Fragmentation Functions for Pions, Kaons, and Protons at Next-to-Leading Order

B.A. Kniehl; B. P\"otter; G. Kramer

REVIEW

Fragmentation Functions for Pions, Kaons, and Protons at Next-to-Leading Order

B.A. Kniehl, G. Kramer, B. Pötter

High Energy Physics - Phenomenology · Submitted 25 Oct 2000 · 40 references

Pith's verdict: The KKP fragmentation functions: a solid, unusually honest global fit that became a standard reference, with one real soft spot in how flavour-tagged charged-hadron data are kept or dropped.

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arXiv IDhep-ph/0010289 (version 1)

Pith IDWGFVDOJ7, Pith's permanent record of this paper and its review

CitationB.A. Kniehl, B. P\"otter, G. Kramer. "Fragmentation Functions for Pions, Kaons, and Protons at Next-to-Leading Order." arXiv:hep-ph/0010289 (2000). https://pith.science/paper/WGFVDOJ7

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Editor's note

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This is the KKP set, and it is what people actually cite when they need NLO fragmentation functions for identified pions, kaons, and protons. What is new relative to the authors' own BKK analysis is real: they replace assumed flavour universality with the flavour-tagged identified-hadron samples from DELPHI and SLD, and they swap the old jet-finding OPAL gluon tag for the Gary-method samples from ALEPH and OPAL. Adding PEP at 29 GeV alongside LEP1 gives a lever on scaling violation, and the alpha_s(M_Z) = 0.1170 extraction is a genuine bonus from that combination. What the paper does well: the fit machinery is standard, and the reporting is unusually honest. Table 1 lists chi-squared for the samples they excluded, Table 4 shows where the momentum sum rule fails and traces it to the non-sea-like d-quark in K±, and Section 4 names the low-x breakdown of the x^alpha(1-x)^beta ansatz. The real tests are the ones outside the fit, DORIS and ARGUS at 5.4 and 9.98 GeV, TASSO at 22 and 34 GeV, and the longitudinal cross section in Fig. 10, and they pass. That is the part that earns trust. Soft spots. The one that matters is the asymmetry the stress-test flags, and I think it holds. ALEPH's flavour-tagged charged-hadron samples are dropped at chi-squared of order 100, and the justification is concrete: the sum of the three tagged cross sections overshoots the sum of the identified pi/K/p cross sections. Fine. But the same test is never run on DELPHI, whose charged-hadron samples are kept and do constrain the light- and b-quark functions. The authors say they proceed as in [18,19] in want of a separate measurement of the excess, so they know. If DELPHI carries a comparable excess, the light- and b-quark normalizations are biased low. That is a real caveat, not a fatal one, and it is stated in the text rather than hidden. Two minor points: the alpha_s error is computed with all other parameters fixed and no scale variation, so competitive is generous; and the gluon function is fitted to and displayed against the same three-jet data in Fig. 5, which is fine but is not an independent check. Who should read it: anyone needing NLO fragmentation functions for identified hadrons, and anyone doing global fits who wants a model of how to report excluded samples. It deserves a serious referee, mainly to push on the DELPHI excess question.

Referee report

Significance

Identified-hadron fragmentation functions at NLO are a standard input for predictions at hadron colliders and in ep and gamma-gamma scattering, and this paper is one of the reference sets in that programme. Several features deserve explicit credit: the chi-squared table (Table 1) reports the samples that were excluded from the fit as well as those included, so the reader can see the tension rather than having it hidden; the predictions for DORIS, ARGUS, and TASSO (Table 3, Figs. 7-9) and for the longitudinal cross section (Table 5, Fig. 10) are genuine tests against data not used in the fit; the momentum sum rule is checked rather than imposed (Table 4) and the resulting deficit is traced to a specific source; and the functions are released as downloadable code, which makes the result reproducible and falsifiable. The alpha_s extraction from scaling violation between 29 and 91.2 GeV is a useful independent cross-check of the world average.

