Pith. sign in

REVIEW 47 cited by

The Three-Loop Splitting Functions in QCD: The Non-Singlet Case

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv hep-ph/0403192 v1 pith:MW5VS7AU submitted 2004-03-17 hep-ph

classification hep-ph
keywords evolutionresultssmallcorrectionsfoundfunctionsnnlonon-singlet
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

We compute the next-to-next-to-leading order (NNLO) contributions to the three splitting functions governing the evolution of unpolarized non-singlet combinations of quark densities in perturbative QCD. Our results agree with all partial results available in the literature. We find that the correct leading logarithmic (LL) predictions for small momentum fractions x do not provide a good estimate of the respective complete results. A new, unpredicted LL contribution is found for the colour factor d^{abc}d_{abc} entering at three loops for the first time. We investigate the size of the corrections and the stability of the NNLO evolution under variation of the renormalization scale. Except for very small x the corrections are found to be rather small even for large values of the strong coupling constant, in principle facilitating a perturbative evolution into the sub-GeV regime.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 47 Pith papers

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

  1. New results on small-x resummation for splitting functions

    hep-ph 2026-03 conditional novelty 8.0 of 10

    A closed-form all-order expression for the qg anomalous dimension, plus new all-order results for the LL gluon anomalous dimension and the finite qg/gg Green functions, derived and implemented in HELL 4.0.

  2. Investigating the universality of five-point QCD scattering amplitudes at high energy

    hep-ph 2024-11 conditional novelty 8.0 of 10

    First extraction of the two-loop universal central-emission vertex in QCD and in N=4 super Yang-Mills from the multi-Regge limit of five-point amplitudes.

  3. The two-loop fully differential soft function for $Q\bar{Q}V$ production at lepton colliders

    hep-ph 2024-11 accept novelty 8.0 of 10

    The two-loop soft function fully differential in the total momentum of real radiation in QQV production is computed analytically in terms of Goncharov polylogarithms.

  4. A Toolbox for $q_T$ and $0$-Jettiness Subtractions at N$^3$LO

    hep-ph 2019-09 conditional novelty 8.0 of 10

    The paper provides the complete three-loop singular subtraction terms for qT and 0-jettiness and derives the first threshold predictions for the three-loop beam-function coefficients, later confirmed by direct calculation.

  5. Relating amplitude and PDF factorisation through Wilson-line geometries

    hep-ph 2019-09 conditional novelty 8.0 of 10

    The difference between form-factor and large-x PDF single-pole anomalous dimensions equals one quarter of the lightlike parallelogram Wilson-loop anomalous dimension, verified at two loops.

  6. Strongly Coupled Soft Functions

    hep-ph 2026-08 conditional novelty 7.0 of 10

    The cusp anomalous dimension at strong coupling is obtained for all rapidity separations from two competing string saddles, and the transversely-separated two-cusp Wilson loop scales as (b_perp^2 Lambda^2)^{-Re Gamma_cusp}.

  7. Event-axis TMD measurements in $e^+e^-$ and SIDIS

    hep-ph 2026-07 unverdicted novelty 7.0 of 10

    Completes soft-operator formulation for thrust-axis TMD in e+e- and SIDIS, proposes nonperturbative model with event-shape dependence, resums logs, and validates against Pythia8.3 simulations.

  8. The Collins-Soper kernel from a vacuum soft function

    hep-lat 2026-06 unverdicted novelty 7.0 of 10

    The Collins-Soper kernel is extracted from lattice computations of a vacuum soft function, showing rapidity dependence consistent with Collins-Soper evolution, comparable errors to hadronic methods, and saturation at ...

  9. Four-loop anomalous dimension of flavor non-singlet quark operator of twist two and Lorentz spin N for general gauge group: transcendental part

    hep-ph 2026-05 unverdicted novelty 7.0 of 10

    Presents the zeta(3)-proportional term of the four-loop non-singlet twist-two quark anomalous dimension for general N in closed form, extracted via analytic reconstruction from published Mellin moments.

  10. The N$^3$LO Twist-2 Matching of Linearly Polarized Gluon TMDs

    hep-ph 2025-09 unverdicted novelty 7.0 of 10

    Computes N³LO twist-2 matching for linearly polarized gluon TMDs with NNLL small-x resummation for fragmentation functions.

  11. Polarized Deep Inelastic Scattering as $x \to 1$ using Soft Collinear Effective Theory

    hep-ph 2025-07 conditional novelty 7.0 of 10

    SCET factorization and one-loop matching for polarized DIS g1(x), g2(x) as x approaches 1, including anomalous dimensions and twist-three operator relations.

  12. Flavour Non-Singlet Splitting Functions at Four Loops in QCD -- The Fermionic Contributions

    hep-ph 2025-05 accept novelty 7.0 of 10

    The n_f-dependent pieces of the four-loop non-singlet QCD splitting functions are derived analytically, yielding the n_f parts of the quark and gluon virtual anomalous dimensions and new soft-gluon threshold coefficients.

