colour structure of the event, the hard-scattering flavour, and PDF choice, and the resulting secondary Lund plane density agrees with the primary Lund plane density of gluon jets from $gg\to gg$ within 10%.

Load-bearing premise

The entire scheme assumes that the subleading jet of the selected dijet pair really is the soft branch of one primary splitting; if ordinary jet clustering, underlying-event activity, or boundary effects break that correspondence, the predicted ~90% gluon purity would not apply to the measured jet.

Editorial extensions

If this is right

  • An LHC measurement of the primary Lund plane density of the subleading jet can constrain gluon-initiated radiation without relying on quark/gluon taggers or statistical demixing.
  • The approximately 90% gluon purity holds for both quark- and gluon-initiated hard scatterings, making the sample largely insensitive to PDF choice and to the flavour composition of the hard process.
  • The secondary Lund plane density from inclusive dijets reproduces the primary Lund plane density of $gg\to gg$ gluon jets within 10%, so it can serve as a practical proxy for pure gluon jets.
  • Differences between Monte Carlo generators in the deep collinear region appear in the secondary plane just as in the pure gluon primary plane, giving the observable similar constraining power for shower and hadronisation models.
  • The selection uses standard anti-$k_t$ jets with $R=0.4$ and a simple fiducial region, so it can be applied directly to existing LHC data and implemented in routine Rivet analyses.
  • Higher gluon purities can be reached by selecting softer subleading jets, at the cost of reduced phase space.

Reading between the lines

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

  • Inference: If the mapping between the subleading jet and the secondary Lund plane survives experimental scrutiny, the same dijet selection could provide gluon-enriched samples for many other substructure observables, such as hadron chemistry, jet charge, and energy correlators, not just Lund plane densities.
  • Inference: The same collinear-and-asymmetric dijet selection could be adapted to heavy-ion collisions as a way to isolate the colour-charge dependence of jet energy loss, though underlying-event contamination would need to be controlled first.
  • Inference: A direct experimental check of the claimed purity would be to apply existing quark/gluon discriminators to the selected subleading jets and compare the extracted gluon fraction with the ~90% prediction, a test the paper itself suggests.
  • Inference: Extending the selection to a trijet configuration with two b-tagged jets and an anti-b tagged third jet could offer a gluon-enriched sample with additional heavy-flavour handles, as the paper notes in passing.
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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. The paper proposes a new experimental strategy to obtain a gluon-enriched jet sample at the LHC by selecting a dijet pair with highly asymmetric transverse momenta and small angular separation (nominal cuts: pT,lead > 700 GeV, 150 < pT,sub < 200 GeV, 1 < DeltaR < 1.2) and measuring the primary Lund plane density of the subleading jet. The authors argue that this subleading jet is practically equivalent to the soft branch of a primary splitting, i.e., a secondary Lund jet plane, and hence is dominantly gluon-initiated. They support this with a leading-order fixed-order calculation (collinear Altarelli-Parisi estimates and exact O(alpha_s) NLOJet++ results) giving gluon fractions around 90% for both quark- and gluon-initiated hard scatterings, and with hadron-level Monte Carlo studies using Pythia8 and Herwig7 that compare the subleading-jet Lund plane density with the primary Lund plane density of gluon jets from gg->gg scatterings, finding agreement within 10%. The paper also studies dependence on the hard-scattering flavor, g->qqbar splittings, and MC generator choices, and discusses applications to MC tuning and alpha_s extraction.

