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On the quarkonium-in-jet collinear fragmentation at moderate-to-large transverse momentum

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

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Pith's one-line read This paper claims that the NRFF1.0 fragmentation functions, built from NLO NRQCD inputs and evolved with the HF-NRevo threshold-aware DGLAP scheme, are a viable foundation for quarkonium-in-jet fragmentation and will supersede the…

desk verdict A clean proceedings-style progress report that lays out a plausible HF-NRevo plan for quarkonium fragmentation and shows two unvalidated CS FF curves; the physics direction is sane but the quantitative support is not yet there. read the letter →

arxiv 2412.05661 v1 pith:WIWRMU6A submitted 2024-12-07 hep-ph hep-exnucl-exnucl-th

Francesco Giovanni Celiberto This is my paper · ORCID
classification hep-phhep-exnucl-exnucl-th
keywords quarkoniumfragmentationNRQCDDGLAPevolutionfragmentingjetfunctionssubstructurecollinearfactorizationheavy-flavortransversemomentum
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

This paper reports progress on HF-NRevo, a framework for quarkonium production in the fragmentation approximation. It builds preliminary next-to-leading-order fragmentation functions, named NRFF1.0, from non-relativistic QCD inputs for all parton-to-quarkonia channels, then uses them to set up collinear quarkonium-in-jet fragmentation via the semi-inclusive fragmenting jet function. The aim is to replace the currently used ZCW19+ and ZCFW22 sets with a unified, threshold-aware DGLAP-evolved set that is valid at moderate-to-large transverse momentum. If the framework is right, quarkonium-in-jet predictions at the HL-LHC and EIC will rest on a single consistent evolution scheme, and energy resummation will translate into a jet-radius resummation.

What carries the argument

The central machinery is HF-NRevo, a three-pillar framework (interpretation, evolution, uncertainties) for quarkonium fragmentation functions. It treats short-distance formation as two-parton fragmentation in a fixed-flavor-number scheme, matches to a variable-flavor-number scheme, performs a symbolic expanded and decoupled DGLAP evolution before an all-order numerical evolution, and quantifies missing higher-order uncertainties with Monte-Carlo-like replicas. The second load-bearing object is the semi-inclusive fragmenting jet function (SIFJF) of Eq. (1), whose convolution of standard collinear FFs with NLO fragmenting-jet coefficients, followed by the two-step DGLAP evolution of Eq. (2), maps single-parton fragmentation into a quarkonium-inside-jet observable and converts energy resummation into jet-radius resummation.

What would settle it

Compute, in the same NRQCD framework, the ratio of the higher-twist heavy-quark-pair fragmentation contribution to the leading-twist single-parton one for quarkonium-in-jet kinematics with jet transverse momentum between about 30 and 120 GeV. If this ratio is not much smaller than one in that range, the central premise of the paper fails; alternatively, a precise LHC measurement of the $z_Q$ distribution of $J/\psi$ or $\Upsilon$ inside anti-$k_T$ jets that disagrees with NRFF1.0jet predictions by the size of the pair contribution would settle the question.

Watch

Extended reading notes

Core claim

At the paper's center is a proposal to put quarkonium-inside-jet predictions on a single, self-consistent footing. The NRFF1.0 fragmentation-function sets combine NLO NRQCD color-singlet initial-scale inputs for all parton channels with a variable-flavor-number-scheme DGLAP evolution whose thresholds are handled first symbolically and then by all-order numerical evolution. Plugging NRFF1.0 into the semi-inclusive fragmenting jet function, Eq. (1), and running the two-step evolution of Eq. (2), from the initial scale $\mu_0$ to a matching scale $\mu_M \approx Q R_J$ and then from $\mu_M$ onward, turns energy resummation into a jet-radius resummation. The paper claims this construction yields the forthcoming NRFF1.0jet SIFJFs, which will supersede the ZCW19+ and ZCFW22 sets and give improved quarkonium-in-jet predictions at moderate-to-large transverse momentum.