  13. Two-loop helicity amplitudes for diphoton production with massive quark loop

    hep-ph 2025-02 conditional novelty 7.0 of 10

    Two-loop helicity amplitudes for diphoton production with a massive top quark loop are computed, providing new analytic results for gluon fusion and benchmark numbers for both channels.

  14. Thrust distribution in electron-positron annihilation at full NNNLL+NNLO (and beyond) in QCD

    hep-ph 2025-02 conditional novelty 7.0 of 10

    Laplace-space resummation of the thrust distribution at N4LL accuracy yields alpha_S(mZ^2) = 0.1181 +/- 0.0018, consistent with the world average, while physical-space resummation gives a lower value.

  15. Resummation for Lattice QCD Calculation of Generalized Parton Distributions at Nonzero Skewness

    hep-ph 2025-01 conditional novelty 7.0 of 10

    A threshold factorization and resummation scheme for quasi-GPD matching in LaMET is derived and shown to be self-consistent on a GPD model.

  16. Beyond Scale Variations: Perturbative Theory Uncertainties from Nuisance Parameters

    hep-ph 2024-11 conditional novelty 7.0 of 10

    A framework that turns missing higher-order perturbative coefficients into fit-able theory nuisance parameters, giving correlated and statistically meaningful theory uncertainties.

  17. Drell-Yan Transverse-Momentum Spectra at N$^3$LL$'$ and Approximate N$^4$LL with SCETlib

    hep-ph 2024-11 conditional novelty 7.0 of 10

    State-of-the-art LHC predictions for W/Z transverse momentum spectra at N3LL' and approximate N4LL accuracy, with a rigorous reduction of nonperturbative TMD physics to one effective function per process.

  18. The Three-Point Energy Correlator in the Coplanar Limit

    hep-ph 2024-11 conditional novelty 7.0 of 10

    A new tau_p projection makes the coplanar limit of the three-point energy correlator a TMD-factorized trijet observable, resummed to N3LL, the first trijet event shape at this order.

  19. Second-order QCD corrections to event shape distributions in deep inelastic scattering

    hep-ph 2019-09 accept novelty 7.0 of 10

    The NNLO QCD corrections to DIS event shape distributions and their mean values are computed for the first time, reducing scale uncertainties and improving the description of H1 and ZEUS data.

  20. Heavy Jet Mass in Hadronic Higgs Decays

    hep-ph 2026-07 conditional novelty 6.0 of 10

    Heavy jet mass in hadronic Higgs decays is predicted at N³LL′ (dijet) plus NNLL (Sudakov shoulder) plus NNLO, with new analytic trijet-region logarithms for H→gg and H→q̄q.

  21. Threshold resummation of Semi-Inclusive Deep-Inelastic Scattering

    hep-ph 2026-01 unverdicted novelty 6.0 of 10

    Derives resummed coefficient functions for SIDIS in double-soft and single-soft threshold limits, with explicit NNLL coefficients extracted in the nonsinglet channel by matching to fixed-order results.

  22. Approximate N$^2$LO and N$^3$LO QCD Predictions for $tW$ Production

    hep-ph 2025-12 conditional novelty 6.0 of 10

    Higher-order QCD corrections to top-plus-W production raise the predicted rate by over 10% and give |Vtb|=0.99±0.03.

  23. Slepton pair production at next-to-leading power

    hep-ph 2025-10 unverdicted novelty 6.0 of 10

    Evaluates next-to-leading power threshold corrections for slepton pair production and finds them significant compared to leading power NLL terms, with underestimated scale errors for large masses.

  24. Soft and virtual corrections to semi-inclusive DIS up to four loops in QCD

    hep-ph 2025-06 conditional novelty 6.0 of 10

    A threshold-resummation formalism for SIDIS yields new approximate N3LO and N4LO soft, virtual, and next-to-soft coefficient functions for the diagonal quark channel.

  25. Soft Factorisation and Exponentiation from Schwinger-Space Geometry

    hep-th 2025-06 conditional novelty 6.0 of 10

    Soft-hard factorization and exponentiation of infrared divergences in QED are derived from graph Laplacians and tropical rays in Schwinger parameter space.

  26. Anomalous dimensions at small spins

    hep-th 2025-06 accept novelty 6.0 of 10

    The quadratic mass-correction combination of twist-two anomalous dimensions stays finite at small spin in the O(N) phi^4, phi^3, and Gross-Neveu-Yukawa models at the computed loop orders, enabling explicit resummations.

  27. Precise Determination of the Strong Coupling Constant from Dijet Cross Sections up to the Multi-TeV Range

    hep-ph 2024-12 conditional novelty 6.0 of 10

    A complete NNLO QCD fit to LHC and HERA dijet data yields alpha_s(m_Z) = 0.1178 with a total uncertainty of 0.0022 and tests the running coupling from 7 GeV up to 7 TeV.

  28. Quark Transverse Spin-Momentum Correlation of the Pion from Lattice QCD: The Boer-Mulders Function

    hep-lat 2024-12 conditional novelty 6.0 of 10

    The pion Boer-Mulders function is computed for the first time from lattice QCD and is found to decay with transverse separation, becoming compatible with zero around 0.5 to 0.6 fm.

