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NRQCD Re-Confronts LHCb Data on Quarkonium Production within Jets

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The paper shows that LHCb's psi(2S) momentum-fraction distributions inside jets, binned in both jet and quarkonium transverse momentum, can discriminate between NRQCD production mechanisms, and that threshold-resummed fragmenting jet…

desk verdict Solid incremental step—threshold resummation in semi-inclusive FJFs applied to LHCb psi(2S) data—but the LDME-discrimination claim outruns the omitted scale uncertainties. read the letter →

arxiv 2507.19022 v1 pith:M6KLEZ24 submitted 2025-07-25 hep-ph

Yunlu Wang , Daekyoung Kang , Hee Sok Chung This is my paper · ORCID
classification hep-ph
keywords quarkoniumproductionNRQCDfactorizationlong-distancematrixelementsfragmentingjetfunctionthresholdresummationpsi(2S)J/psifragmentation
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 argues that the momentum fraction a psi(2S) carries inside a jet, measured by LHCb in bins of both the jet's transverse momentum and the meson's transverse momentum, can tell apart competing sets of NRQCD long-distance matrix elements, something inclusive cross sections have not been able to do. Using the semi-inclusive fragmenting jet function formalism with DGLAP evolution and, for the first time in this framework, threshold resummation, the authors compute z_H distributions for J/psi and psi(2S) at LL+NLO accuracy. They compare three representative LDME sets and find that the psi(2S) data discriminate between them, even though no single set reproduces every bin. The comparison also reveals where the leading-power calculation fails: a low-z_H region that needs mass corrections and sharp peaks at z_H=1 that point to a double-parton production process. If correct, quarkonium-in-jet distributions become a decisive probe of how quarkonia form, and the psi(2S) measurement is a stronger version of that probe than the existing J/psi data.

What carries the argument

The carrying object is the semi-inclusive fragmenting jet function (FJF), which factorizes the cross section into a convolution $G_i^H(z,z_H,p_TR,\mu)=\sum_j J_{ij}(z,z_H,\mu)\otimes D_j^H(z_H,\mu)$, where $J_{ij}$ describes a mother parton splitting into a daughter parton inside the jet and $D_j^H$ is the quarkonium fragmentation function. The hierarchy $m_H \ll p_TR \ll p_T$ produces large logarithms $\ln(p_TR/m_H)$ and $\ln R$; the paper resums them by DGLAP evolution of the fragmentation function from $2m_c$ to the jet scale $p_TR$, then FJF evolution from $p_TR$ to the hard scale $p_T$, all at LL, reaching LLR + LL_threshold + NLO. Threshold resummation of the double logarithms $\log(1-z_H)/(1-z_H)$ is what makes the $z_H \to 1$ predictions finite and positive-definite. The experimental acceptance is implemented by modeling quarkonium decays as unpolarized and isotropic in the rest frame, boosting the muons to the lab frame, and applying the LHCb muon cuts, which produces the $z_H$-dependent acceptance that shapes the predictions.

What would settle it

Measure the polarization of prompt psi(2S) inside jets from the angular distribution of the two muons in the quarkonium rest frame and recompute the acceptance-corrected z_H predictions with that polarization; if the three LDME sets no longer separate in the binned distributions, or if the shape agreement changes materially, the discrimination claim fails. Alternatively, add the double-parton fragmentation contribution and test whether the z_H = 1 peaks in the LHCb data are reproduced; if they persist unexplained, the framework is missing another ingredient.