Major objections (3)

[Section 2, Table 1] The data-selection asymmetry is load-bearing for the light- and b-quark fragmentation functions and is only half checked. The DELPHI charged-hadron rows sigma_h(uds) (chi-squared per degree of freedom 0.20) and sigma_h(b) (0.43) are included in the fit, while the corresponding ALEPH [14,15] and OPAL [23] rows (89.4, 221, 5.10, 6.63) are excluded. The justification given for excluding ALEPH is concrete and I accept it: the sum of the three flavour-tagged charged-hadron cross sections [14] agrees with the untagged one [15] but overshoots the sum of the identified pi, K, p cross sections [16]. The problem is that this test is never applied to DELPHI. The text itself states that the DELPHI and SLD analyses assume the sum of pi, K, p exhausts the charged-hadron sample and that the authors proceed as in Refs. [18,19] 'in want of a separate measurement of the excess.' Including DELPHI/SLD charged-hadron rows and excluding ALEPH/OPAL therefore rests on opposite verdicts about the same unmeasured excess, and only one side is tested. Please provide a sensitivity study: refit with the DELPHI and SLD charged-hadron rows removed (retaining the identified pi, K, p rows), or with a free normalization for the excess, and report how much the light- and b-quark parameters of Table 2 and alpha_s(M_Z) move. If the shifts are small, the point is settled and the paper is strengthened; if they are not, the quoted uncertainties on those functions should reflect it.
[Section 2, alpha_s extraction] The headline result alpha_s(M_Z) = 0.1170 (+0.005, -0.007) at NLO (abstract:s4) is quoted with an experimental error only. The text acknowledges that theoretical errors 'may be estimated through variations of the overall scale mu = M_f' but does not perform the estimate. Since the extraction rests on the scaling violation between 29 and 91.2 GeV and on the assumed absence of 1/Q power corrections, a scale-variation band is needed before the word 'competitive' in the abstract can be assessed. Please also state explicitly that the Delta-chi-squared = 1 prescription with all other parameters held fixed is conservative relative to profiling over them, so the reader knows the direction of the approximation.
[Section 3, Table 5 and Fig. 10] The abstract (abstract:s5) and Section 3 state that the longitudinal cross section data 'nicely agree' with the predictions, and the text singles out the flavour-separated case as confirming the relative weight of the light- and b-quark functions against the gluon. Table 5 contradicts this for one row: sigma_L^h(uds) from DELPHI [28] gives chi-squared per degree of freedom 7.98 at NLO, by far the largest entry in the table and larger than the corresponding LO value of 1.05. That entry is not discussed. Either explain the discrepancy (for example, whether it is driven by the lowest-x bins where the fit was not constrained) or soften the claim in the abstract and Section 3 so that it matches the table.

Minor objections (7)

[Fig. 11 caption] The caption attributes the dotted curves to 'DELPHI [21]', but Ref. [21] is OPAL; the DELPHI gluon fragmentation function is Ref. [30]. Please correct the citation.
[References] Ref. [5] gives 'Nucl. Phys. B 136 (1998) 1' for Field and Feynman; the year is presumably 1978. Please check.
[Section 2, Eq. (2)] The three-parameter ansatz with no separate valence and sea components is a strong assumption, and the paper is commendably explicit that the u, d, and s quarks are always combined in the data. It would help to state in one sentence how many data points constrain each gluon parameter, since the gluon function for each hadron species is fixed by only the 5 ALEPH [20] and 12 OPAL [21] three-jet points.
[Section 3, Table 4] The momentum sum rule check is well handled and the deficit is traced to the non-sea-like d-quark component in K±. It would be worth stating in the text that the sum rule was deliberately not imposed as a fit constraint, so that Table 4 is a diagnostic rather than a failure of the fit.
[Section 4] The statement that the functions are bound to break down at very low x and that an MLLA modification is deferred to Ref. [35] is appropriate. Since Ref. [35] is listed as 'in preparation', please indicate what the reader should use in the interim below x = 0.1.
[Table 1] The LO and NLO chi-squared columns are difficult to read as typeset, with the LO values interleaved among the NLO ones. Consider separating them into distinct columns or a supplementary table.
[Note added] Citing the Kretzer preprint [39] that appeared after submission is good practice; consider also mentioning it in the introduction where the earlier NLO sets are reviewed.

