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Impact of Open Heavy-Flavour Production on nCTEQ Nuclear PDFs

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Jan Wissmann, Tomáš Ježo, Michael Klasen, Ingo Schienbein, Hubert Spiesberger

High Energy Physics - Phenomenology · Submitted 29 Sep 2026 · 19 references

Pith's verdict: A transparent, genuinely new validation showing Crystal-Ball and SACOT open heavy-flavor treatments give compatible nPDFs, but the compatibility claim rests on an unquantified scale compensation the authors acknowledge leaving to future work.

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arXiv ID2609.37152 (version 1)
Pith IDGYVWEHKP, Pith's permanent record of this paper and its review
CitationHubert Spiesberger, Ingo Schienbein, Jan Wissmann, Michael Klasen, Tom\'a\v{s} Je\v{z}o. "Impact of Open Heavy-Flavour Production on nCTEQ Nuclear PDFs." arXiv:2609.37152 (2026). https://pith.science/paper/GYVWEHKP
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The paper

The paper claims

This paper shows that replacing the fitted Crystal-Ball effective matrix element with a full perturbative QCD calculation for open heavy-flavor production leaves the extracted nuclear PDFs unchanged within uncertainties, and concludes…

The reading

This paper asks whether the effective matrix element used to describe open heavy-flavor production in the nCTEQ26 nuclear PDF framework is consistent with a proper perturbative QCD calculation. The answer is yes: replacing the Crystal-Ball function with an SACOT general-mass variable-flavor-number scheme calculation in a new fit, nCTEQ26OHF, yields nuclear PDFs whose central values agree with the main nCTEQ26 release within uncertainties. The authors conclude that open heavy-flavor data alone hold significant constraint on the nuclear gluon at low $x$, and that the Crystal-Ball function is broadly compatible with the SACOT calculation. The result matters because it validates the computationally cheaper effective-matrix-element approach used in the flagship global analysis.

What carries the argument

The load-bearing object is the SACOT general-mass variable-flavor-number scheme calculation for open heavy-flavor production, implemented as PineAPPL grids, which replaces the Crystal-Ball function, a fitted effective matrix element, for the OHF predictions. The scale choice $(\xi_r, \xi_f, \xi'_f) = (1, 0.6, 2.5)$ for $\mu_i = \xi_i \sqrt{p_T^2 + 4m_c^2}$ carries the argument: tuned to the proton-proton baseline data used to fit the Crystal-Ball parameters, it compensates for the fact that no theory uncertainties are currently used in nCTEQ global analyses and gives a much better description of the proton-lead data. The paper acknowledges that uncertainties on the $\xi_i$ coefficients are not included and are left for future work.

Extended reading notes

Core claim

The central claim is that the Crystal-Ball effective matrix element and a full pQCD SACOT calculation give compatible descriptions of open heavy-flavor production when used inside the nCTEQ26 global framework. The new fit, nCTEQ26OHF, retains the nCTEQ26 setup but swaps the Crystal-Ball prediction for the SACOT calculation (with KKKS08 fragmentation functions), drops the quarkonium data entirely, and returns PDFs that agree with nCTEQ26 within uncertainties for all observables. The gluon uncertainty band is only slightly larger in the OHF fit because the OHF data alone, flanked by W/Z production data on the positive side of the gluon parameter, still constrain it strongly at low $x$. The paper attributes the rise in the OHF $\chi^2$ per point from 1.12 to 2.04 partly to the absence of Crystal-Ball parameter uncertainties, which are present in nCTEQ26 but absent in nCTEQ26OHF, rather than to a genuinely worse description of the data.

Load-bearing premise

The compatibility conclusion rests on the tuned scale coefficients $(\xi_r, \xi_f, \xi'_f) = (1, 0.6, 2.5)$, calibrated against proton-proton baseline data rather than proton-lead data, with no uncertainty on those coefficients included; if this calibration is inappropriate for proton-nucleus kinematics, the OHF predictions and the extracted gluon would be biased.

Editorial extensions

If this is right

  • If the SACOT calculation yields the same nuclear gluon as the Crystal-Ball function, the cheaper effective-matrix-element treatment used in the nCTEQ26 release will not need to be redone.
  • Open heavy-flavor data alone, without quarkonium data, are enough to constrain the nuclear gluon at low $x$.
  • OHF data constrain the gluon parameter on the negative side while W/Z production data constrain it on the positive side, so both data classes must be kept to reach the quoted gluon uncertainty.
  • The rise in the OHF $\chi^2$ per point from 1.12 to 2.04 reflects the missing Crystal-Ball parameter uncertainties rather than a worse description of the data.