Watch

Extended reading notes

Core claim

The central claim is that the LHCb psi(2S) z_H distribution, measured separately in bins of jet pT and of psi(2S) pT, has enough discriminating power to tell apart competing sets of NRQCD long-distance matrix elements, something inclusive quarkonium pT spectra have failed to do. The paper reaches this by computing the distribution with semi-inclusive fragmenting jet functions at LL+NLO accuracy, including DGLAP evolution and, for the first time in this framework, threshold resummation of the double logarithms log(1-z_H)/(1-z_H). The threshold resummation cures the divergent growth toward z_H = 1 that plagued earlier FJF predictions. Comparing three representative LDME sets, the paper finds that none reproduces the full LHCb psi(2S) spectrum: one set does better at low z_H, a second at high z_H, and the third is less constraining because of its large uncertainties and negative direct-production predictions. The peaks the data show at z_H = 1, which the leading-power calculation cannot produce, are attributed to power-suppressed double-parton fragmentation, while low-z_H deviations in fixed jet-pT bins signal kinematical mass corrections of order (m_H/p_H^T)^2. The conclusion is that quarkonium production within jets is a critical probe of the NRQCD production mechanism, and that the psi(2S) dual-binning measurement is a sharper version of that probe than the pT-integrated J/psi measurement.

Load-bearing premise

The calculation assumes the quarkonia decay unpolarized and isotropically in their rest frame when modeling the LHCb muon acceptance; if prompt J/psi or psi(2S) are strongly polarized, the z-dependent acceptance corrections change and the comparison between LDME sets could shift.

Editorial extensions

If this is right

  • The psi(2S) dual-binning strategy can separate LDME sets that inclusive pT spectra cannot, making it a practical discriminator for the quarkonium production mechanism.
  • Threshold resummation turns the previously divergent z_H -> 1 predictions into finite, positive-definite distributions, so high-z_H bins become usable for comparisons.
  • The z_H = 1 excess seen in the LHCb psi(2S) data, which grows at lower pT, indicates that power-suppressed double-parton fragmentation must be included for a complete description.
  • For J/psi, the current pT-integrated data are less discriminating; analogous J/psi measurements binned in both pT variables would be needed to resolve LDME tensions in that channel.
  • The calculation validates the semi-inclusive FJF framework against high-pT bins where mass corrections are small, supporting the use of this formalism for future quarkonium-in-jet analyses.

Reading between the lines

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

  • A natural next step, not performed here, is a global fit that treats NRQCD LDMEs and the double-parton fragmentation strength as free parameters against the binned psi(2S) data; the current paper stops at comparing three fixed LDME sets.
  • The same dual-binning logic could be applied to other identified hadrons inside jets, such as B mesons or charmed baryons, to test whether their fragmentation functions also separate competing nonperturbative matrix elements.
  • The unpolarized-decay acceptance model could be checked by computing polarization-dependent dimuon distributions from the same NRQCD channels; if the z-dependent acceptance is sensitive, the discrimination statement would need to be made polarization-dependent.
  • Because the paper normalizes predictions to the mid-z_H region, a next test is to insist on absolute normalization, which would turn the overall yield into an additional constraint on the LDME sets rather than just the shape.
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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 / 5 minor

Summary. This letter compares LHCb measurements of J/psi and psi(2S) transverse-momentum-fraction (z_H) distributions within jets with NRQCD predictions based on the semi-inclusive fragmenting jet function (FJF) formalism. The calculation uses NLO partonic cross sections, DGLAP evolution of fragmentation functions, threshold resummation in the z_H -> 1 limit, and a model of the LHCb muon acceptance. Three representative color-octet LDME sets are taken from the literature and compared visually with the data. The paper claims that the psi(2S) data, binned in both jet pT and quarkonium pT, have the potential to discriminate between NRQCD production mechanisms.

Significance. If the discrimination claim is quantitatively established, this would be a valuable step: it would show that quarkonium-in-jet distributions provide sharper constraints on NRQCD production mechanisms than inclusive cross sections, and it would validate the threshold-resummed, semi-inclusive FJF framework against new LHCb data. The technical advance over Ref. [10] is real, including the use of semi-inclusive FJFs matched to LHCb kinematics, threshold resummation that cures the earlier z_H -> 1 divergence, and the first comparison to the binned psi(2S) data. The paper also avoids circularity by using independent LDME sets rather than fitting new ones. However, the central claim is not yet demonstrated because perturbative scale uncertainties are omitted, the comparisons are normalized to the data in a mid-z_H window and judged visually, and no goodness-of-fit statistic is reported. These are fixable within a revision, so I do not regard the current form as ready for publication.