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The paper

The paper claims

A single set of fragmentation functions, fitted at the Z peak, also reproduces hadron production at five lower energies and pins down the strong coupling.

The reading

When an electron and a positron annihilate, the quarks and gluons that come out cannot be observed directly; they turn into sprays of hadrons, and the probability that a given parton carries away a fraction $x$ of the momentum and ends up as a particular hadron is encoded in a fragmentation function $D_a^h(x,Q^2)$. This paper's aim is to extract those functions for charged pions, charged kaons, and protons/antiprotons, at both leading and next-to-leading order in the strong coupling, using the most informative data then available. The strategy is to exploit the fact that LEP1 and SLC delivered samples enriched in light, charm, and bottom quarks, plus gluon-tagged three-jet events, so that each parton flavour can be constrained separately rather than assumed to behave like the others. Adding PEP data at $29$ GeV gives the fit a lever on how the functions change with energy scale, which is what makes a determination of $O(1)$ possible. The payoff claimed is a set of functions that not only fits the input data at about one unit of chi-squared per degree of freedom, but also, without further tuning, describes independent data at $5.4$ to $34$ GeV and the longitudinal cross section on the Z resonance.

What carries the argument

The machinery is a global fit in which the $x$ dependence of each fragmentation function is fixed by a three-parameter form $N x^alpha (1-x)^beta$ at a flavour-dependent starting scale ($sqrt{2}$ GeV for light quarks and the gluon, the $eta_c$ mass for charm, the $Upsilon$ mass for bottom), and the scale dependence is generated by the timelike Altarelli-Parisi evolution equations solved in Mellin space. What carries the argument is the flavour separation: light-, charm-, and bottom-enriched samples plus gluon-tagged three-jet events let the fit treat each parton independently, subject only to the symmetry relations $D_u^{pi^pm} = D_d^{pi^pm}$, $D_u^{K^pm} = D_s^{K^pm}$, and $D_u^{p/bar p} = 2 D_d^{p/bar p}$ suggested by valence content. The two-energy fit, with $29$ GeV data included alongside the Z peak, is what converts the fit from a description of one energy into a measurement of scaling violation and hence of $alpha_s$.

Extended reading notes

Core claim

The paper reports new leading-order and next-to-leading-order sets of fragmentation functions for $h = $ sum over $h$ of $D_a^h(x,Q^2)$, with $h$ standing for the charge-summed $h$, $K^pm$, and $p/bar p$, parameterized at three starting scales as $D_a^h(x,Q_0^2) = N x^alpha (1-x)^beta$. With 46 free parameters, including the QCD scale parameter, the fit achieves an overall $chi^2$ per degree of freedom of $0.98$ at NLO and $0.97$ at LO across the ALEPH, DELPHI, OPAL, SLD, and TPC samples used as input. Because data at $29$ GeV and $91.2$ GeV enter together, the fit is sensitive to the running of the coupling and returns $Lambda_{overline{MS}}^{(5)} = 213^{+75}_{-73}$ MeV and $alpha_s(M_Z) = 0.1170^{+0.005}_{-0.007}$ at NLO, values the authors note agree with the then-current world average. The authors treat the agreement with the longitudinal cross section, where the gluon function already enters at leading order, as an independent confirmation of the gluon fragmentation function, and they check that the momentum sum rule, which they did not impose, comes out reasonably close to unity over the range $0.05 le x le 1$.

Load-bearing premise

The fit's light-quark and bottom-quark fragmentation functions are fixed by keeping the DELPHI and SLD flavour-tagged samples and discarding the ALEPH and OPAL ones, on the belief that an unmeasured population of charged hadrons other than pions, kaons, and protons explains why those discarded samples sit far above the predictions.