Significance. If the central claim holds, the proposal offers a simple, experimentally accessible way to obtain high-purity gluon jets without taggers or statistical demixing, which would be valuable for constraining gluon fragmentation in MC generators and for reducing the quark/gluon-fraction degeneracy in alpha_s extractions. The paper's strengths include a parameter-free analytic estimate using standard splitting functions, a cross-check with exact fixed-order matrix elements, and a broad MC validation with two generators and three parton-shower variants. The fixed-order derivation is clean and the density comparisons are suggestive. However, the headline 90% purity is supported only at leading order, and the hadron-level MC confirmation is indirect because it never measures the truth-level gluon fraction of the selected jets. The paper is a useful phenomenological proposal, but the strength of the claims needs to be tempered or the missing direct validation added.

major comments (3)
  1. [Sec. 3] The abstract and Sec. 4 state that the ~90% gluon fraction is 'confirmed using hadron-level Monte Carlo generated events,' but Sec. 3 never reports a truth-level gluon purity for the selected subleading jets. The comparisons in Figs. 3-6 are between Lund plane densities (the secondary density of the subleading jet and the primary density of gluon jets from gg->gg scatterings), which constrain the average color factor of emissions but do not directly measure the fraction of gluon-initiated jets. Because the paper itself adopts an MC-interpreted definition of gluon-enrichment (footnote 2), a direct extraction of the truth-label gluon fraction should be provided, or the abstract and conclusions should be reworded to state that the MC supports the density proxy rather than confirming the 90% purity.
  2. [Sec. 2.1/2.2] The dijet selection identifies the subleading anti-kT jet with the soft branch of a primary C/A splitting without derivation. The analytic estimate in Eq. (2.9) uses the splitting variable z = pT,sub/(pT,lead+pT,sub) and the angular separation DeltaR as the splitting angle, which is only valid if the two jets are the two branches of a single primary emission. In the nominal dijet setup, the two jets are separate R=0.4 anti-kT jets, and the subleading jet is not constructed by declustering a common parent. The MC comparison in Sec. 3 is the only evidence for this equivalence; it shows density agreement but not that the per-jet identification holds. The 90% purity should be either verified by matching the subleading jet to the soft branch of the C/A tree in MC, or explicitly stated as applying to the idealized single-splitting configuration.
  3. [Sec. 2.2] The purity estimate is leading-order and double-logarithmic, with resummation and higher-order corrections postponed (as acknowledged in the text). While this is an acceptable first step for a proposal, the central quantitative claim of 'around 90%' is presented without an estimate of perturbative uncertainty; the exact O(alpha_s) NLOJet++ results in Fig. 2 are close to the collinear approximation, but both are leading order in the relevant splitting. To support the headline number, the authors should either provide an estimate of higher-order effects (e.g., a simple resummed estimate or a scale-variation band on the purity) or clearly qualify the 90% as a leading-order estimate in the abstract.
minor comments (4)
  1. [Sec. 2] The word 'infrarred' in 'infrarred-and-collinear (IRC) safe' should be corrected to 'infrared-and-collinear'.
  2. [Fig. 3] The lower panels are labeled 'Ratio-to-incl.' but the captions do not state explicitly whether the bands are statistical only; please clarify in the caption.
  3. [Sec. 3] The statement that about O(10^5) 'gluon-like jets' are obtained should define how 'gluon-like' is determined at generator level (e.g., by the hard-scattering process or by parton flavor), to avoid ambiguity.
  4. [Sec. 2.2] Eq. (2.8) defines the gluon fraction conditional on a leading quark or gluon, but the text does not give the formula for the inclusive purity that combines both; adding this would make the transition from Fig. 2 to the inclusive MC results clearer.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the ~90% gluon fraction is a parameter-free fixed-order QCD prediction, and the MC studies are consistency checks rather than fitted inputs.