major comments (3)
  1. [Numerical calculation] The statement that "we intentionally exclude perturbative uncertainties from scale variations" directly undermines the discrimination claim. Because the B&K LDME uncertainties in Table I are very small, the apparent separation between the B&K band and the Brambilla/Bodwin bands in Fig. 1 could be inflated by the missing scale uncertainty. The authors should estimate scale uncertainties, for example by varying the fragmentation scale, the FJF scale, and the renormalization scale in the NLO cross section and in the resummation, and show that the three LDME sets remain visually and statistically separated after adding the scale uncertainty in quadrature.
  2. [Prompt-psi(2S) results] The claim that "the Brambilla set provides a better description at low zH and the B&K set performs better at high zH" is based only on visual inspection after normalizing the theory to the data area in 0.5 < zH < 0.8, and no chi-square, likelihood, or other goodness-of-fit statistic is reported. The choice of normalization window can itself trade against shape differences, so the current evidence does not quantitatively support the abstract's conclusion that the psi(2S) data can discriminate between production mechanisms. The authors should provide a quantitative comparison, ideally a chi-square or likelihood per LDME set using the experimental covariance matrix, or explicitly weaken the conclusion to an illustrative comparison.
  3. [Numerical calculation (acceptance model)] The acceptance model assumes "unpolarized quarkonium decays with isotropic mu+mu- angular distributions in the quarkonium rest frame." Since NRQCD allows significant quarkonium polarization and the z_H-dependent acceptance of the LHCb muon cuts is polarization-dependent, this assumption could change the predicted shapes and hence the discrimination conclusions. The authors should quantify the sensitivity by repeating the acceptance computation with maximally longitudinal and maximally transverse polarization scenarios, or by using measured polarizations where available, and state whether the discrimination conclusions survive.
minor comments (5)
  1. [Fig. 1 caption] The caption refers to "the factor sigma" but does not define it; please define it explicitly or point to the corresponding equation in the text.
  2. [Supplementary material] Figs. 3 and 4 are not referenced in the main text; add explicit references when describing the lower-pT bins in the supplementary material.
  3. [Prompt-psi(2S) results] In the sentence "This complimentary dual binning", "complimentary" should be "complementary".
  4. [Table I] In the psi(2S) row for Bodwin et al., the color-singlet LDME is listed as 0.76[16] with no uncertainty; please state whether this value is held fixed when propagating LDME uncertainties.
  5. [Abstract] The abstract's phrase "has the potential to discriminate" is weaker than the conclusions' phrasing that the data "enable discrimination"; please harmonize these statements with the level of quantitative support provided in the paper.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the LDME sets and perturbative FJF inputs are independent, and the psi(2S) comparison is a genuine forward prediction.

full rationale

The paper does not fit any LDME to the data it compares against. The three LDME sets in Table I are taken from independent global fits (Brambilla et al. [13], Bodwin et al. [14], Butenschoen and Kniehl [15,17]), and the LHCb psi(2S) data [9] postdates the fits used, so the z_H distributions are genuine predictions rather than refits. The FJF formalism and threshold resummation are independent perturbative ingredients: the cited threshold resummation formula [12] shares an author with this paper but is a parameter-free result whose stated assumptions do not include the LHCb quarkonium-in-jet distributions, so citing it is not a circular load-bearing step. The only data-dependent step is the common area normalization over the mid-z_H region (0.5 < z_H < 0.8), which rescales all predictions by the same overall factor and therefore cannot manufacture the shape differences among the three LDME sets; it also does not enter the LDME parameters themselves. The decision to omit perturbative scale uncertainties and the absence of a quantitative chi-square comparison are accuracy and evidentiary concerns, not circularity. Relative to the external LHCb benchmark, the derivation is self-contained and its central discriminator claim rests on independent model inputs, so no circular step is present.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central predictions rest on literature-fitted LDMEs, the FJF factorization, a cited threshold resummation, and a polarization-blind acceptance model. The only parameter fitted to the data being compared is the mid-zH normalization factor. No new particles or forces are introduced.