Editorial extensions

If this is right

The extracted functions can be inserted into predictions for single-hadron production in $p bar p$, $e p$, $gamma p$, and $gamma gamma$ scattering, since the factorization theorem makes them process-independent.
The NLO value $alpha_s(M_Z) = 0.1170^{+0.005}_{-0.007}$ from a single class of observables provides an independent cross-check on averages built from many different measurements.
The agreement with DORIS and PETRA data at $5.4$ to $34$ GeV supports the assumption that power corrections suppressed by $1/Q$ are negligible over the energy range of the fit.
The gluon fragmentation function, constrained by gluon-tagged three-jet events and tested by the longitudinal cross section, is made available for use in other processes where gluon fragmentation dominates.
The public FORTRAN routine released with the paper lets other analyses evaluate $D_a^h(x,Q^2)$ directly, which is what makes the set usable outside this paper.

Reading between the lines

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

The decision to exclude the ALEPH and OPAL flavour-tagged charged-hadron samples, which give chi-squared per degree of freedom of order $100$ against these predictions, is the hinge on which the light- and bottom-quark functions turn; a future measurement of the yield of charged hadrons beyond $pi^pm$, $K^pm$, and $p/bar p$ in tagged Z decays would either vindicate or overturn it.
Because the fit does not impose the momentum sum rule, the shortfall in Table 4 (the $s$-quark entry sits near $0.6$ and the gluon above unity at low scales) is a diagnostic of how weakly the individual light-quark flavours are constrained rather than a refutation; the imbalance is traced to the $d$-quark component of the kaon behaving unlike a sea quark.
The parameterization $N x^alpha (1-x)^beta$ is bound to fail at very small $x$, where the authors themselves point to modified leading-logarithmic resummation; a natural extension is to refit with an MLLA-motivated form and see whether the gluon function and the extracted $alpha_s$ shift.
Since the same functions should describe fragmentation in hadron-hadron and lepton-hadron collisions, the sharpest external test is a prediction for inclusive identified-hadron cross sections at a scale far from the Z peak, where the evolution rather than the fit dominates.

Original abstract

We present new sets of fragmentation functions for charged pions, charged kaons, and protons, both at the leading and next-to-leading orders. They are fitted to the scaled-momentum distributions of these hadrons measured in e+e- annihilation on the Z-boson resonance at CERN LEP1 and SLAC SLC. These data partly come as light-, charm-, bottom-quark-enriched and gluon-jet samples, which allows us to treat all partons independently, after imposing the SU(2) flavour symmetry relations. In order to gain sensitivity to the scaling violation in fragmentation, we also include data from SLAC PEP, with center-of-mass energy root(s)=29 GeV, in our fits. This allows us to also determine the strong-coupling constant, with a competitive error. LEP1 data on the longitudinal cross section as well as DESY DORIS and PETRA data at lower energies nicely agree with theoretical predictions based on our fragmentation functions.

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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,009 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.11 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.39 · compares with prior results 0.33 · mentions code or data availability 0.03.

The abstract, sentence by sentence

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

We present new sets of fragmentation functions for charged pions, charged kaons, and protons, both at the leading and next-to-leading orders. They are fitted to the scaled-momentum distributions of these hadrons measured in e+e- annihilation on the Z-boson resonance at CERN LEP1 and SLAC SLC. These data partly come as light-, charm-, bottom-quark-enriched and gluon-jet samples, which allows us to treat all partons independently, after imposing the SU(2) flavour symmetry relations. In order to gain sensitivity to the scaling violation in fragmentation, we also include data from SLAC PEP, with center-of-mass energy root(s)=29 GeV, in our fits. This allows us to also determine the strong-coupling constant, with a competitive error. LEP1 data on the longitudinal cross section as well as DESY DORIS and PETRA data at lower energies nicely agree with theoretical predictions based on our fragmentation functions.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We present new sets of fragmentation functions for charged pions, charged kaons, and protons, both at the leading and next-to-leading orders.	contribution 1.00	0.95	0.60	asserted 1.00
s1	They are fitted to the scaled-momentum distributions of these hadrons measured in e+e- annihilation on the Z-boson resonance at CERN LEP1 and SLAC SLC.	method 0.96	0.80	0.07	asserted 1.00
s2	These data partly come as light-, charm-, bottom-quark-enriched and gluon-jet samples, which allows us to treat all partons independently, after imposing the SU(2) flavour symmetry relations.	method 0.99	0.40	0.05	asserted 0.99
s3	In order to gain sensitivity to the scaling violation in fragmentation, we also include data from SLAC PEP, with center-of-mass energy root(s)=29 GeV, in our fits.	method 0.96	0.78	0.03	asserted 0.96
s4	This allows us to also determine the strong-coupling constant, with a competitive error.	result 0.97	0.92	0.12	asserted 0.99
s5	LEP1 data on the longitudinal cross section as well as DESY DORIS and PETRA data at lower energies nicely agree with theoretical predictions based on our fragmentation functions.	result 0.91	0.55	0.19	asserted 0.95