Load-bearing premise

The argument assumes that at moderate-to-large transverse momentum the quarkonium yield is dominated by leading-twist fragmentation of a single parton, with the contribution from a heavy-quark pair produced in the hard scattering being negligible; the paper gives no numerical estimate of how small that higher-twist term actually is.

Editorial extensions

If this is right

  • NRFF1.0 will supersede ZCW19+ and ZCFW22 as the default collinear fragmentation input for vector quarkonia and charmed B mesons.
  • The two-step evolution yields NRFF1.0jet SIFJFs, enabling NLO quarkonium-in-jet predictions for anti-$k_T$ and cone jets with jet-radius resummation.
  • The same framework extends to quarkonium-in-jet angularities and other resummation-sensitive jet-substructure observables.
  • The threshold-aware VFNS DGLAP scheme removes ambiguities in quarkonium FF evolution by treating thresholds of all parton species symbolically before all-order evolution.
  • Missing higher-order uncertainties are quantified by simultaneous renormalization- and factorization-scale scans, aligned with modern PDF uncertainty methodology.

Reading between the lines

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

  • One consequence the paper leaves implicit is that the same NRFF1.0 inputs could be reused for quarkonium production in processes other than jets, such as semi-inclusive deep inelastic scattering at the EIC, by swapping the fragmenting-jet coefficients for the appropriate collinear or transverse-momentum-dependent matching factors.
  • If the higher-twist heavy-quark-pair contribution is indeed negligible only above some transverse-momentum threshold, NRFF1.0jet predictions will carry a $p_T$-dependent systematic floor; a dedicated calculation of that contribution would turn the paper's regime assumption into a tested boundary.
  • The Monte-Carlo replica approach for missing higher-order uncertainties points toward a data-driven extraction of quarkonium fragmentation functions from future LHC and EIC measurements, with NRFF1.0 as the prior.
  • A testable extension is to measure the ratio of $\Upsilon$ to $J/\psi$ yields inside jets as a function of $z_Q$ and jet $p_T$; since NRFF1.0 treats the $b$ and gluon channels separately, this ratio would discriminate the framework's flavor thresholds from the ZCW19+ and ZCFW22 baselines.
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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

4 major / 4 minor

Summary. This short proceedings article reports progress on the HF-NRevo framework and on NRFF1.0, a preliminary set of NLO NRQCD-based collinear fragmentation functions (FFs) for quarkonia, evolved in a variable-flavor-number scheme with DGLAP evolution. Two illustrative channels, b→Υ and g→Υ, are shown at three factorization scales. The manuscript then sketches how these FFs would enter the semi-inclusive fragmenting jet function (SIFJF) formula, Eq. (1), through the two-step evolution depicted in Eq. (2), and states that NRFF1.0 will supersede the ZCW19+ and ZCFW22 sets. The paper is explicitly a progress report, not a full phenomenological study.

Significance. If the NRFF1.0 set is delivered with the claimed NLO NRQCD inputs and validated against data or against existing FF sets, it could provide a useful new input for quarkonium-in-jet studies at moderate-to-large transverse momentum. The manuscript's strength is that it clearly connects an existing factorization formula, Eq. (1), to a concrete new FF-evolution pipeline, and it presents the qualitative behavior of two channels in a transparent way. The significance is conditional, however, because the paper contains no comparison to data, to earlier FF sets, or to a full NRQCD computation, and because two load-bearing assumptions—leading-twist dominance and the completeness of the partonic channel set—are stated but not quantified.