free parameters (3)
  • J/psi color-octet LDMEs (3S1[8], 1S0[8], 3PJ[8]) from Refs. [13-15] = Three sets, see Table I: Brambilla 1.40, -0.63, 2.33; Bodwin -0.71, 11.0, -0.31; B&K 0.22, 4.97, -0.72 (times 10^-2…
    Nonperturbative inputs fitted to inclusive production data in earlier papers; the central claim of LDME discrimination depends on these values.
  • psi(2S) color-octet LDMEs from Refs. [13,14,17] = Table I: Brambilla 0.84, -0.37, 1.55; Bodwin -0.16, 3.14, -0.12; B&K 0.054, 1.00, -0.217 (times 10^-2 GeV^3)
    Nonperturbative inputs fitted to other data; predictions for psi(2S) shapes are directly controlled by these numbers.
  • Mid-zH normalization factor for each comparison = Not quoted; chosen so the theory area matches the data area in 0.5 < zH < 0.8
    The text states predictions are normalized to the data area in the mid-zH region, so a normalization constant is effectively fitted to the same data being compared, reducing the comparison to shape only.
assumptions (5)
  • domain assumption NRQCD factorization with the four channels 3S1[1], 3S1[8], 1S0[8], and 3PJ[8] describes J/psi and psi(2S) production at LHCb pT.
    Introduced in Eq. (1) with a truncation of the sum; standard in the field but not derived in this letter.
  • domain assumption Semi-inclusive FJF factorization, G_i^H = sum_j J_ij tensor D_j^H, holds for m_H << pT R << pT with the coefficients J_ij from Ref. [11].
    Eq. (2); the factorization is assumed valid for the LHCb kinematics of anti-kT jets with R=0.5.
  • domain assumption The threshold resummation formula of Ref. [12] can be embedded in the FJF framework and removes the zH to 1 divergence without double counting DGLAP logarithms.
    Adopted for the first time in the FJF framework; the formula is cited rather than re-derived in this letter.
  • domain assumption Unpolarized isotropic decays for J/psi and psi(2S) in the acceptance modeling.
    The text explicitly assumes unpolarized decays; polarization would change the z-dependent muon acceptance and therefore the predicted shapes.
  • domain assumption The three chosen LDME sets are representative of all published sets, with similar predictions within each category.
    The paper defines three categories and selects one representative set each; it does not scan the full space of published LDMEs.

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Cite this review

Pith. "Pith review of NRQCD Re-Confronts LHCb Data on Quarkonium Production within Jets." pith.science (2026). https://pith.science/paper/M6KLEZ24

@misc{pith2026250719022,
  author       = {Pith},
  title        = {Pith review of: NRQCD Re-Confronts LHCb Data on Quarkonium Production within Jets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/M6KLEZ24}},
  note         = {Machine review of arXiv:2507.19022}
}
abstract

We compare LHCb measurements of $J/\psi$ and $\psi(2S)$ transverse momentum distributions within jets with QCD calculations, which may be crucial in understanding the quarkonium production mechanism. Our theoretical calculations are based on the fragmenting jet function formalism, while the nonperturbative formation of quarkonia is described by the nonrelativistic QCD factorization formalism. We include the newest refinements in the perturbative calculation including resummation of threshold and DGLAP logarithms. We find that the $\psi(2S)$ data has the potential to discriminate between the different production mechanisms proposed in the literature.

Figures

Figures reproduced from arXiv: 2507.19022 by the authors.

Figure 1
Figure 1. FIG. 1. Prediction for [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Prediction for [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Predicted [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Predicted [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

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Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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  3. The role of the soft scale for $J/\psi$ production in the transverse momentum dependent framework

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  4. Heavy Quark Pair Energy Correlators: From Profiling Partonic Splittings to Probing Heavy-Flavor Fragmentation

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  5. $\psi(2S)$ production in jets using NRQCD

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    Applying NRQCD fragmenting jet functions and gluon-fragmentation-improved Pythia to psi(2S) in jets, the authors find that the LHCb data favor the Bodwin et al. LDME set and expose large tensions with other extractions.

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    2025 arXiv

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.