What kind of paper the classifier reports this is: dataset or benchmark 0.46 · evidence from analysis of existing data 1.00.

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.** Normalized differential cross section of inclusive hadron pr

**Figure 2.** Same as in Fig. 1, but for the light-quark-enriched samples

**Figure 3.** Same as in Fig. 1, but for the

**Figure 4.** Same as in Fig. 1, but for the

**Figure 5.** Gluon FF for charged-hadron production as a function of

**Figure 6.** Normalized differential cross section of inclusive charged-

**Figure 7.** Normalized differential cross section of inclusive

**Figure 8.** Same as in Fig. 7, but for

**Figure 9.** Normalized differential cross section of inclusive

**Figure 10.** Normalized differential longitudinal cross section of inclus

**Figure 11.** Gluon FFs for charged-hadron production as functions

Figures reproduced from arXiv:hep-ph/0010289 by the authors.

References

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(in this order from top to bottom). Each pair of curves is resca led relative to the nearest upper one by a factor of 1/30. 27 Dg(x,Q2) x e+e- → Z0 → qq– 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 1 10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure 11: Gluon FFs for charged-hadron production as functions of x at Mf = 10, 52.4, 80.2, and 200 GeV from ...

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A first unbiased global determination of polarized PDFs and their uncertainties
hep-ph 2014-06 conditional novelty 6.0 of 10

A global fit of polarized parton distributions that adds RHIC jet, W-boson, and COMPASS open-charm data to polarized DIS finds a positive gluon polarization at x between 0.02 and 0.5 and separates up and down antiquar...
Multiplicity distributions in p+p, p+A and A+A collisions from Yang-Mills dynamics
hep-ph 2013-11 conditional novelty 6.0 of 10

The IP-Glasma model, with color charge fluctuations constrained by HERA data, reproduces charged-particle multiplicity distributions across p+p, p+A and A+A collisions once an energy-dependent normalization and a tune...
Evidence for BFKL and saturation dynamics from di-hadron spectra at the LHC
hep-ph 2012-10 conditional novelty 6.0 of 10

Combining Glasma graphs from saturation physics with BFKL-resummed back-to-back emission quantitatively reproduces CMS di-hadron spectra in high-multiplicity p+p collisions and predicts a ridge in p+Pb.
Impact-parameter dependent nuclear parton distribution functions: EPS09s and EKS98s and their applications in nuclear hard processes
hep-ph 2012-05 conditional novelty 6.0 of 10

A four-term fit in nuclear thickness converts the measured mass-number dependence of averaged nuclear PDFs into an impact-parameter-dependent profile, released as EPS09s and EKS98s and applied to centrality-dependent ...
Azimuthal collimation of long range rapidity correlations by strong color fields in high multiplicity hadron-hadron collisions
hep-ph 2012-01 conditional novelty 6.0 of 10

Color Glass Condensate calculations using rcBK-evolved unintegrated gluon distributions reproduce the CMS per-trigger ridge yields in high-multiplicity pp collisions and bound radial flow in pp to beta of about 0.25.
EPS09 - a New Generation of NLO and LO Nuclear Parton Distribution Functions
hep-ph 2009-02 conditional novelty 6.0 of 10