major comments (4)
  1. [Abstract; Sec. 1] The manuscript repeatedly asserts that at moderate-to-large transverse momentum 'the leading-twist collinear fragmentation of a single parton prevails over the higher-twist fragmentation from a constituent heavy-quark pair produced in the hard scattering,' but no quantitative estimate or kinematic criterion is given. This premise is load-bearing because Eq. (1) convolves only standard single-parton FFs; any contribution from a hard-scattered QQbar pair not produced through a single-parton fragmentation chain is absent by construction. The manuscript should specify the transverse-momentum range in which this approximation is intended to hold and provide a concrete estimate of the neglected contribution, for example by comparing the leading-twist FF-based result with a full NRQCD calculation for a simple process such as J/psi+jet at LHC energies.
  2. [Sec. 2; Fig. 1; Sec. 4] There is an inconsistency between the abstract, which claims NLO NRQCD inputs for 'all the parton-to-quarkonia fragmentation channels,' and the body of the paper, which states that the inputs are 'NRFF1.0_cs_nlo' and 'CS initial-scale inputs.' Color-octet channels, in particular the gluon fragmentation channel via the ^3S_1^[8] intermediate state, can be numerically important for vector quarkonia in the moderate-pT regime, and Eq. (1) sums over all partonic channels j. The manuscript gives no LDME values and no discussion of why color-octet contributions can be neglected. Either the color-octet channels should be included, or the claims should be explicitly restricted to color-singlet inputs with a quantitative justification for that restriction.
  3. [Sec. 4] The statement that NRFF1.0 'will supersede the ZCW19+ and ZCFW22 functions' is not supported by the evidence presented in this manuscript. Figure 1 shows only the new FFs at three scales, with no overlay of ZCW19+ or ZCFW22, no comparison to experimental data, and no comparison to a full NRQCD computation. The paper itself labels the FFs as 'preliminary,' so the supersession claim should be softened to an outlook item or, preferably, accompanied by a validation plot in the same figure. As written, the claim goes beyond what the data shown can establish.
  4. [Sec. 2] The manuscript states that MHOUs are quantified through a Monte-Carlo replica-like approach and through simultaneous variation of mu_F and mu_R by factors of 1/2 to 2, but Figure 1 contains no uncertainty bands, no replica spread, and no description of how the replica procedure is implemented or calibrated. Since the treatment of uncertainties is one of the three 'pillars' of the HF-NRevo methodology, the reader needs at least a sample uncertainty band or a precise reference to the companion papers where the replica construction is defined. Without this, the claim of quantified MHOUs is not checkable from the present manuscript.
minor comments (4)
  1. [Sec. 3] The sentence 'Jet substructure measurements have recently gained prominence as a powerful sounds for core nature of the strong force' contains a typo: 'sounds' should be 'tools'.
  2. [Sec. 3] The phrase 'de factotranslates' in the paragraph following Eq. (2) is missing a space and should read 'de facto translates'.
  3. [Fig. 1] The figure caption would be clearer if it stated explicitly that the plotted quantity is z times the fragmentation function, and if the ratio panels were defined, for example as the ratio to a chosen reference scale.
  4. [Eq. (2)] Equation (2) is only a schematic arrow diagram; a formal expression for the matching at mu_M, even in the simplest case, would make the two-step DGLAP statement in the surrounding text more checkable.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the load-bearing equations are standard cited factorization results; NRFF1.0 is a proposed input set, not a fitted prediction.

full rationale

The paper's central equations are not derived from the quantities they are meant to predict. Eq. (1) is the standard SIFJF convolution quoted from Kang et al. (refs. [70,72]), and Eq. (2) is an explicitly labeled schematic for two-step DGLAP evolution. Neither equation is constructed so that its output reproduces NRFF1.0 by definition. The NRFF1.0 inputs are NLO NRQCD-based color-singlet initial-scale fragmentation functions; the paper performs no fit to data and makes no numerical prediction that could be forced by a fitted parameter. The assertion that leading-twist single-parton fragmentation prevails is a physics assumption, not a self-referential derivation, and the unsupported claim that NRFF1.0 'will supersede' ZCW19+/ZCFW22 is a statement of ambition rather than a circular reduction. The framework relies heavily on the author's own prior work (HF-NRevo refs. [39,40], symJETHAD refs. [45-54]), but self-citation alone is not circularity: the cited methodology is described in the paper, and no external 'uniqueness theorem' or fitted quantity is invoked to force the announced results. Because no central claim reduces by construction to its input, the circularity score is 0.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The ledger is short because the paper is a progress report that borrows most of its machinery from existing literature. Eq. (1) and the two-step matching are taken from Kang et al. [70,72], and HF-NRevo and symJETHAD are from the author's previous publications [39,40,45-54]. The numerical FFs depend on externally fitted NRQCD LDMEs and on scale choices that are not documented here, so the paper's net new content is difficult to separate from its input assumptions.