Reading between the lines

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

  • A natural next check is a refit at an alternative scale choice such as $(1,1,1)$ or $(1,2,2)$, or with the $\xi_i$ uncertainties propagated; if the gluon shifts appreciably, the compatibility conclusion would be scale-choice dependent rather than robust.
  • The same Crystal-Ball-versus-pQCD validation could be run for quarkonium production, whose effective description is left untested in this work.
  • If the compatibility holds at other scale choices, the OHF data may already be saturating the low-$x$ gluon constraint, so future D-meson measurements would sharpen rather than move the gluon.
Original abstract

We present nCTEQ26OHF, a global analysis of nuclear parton distribution functions (nPDFs) within the nCTEQ framework. In this analysis, constrasting the main nCTEQ26 release, we replace the Crystal-Ball function, an effective matrix element that is used in nCTEQ26 for open heavy-flavor (OHF) and quarkonium production, by an SACOT GM-VFNS calculation for the OHF predictions. The resulting nCTEQ26OHF PDFs are compatible with the nCTEQ26 PDFs within uncertainties, implying that the OHF data alone provide ample constraint.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-30: 1 request, 3,059 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.28 · human participants 0.01 · controlled comparison 0.79 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.97 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We present nCTEQ26OHF, a global analysis of nuclear parton distribution functions (nPDFs) within the nCTEQ framework. In this analysis, constrasting the main nCTEQ26 release, we replace the Crystal-Ball function, an effective matrix element that is used in nCTEQ26 for open heavy-flavor (OHF) and quarkonium production, by an SACOT GM-VFNS calculation for the OHF predictions. The resulting nCTEQ26OHF PDFs are compatible with the nCTEQ26 PDFs within uncertainties, implying that the OHF data alone provide ample constraint.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We present nCTEQ26OHF, a global analysis of nuclear parton distribution functions (nPDFs) within the nCTEQ framework. contribution 1.00 0.92 0.06 asserted 1.00
s1 In this analysis, constrasting the main nCTEQ26 release, we replace the Crystal-Ball function, an effective matrix element that is used in nCTEQ26 for open heavy-flavor (OHF) and quarkonium production, by an SACOT GM-VFNS calculation for the OHF predictions. method 0.86 0.89 0.06 asserted 0.99
s2 The resulting nCTEQ26OHF PDFs are compatible with the nCTEQ26 PDFs within uncertainties, implying that the OHF data alone provide ample constraint. interpretation 0.77 0.92 0.80 asserted 0.75

What kind of paper the classifier reports this is: method or tool 0.50 · evidence from analysis of existing data 0.86.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. Kinematic coverage of the nCTEQ26 data. In nCTEQ26OHF we leave out the quarkonium data here labeled ONIA. 2
Figure 2. Comparison of nCTEQ26 and nCTEQ26OHF PDFs. proton PDF parametrization by adding an 𝐴-dependent part to its parameters. In contrast to nCTEQ15, we choose CJ15 [15] as our new proton baseline in nCTEQ26, thus using 𝑢𝑣, 𝑑𝑣, 𝑢¯ + 𝑑¯, 𝑑¯/𝑢¯, 𝑠 + 𝑠¯ and 𝑔 as our flavor basis and switching to the parametrization 𝑥 𝑓 (𝑥, 𝑄0) = 𝑐0𝑥 𝑐1 (1 − 𝑥) 𝑐2 (1 + 𝑐3 √ 𝑥 + 𝑐4𝑥)𝑒 𝑐5 √ 𝑥 (1) at the initial scale 𝑄0 = 1.3 GeV. The 𝑑𝑣 PDF receives 𝑢𝑣-dependent admixture in addition to eq. (1), and 𝑑¯/𝑢¯ is parametrized differently as it is a ratio. The 𝑐5 parameter is not present in the CJ15 analysis,
Figure 3. Scan of the nCTEQ26OHF 𝜒 2 function along the 𝑎1 gluon parameter, split into the fitted processes. Each curve is shifted along the 𝑦 axis such that it intersects the origin at the minimum of the total 𝜒 2 . Highlighted are the processes that show the most constraint. processes and employ the same cuts. Following previous works [20, 21], we choose a coefficient different from unity in the scale choice 𝜇𝑖 = 𝜉𝑖 √︃ 𝑝 2 T + 4𝑚2 𝑐 , namely (𝜉𝑟 , 𝜉 𝑓 , 𝜉′ 𝑓 ) = (1, 0.6, 2.5) for the renormalization, initial-state factorization and final-state factorization (fragmentation) scales
Figure 4. 𝜒 2 breakdown for the open heavy-flavor data included in nCTEQ26 and nCTEQ26OHF. in the nCTEQ26OHF fit than in the nCTEQ26 fit. Again, this can be traced back to the CB parameter uncertainties for some datasets, which decrease the 𝜒 2 in the nCTEQ26 fit even though the description of the data is not necessarily worse. 5. Conclusion In summary, we presented improvements of the new nCTEQ26 global analysis over the nCTEQ15 analysis [6] and select intermediate releases [4, 13, 14], in total increasing the num￾ber of data points from 740 to 3598. Furthermore, we showed the nCTEQ26OHF fit,

Figures reproduced from arXiv:2609.37152 by the authors.

References

Discussion

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