Next-to-leading-order nuclear parton distributions are extracted from DIS, Drell-Yan and RHIC pion data and released as a central set plus 30 error sets for propagating uncertainties to nuclear cross-sections.
Calculating Quenching Weights
hep-ph 2003-02 conditional novelty 6.0 of 10

Treating the finite in-medium path length exactly cuts off soft gluon emission, which flattens the predicted suppression of high-momentum hadrons and brings energy-loss models into agreement with RHIC pion data.
Predictions for $R_{AA}$ in 5.36 TeV C+C, O+O, and Ne+Ne collisions at the LHC
hep-ph 2025-09 conditional novelty 5.0 of 10

LHC light-ion R_AA measurements could discriminate between scenarios with and without mini-QGP formation in pp collisions, with the largest difference predicted for carbon.
EPPS21: A global QCD analysis of nuclear PDFs
hep-ph 2021-12 accept novelty 5.0 of 10

New LHC proton-lead dijet and D-meson data shrink the uncertainty on nuclear gluon distributions by a large factor and confirm gluon shadowing and antishadowing in lead.
Jet Quenching from QCD Evolution
hep-ph 2015-09 conditional novelty 5.0 of 10

Medium-modified DGLAP evolution of fragmentation functions reproduces LHC hadron suppression data and contains traditional parton energy loss as its soft-gluon emission limit.
nCTEQ15 - Global analysis of nuclear parton distributions with uncertainties in the CTEQ framework
hep-ph 2015-09 accept novelty 5.0 of 10

nCTEQ15 provides nuclear parton distributions with Hessian uncertainty bands for any nucleus up to lead, fitted to 740 DIS, Drell-Yan and RHIC pion-production data points.
Explanation of systematics of CMS p+Pb high multiplicity di-hadron data at $\sqrt{s}_{\rm NN} = 5.02$ TeV
hep-ph 2012-11 conditional novelty 5.0 of 10

The Color Glass Condensate framework, with parameters fixed from proton-proton fits, reproduces the centrality and transverse-momentum systematics of CMS proton-lead di-hadron correlations.
CGC predictions for p+Pb collisions at the LHC
hep-ph 2012-09 conditional novelty 5.0 of 10

Running-coupling BK evolution with Monte Carlo nuclear geometry predicts RpPb near 0.6 at midrapidity rising toward unity at high transverse momentum, and no Cronin peak at LHC energies.
TMD Parton Distribution and Fragmentation Functions with QCD Evolution
hep-ph 2011-01 conditional novelty 5.0 of 10

Starting from existing fits and the Collins-Soper-Sterman formalism, the authors produce evolved transverse-momentum-dependent quark distributions and fragmentation functions and show that QCD evolution suppresses the...
Phenomenological extraction of fragmentation functions in a $p\bar{p}$ environment
hep-ph 2026-07 conditional novelty 4.5 of 10

Kinematic cuts in Tevatron p-pbar photon-hadron production make cross-section ratios of kaons to pions approximate u-quark fragmentation-function ratios, enabling flavour-separated FF constraints.
Comparison of the Color Glass Condensate to di-hadron correlations in proton-proton and proton-nucleus collisions
hep-ph 2013-02 conditional novelty 4.0 of 10

The Color Glass Condensate framework, with one normalization per collision system, reproduces the long-range di-hadron ridge in p+p and p+Pb data from CMS, ALICE and ATLAS, supporting a gluon-saturation origin.
Comparison of Jet Quenching Formalisms for a Quark-Gluon Plasma "Brick"
hep-ph 2011-06 accept novelty 4.0 of 10

A controlled comparison of four perturbative-QCD jet-quenching formalisms on the same uniform-medium benchmark finds sizable differences in gluon radiation and energy loss, traceable mainly to large-angle and finite-l...
The Surprising Transparency of the sQGP at LHC
hep-ph 2011-04 conditional novelty 4.0 of 10