free parameters (2)
  • NRQCD color-singlet LDMEs
    The initial-scale FFs in NRFF1.0 depend on nonperturbative LDMEs obtained from external fits; no values or extraction set are given, so the plotted curves cannot be reproduced from the paper alone.
  • Initial fragmentation scale mu0 per parton channel
    The text mentions evolution from the lowest scale mu0 to the matching scale muM but never specifies mu0 for the b and g channels used in Fig. 1; the FF shapes depend on this choice.
assumptions (5)
  • domain assumption Leading-twist collinear single-parton fragmentation prevails over higher-twist heavy-quark-pair fragmentation at moderate-to-large transverse momentum.
    Invoked in the abstract and Section 1 to justify restricting to single-parton fragmentation; no quantitative estimate of higher-twist suppression is given.
  • domain assumption NRQCD factorization with a color-singlet Fock state truncation describes quarkonium fragmentation at the initial scale.
    Section 1 and Section 2 state initial inputs are NLO NRQCD color-singlet; no color-octet contributions are included, and LDMEs are taken from external fits.
  • standard math The SIFJF factorizes as a convolution of collinear fragmenting jet coefficients and standard FFs, Eq. (1), at leading power.
    Eq. (1) is borrowed from Kang et al. [70,72]; the paper provides no derivation but it is established literature.
  • domain assumption Time-like DGLAP evolution can be split in two steps, with matching scale muM approximately Q times RJ, so that energy resummation becomes jet-radius resummation.
    Section 3, Eq. (2); relies on the scale-choice argument from [70,72].
  • domain assumption The initial-scale FF inputs are obtainable from nonrelativistic NLO calculations.
    Section 2 states reliance on NLO NRQCD-based inputs; no explicit LDME values are given.

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Cite this review

Pith. "Pith review of On the quarkonium-in-jet collinear fragmentation at moderate-to-large transverse momentum." pith.science (2026). https://pith.science/paper/WIWRMU6A

@misc{pith2026241205661,
  author       = {Pith},
  title        = {Pith review of: On the quarkonium-in-jet collinear fragmentation at moderate-to-large transverse momentum},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WIWRMU6A}},
  note         = {Machine review of arXiv:2412.05661}
}
read the original abstract

We report progress on the Heavy-Flavor Non-Relativistic Evolution (HF-NRevo) setup, a novel methodology to address quarkonium formation within the fragmentation approximation. Our study sheds light on the moderate to large transverse-momentum sector, where the leading-twist collinear fragmentation of a single parton prevails over the higher-twist fragmentation from a constituent heavy-quark pair produced in the hard scattering. As for the initial energy-scale inputs, we rely on nonrelativistic next-to-leading calculations for all the parton-to-quarkonia fragmentation channels. Preliminary sets of variable-flavor number-scheme (VFNS) fragmentation functions, named NRFF1.0, are built via an evolution-threshold enhanced DGLAP scheme. Taking NRFF1.0 as a starting point, we use HF-NRevo to address the collinear fragmentation of quarkonia inside jets.

Figures

Figures reproduced from arXiv: 2412.05661 by the authors.

Figure 1
Figure 1. Preliminary results for (b, g → Υ) NRFF1.0 CS fragmentation. 3. Quarkonium-in-jet fragmenting functions Jet substructure measurements have recently gained prominence as a powerful sounds for core nature of the strong force. Beyond that, they present exciting opportunities for uncovering physics beyond the Standard Model [58, 59]. Advancing our theoretical comprehension of QCD dynamics by unveiling the substructure o… view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

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Pith tools

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