full rationale

The central claim (subleading-jet gluon fraction of about 90%) is derived at fixed order from standard Altarelli-Parisi splitting functions in Eqs. (2.7)-(2.10), with no parameter fitted to the target observable; the same integrals are evaluated both in the collinear approximation and with NLOJet++, making it a genuine parameter-free QCD prediction. The hadron-level MC studies in Sec. 3 do not fit or invert this calculation; they compare the secondary Lund plane density with a MC-generated primary Lund plane of gluon jets (Figs. 4-6), which is a consistency check of the proxy, not a fit to the purity. The paper itself flags the operational meaning of gluon enrichment in footnote 2 ('as interpreted by some suitable, though fundamentally ambiguous, criterion'), and the absence of a direct truth-level purity extraction in Sec. 3 (the density comparison is not a purity measurement) is an evidentiary limitation rather than a circular reduction. The self-citations (Refs. [46], [53], [58]) define the Lund-plane framework or provide auxiliary calculations; they are not load-bearing for the 90% result. Therefore no step reduces by construction to its inputs.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The central claim rests on standard QCD splitting functions, a mapping between the selected dijet and the secondary Lund plane, and MC references. The phase-space cuts are chosen by hand to maximize purity and are free parameters of the proposal.

free parameters (6)
  • zmin (grooming setup) = 0.1
    Lower bound on the momentum fraction of the selected primary emission; chosen to enhance gluon purity, Sec 2.1.
  • zmax (grooming setup) = 0.2
    Upper bound on the momentum fraction; chosen to keep the soft branch gluon-dominated, Sec 2.1.
  • Deltamin (grooming setup) = 0.8
    Minimum opening angle between prongs; chosen to avoid deep-collinear boundary effects, Sec 2.1.
  • pt,min (dijet subleading jet) = 150 GeV
    Lower cut on subleading jet transverse momentum in the nominal dijet selection, Sec 2.1.
  • pt,max (dijet subleading jet) = 200 GeV
    Upper cut on subleading jet transverse momentum, Sec 2.1.
  • DeltaR window (dijet selection) = 1 < DeltaR < 1.2
    Angular separation between the two jets; chosen so the pair is collinear but non-overlapping, Sec 2.1.
assumptions (4)
  • standard math Altarelli-Parisi splitting functions P_ab(z) describe the first splitting in the collinear limit
    Used in Eqs. (2.7)-(2.10) to compute the gluon fractions.
  • domain assumption The softest branch in a q -> qg or g -> gg splitting is the gluon with probability given by the soft singularity
    This is the physical basis for the method, stated in Sec 2 around Eq. (2.6).
  • ad hoc to paper The subleading anti-kt jet in the selected dijet pair can be identified with the soft branch of a primary splitting (secondary Lund plane)
    Sec 2.1: 'practically equivalent to a secondary Lund jet plane'; tested by MC in Sec 3 but not derived analytically.
  • domain assumption MC generators Pythia8 and Herwig7 provide a reliable reference for gluon-initiated jet densities
    Used as the baseline comparison in Figs 3-6; the paper acknowledges MC gluon modeling is uncertain, which is the motivation.

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Cite this review

Pith. "Pith review of Secondary Lund jet plane as a gluon enriched sample." pith.science (2026). https://pith.science/paper/SDLBFVPY

@misc{pith2026241214247,
  author       = {Pith},
  title        = {Pith review of: Secondary Lund jet plane as a gluon enriched sample},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SDLBFVPY}},
  note         = {Machine review of arXiv:2412.14247}
}
read the original abstract

We propose a new strategy to obtain a high-purity sample of gluon-initiated jets at the LHC. Our approach, inspired by the Lund jet plane picture, is to perform a dijet selection where the two jets are collinear to each other and their momentum fraction share is highly asymmetric, and to measure the primary Lund plane density of emissions of the subleading jet. The subleading jet in this topology is practically equivalent to a secondary Lund jet plane. We demonstrate by means of fixed-order calculations that such a simple setup yields gluon jet fractions of around 90% for the subleading jet for both quark- and gluon-initiated jets. This observation is confirmed using hadron-level Monte Carlo generated events. We also show that the extracted gluon purities are highly resilient to the overall colour structure of the event, to the flavour of the hard-scattering process, and to the parton distribution functions. This strategy is well-suited for constraining the radiation pattern of gluon-initiated jets using a set of fiducial cuts that can readily be tested at the LHC, without relying on taggers or statistical demixing.

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Reference graph

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.