A perturbative QCD energy-loss model, anchored to RHIC pion suppression and scaled by the LHC charged-particle multiplicity, over-predicts jet quenching relative to ALICE central-to-peripheral data.
Novel Collective Phenomena in High-Energy Proton-Proton and Proton-Nucleus Collisions
nucl-ex 2015-09 accept novelty 3.0 of 10

High-multiplicity proton-proton and proton-lead collisions show heavy-ion-like long-range azimuthal correlations, and neither hydrodynamic nor Color Glass Condensate explanations is yet ruled out by the data.
Azimuthal and Single Spin Asymmetries in Hard Scattering Processes
hep-ph 2007-12 conditional novelty 2.0 of 10

Large left-right asymmetries in pion production off polarized protons are best described by a transverse-momentum-dependent Sivers function, but the factorization underpinning single-inclusive hadroproduction remains ...
Hadronization in QCD and Fragmentation Functions
hep-ph 2026-10 accept novelty 1.0 of 10

This review maps the NNLO and NNLL theory of collinear fragmentation functions, the world data sets, and current pion, kaon, and charged-hadron extractions, comparing four recent pion fits.

How later papers used it

80 later papers cite it

Evidence: substantial. 80 of the citing papers share no author with it, and 22 of those carry a confident label from Pith's citation classifier.

Pith read 28 of the 98 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

10 later papers by other authors are listed below: 8 used its method or tool, 1 used its data or values and 1 compared its own results with it.

Uses its method or tool 8 of 14 papers with this label

Employed the next-to-leading order KKP fragmentation functions from this paper to obtain the charged hadron pseudo-rapidity density from the gluon spectrum.

Accessing subnuclear fluctuations and saturation with multiplicity dependent $J/\psi$ production in p+p and p+Pb collisions (2021) · 0.94 · paraphrased: the licence does not allow quoting
Used the fragmentation functions from this paper to obtain the pionic R_AA from the partonic one, neglecting the gluon contribution.

Holographic light quark jet quenching at RHIC and LHC via the shooting strings (2014) · 0.95 · paraphrased: the licence does not allow quoting
Computed charged hadron production in p+p(A) collisions by convoluting the inclusive gluon production cross-section with the KKP fragmentation function from this paper.

Unified framework for heavy flavor and quarkonium production in high multiplicity p+p and p+A collisions at RHIC and LHC (2018) · 1.00 · paraphrased: the licence does not allow quoting
We convoluted the parton spectra with Binnewies-Kniehl-Kramer (BKK) [ref] and Kniehl-Kramer-Potter (KKP) [ref] fragmentation functions (FFs) using the program [ref] [<http://lapth.cnrs.fr/PHOX_FAMILY/readme_inc.html>] modified to use LHAPDF grids [ref] .

Discovering partonic rescattering in light nucleus collisions (2020) · Introduction · 0.97
Computed the charged hadron distribution from the gluon distribution using the next-to-leading order KKP fragmentation functions from this paper.

Multiplicity distributions in p+p, p+A and A+A collisions from Yang-Mills dynamics (2013) · 0.98 · paraphrased: the licence does not allow quoting
Generated partonic spectra and used the KKP fragmentation function from this paper to generate leading hadron spectra.

Event-by-Event Simulations of Jet Modification Using the MATTER Event Generator (2017) · 0.94 · paraphrased: the licence does not allow quoting
Showed results using the NLO KKP parameterization from this paper of fragmentation functions for gluon to charged hadrons.

Novel Collective Phenomena in High-Energy Proton-Proton and Proton-Nucleus Collisions (2015) · 0.89 · paraphrased: the licence does not allow quoting
Set up grids for inclusive pion production in DAu collisions at RHIC using the INCNLO code with the KKP fragmentation functions from this paper.

EPPS16: Nuclear parton distributions with LHC data (2016) · 0.97 · paraphrased: the licence does not allow quoting

Uses its data or values 1 of 6 papers with this label

Employed the NLO parametrization of the KKP fragmentation function from this paper for charged hadron production at mu=2 GeV.

Event engineering studies for heavy flavor production and hadronization in high multiplicity hadron-hadron and hadron-nucleus collisions (2018) · 0.95 · paraphrased: the licence does not allow quoting

Compares with it 1 of 2 papers with this label

Found that its own microcanonical Tsallis fragmentation function differs from the HKNS and KKP fragmentation functions from this paper at lower energy scales and momenta.

Non-extensive Motivated Parton Fragmentation Functions (2018) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

75 arXiv papers cite this in 92 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 59 sentences without a confident label

Uses its method or tool 13 papers

KRE [ref] , KKP [ref] , HKNS [ref] , AKK08 [ref] , and DSS [ref] FFs are used with the same scale $μ= 1.2 p_T$ for single hadrons and $μ= 1.2 M$ for dihadrons, respectively.

Extracting the jet transport coefficient from hadron suppressions by confronting current NLO parton fragmentation functions · Extracting $q̂_0$ in central $Au+Au$ collisions at $√(s_NN)=200$ GeV · 0.86
We compute gluon production using $k_T$-factorized cross sections [ref] and hadronize using KKP fragmentation functions [ref] .

Accessing subnuclear fluctuations and saturation with multiplicity dependent $J/\psi$ production in p+p and p+Pb collisions · Introduction · 0.98
Finally, we use the fragmentation functions [ref] to obtain the pionic $R_AA$ from the partonic one (neglecting the gluon contribution).

Holographic light quark jet quenching at RHIC and LHC via the shooting strings · Calculation of $R_AA$ · 0.95

Uses its data or values 5 papers

The parton distribution functions are denoted by $f_i/p (x_1, μ^2 )$ and are given by the CTEQ6 parameterization [ref] . $D^0_h/i(z_i,μ^2)$ are the unmodified fragmentation functions given by the KKP parameterization [ref] .

Three and two-hadron correlations in \sqrt{s_{NN}}=200 GeV proton-proton and nucleus-nucleus collisions · Introduction · 0.81
For the vacuum FFs $D_h/j(z,Q_0)$ we use the KKP [ref] parametrization with $Q_0=2$ GeV.

Updated analysis of jet quenching at RHIC and LHC within the light cone path integral approach · Nuclear modification factor · 0.83
Using Refs. [ref] for the integrated FFs, we can then calculate the TMD FF using Eq. [ref].

TMD Parton Distribution and Fragmentation Functions with QCD Evolution · TMD FFs · 0.96

Compares with it 2 papers

We obtained that our microcanonical Tsallis FF differs from the HKNS [ref] and KKP [ref] FFs at lower energy scales and momenta, which could affect the low momentum calculations of proton-proton collisions.

Non-extensive Motivated Parton Fragmentation Functions · Conclusion · 1.00
This may explain why, despite the very different theoretical constraints on the KKP [ref] and Kretzer [ref] sets, the values for this FF from these sets are very similar in the fit range of $x$, except at large $z$ because the data at large $x$ are scarce (see Fig. [ref]).

The hadronization of partons · Global fitting of fragmentation functions from $e^+ e^-$ reaction data · 0.96

Cites it as background 10 papers

Recent determinations of the pion FFs include results by several groups such as HKNS [ref] , NNFF [ref] , JAM [ref] , SGKS [ref] , SGK [ref] , and other studies available in the literature including KKP [ref] , BKK [ref] , and KLC [ref]

QCD analysis of pion fragmentation functions in the xFitter framework · Introduction · 0.96
Gluon fragmentation functions from different authors are available for the use in perturbative QCD calculations, e.g., KRE [ref] , BKK [ref] , KKP [ref] , AKK [ref] , DSS [ref] .

Production of Neutral Pions and Eta-mesons in pp Collisions Measured with ALICE · Introduction · 0.85
Fragmentation functions have first been determined from global fits of data (e.g. BFGW [ref] , KKP [ref] , Kretzer [ref] ), at LEP and other facilities at lower energies.

Probing fragmentation functions from same-side hadron-jet momentum correlations in p-p collisions · Introduction · 1.00

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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