  29. Three-loop jet function for boosted heavy quarks

    hep-ph 2024-12 conditional novelty 6.0 of 10

    The three-loop inclusive bHQET jet function for boosted heavy quarks is computed analytically, completing the fixed-order ingredients for N3LL' top-mass observables.

  30. Heavy quark mass effects in the Energy-Energy Correlation in the back-to-back region

    hep-ph 2024-12 conditional novelty 6.0 of 10

    Massive quark Sudakov resummation for e+e- energy-energy correlations is extended to NNLL accuracy, and the NLL dead cone angle is enlarged by sqrt(e).

  31. Threshold Resummation for Semi-Inclusive Single-Hadron Production with Effective Field Theory

    hep-ph 2024-11 accept novelty 6.0 of 10

    Momentum-space SCET threshold resummation for SIA is extended to N4LL for quark and gluon channels, with new large-x coefficients through N3LO and partial N4LO.

  32. Parton Distribution Functions from Ioffe time pseudo-distributions

    hep-lat 2019-08 conditional novelty 6.0 of 10

    A dynamical lattice QCD calculation using Ioffe-time pseudo-distributions produces an isovector nucleon valence PDF and first two moments at M_pi ~ 400 MeV, with estimates of lattice-spacing and finite-volume systematics.

  33. Open-source QCD analysis of nuclear parton distribution functions at NLO and NNLO

    hep-ph 2019-08 accept novelty 6.0 of 10

    The authors produce the TUJU19 nuclear PDF sets at NLO and NNLO from a global fit of lepton and neutrino DIS data using a modified open-source xFitter framework.

  34. Soft corrections to inclusive DIS at four loops and beyond

    hep-ph 2019-08 conditional novelty 6.0 of 10

    The fourth-order (N4LL) soft-gluon exponentiation coefficient for inclusive DIS is derived in the large-nc limit and is shown to give corrections below one percent.

  35. Candia-v2: Logarithmic expansions for DGLAP evolution in $x$-space

    hep-ph 2026-07 conditional novelty 5.0 of 10

    Candia-v2 implements (approximate) N3LO x-space DGLAP evolution — exact four-loop non-singlet splitting functions, envelope-approximated singlet inputs, three-loop heavy-quark matching — as a public C++ package with G...

  36. Polarized Deep-Inelastic Scattering with Spin Correlations in Herwig 7

    hep-ph 2026-06 unverdicted novelty 5.0 of 10

    Herwig 7 now supports NLO POWHEG-matched polarized DIS including neutral and charged currents, with spin-density matrix propagation that affects some shower observables but not others.

  37. PDF evolution in alternative factorisation schemes

    hep-ph 2026-06 unverdicted novelty 5.0 of 10

    Derives NLO splitting functions and anomalous dimensions for PDFs in alternative factorization schemes and interprets their leading x-behavior as a modified effective evolution scale.

  38. Associated $ZH$ production in gluon fusion process at NLO+NLL

    hep-ph 2026-05 unverdicted novelty 5.0 of 10

    NLO+NLL QCD corrections to gluon-fusion ZH production increase the cross-section by ~20% and reduce scale uncertainties from 20% to 12% at LHC energies, combined with Drell-Yan N3LL results.

  39. New CTEQ global analysis of quantum chromodynamics with high-precision data from the LHC

    hep-ph 2019-12 unverdicted novelty 5.0 of 10

    New CT18 PDFs at NLO and NNLO from global fit to HERA plus LHC jet, Drell-Yan, top-pair and Z data, with Hessian errors, Lagrange-multiplier studies, and alternate sets for data tensions and scale choices.

  40. NNLO Determination of Polarized Parton Distribution Functions with Higher-Twist and Target-Mass Corrections

    hep-ph 2026-07 accept novelty 4.0 of 10

    KLS26 is an NNLO polarized PDF set from inclusive DIS that includes TMC, additive and multiplicative higher-twist terms, and positivity, with the largest NNLO shifts in the strange-quark helicity distribution.

  41. Entanglement entropy, Monte Carlo event generators, and soft gluons DIScovery

    hep-ph 2025-09 unverdicted novelty 4.0 of 10

    Including soft gluons in Monte Carlo generators for DIS aligns parton distributions with inclusive PDFs and makes entropy grow with decreasing x, indicating initial-state origin of the bulk entropy.

  42. Analytical solution to DGLAP integro-differential equation via complex maps in domains of contour integrals

    hep-th 2019-12 unverdicted novelty 3.0 of 10

    In the single-term splitting function model, complex maps turn DGLAP contour integrals into Laplace transforms whose inverse yields Barnes integrals for the Bessel solution.

  43. Global analyses of helicity-dependent parton distribution functions

    hep-ph 2026-07 accept novelty 2.0 of 10

    Modern global QCD analyses agree that up-quark helicity is positive and down-quark helicity negative, with positive gluon polarisation at moderate x, while the full gluon spin moment remains limited by the unmeasured ...

  44. QCD for electroweak precision measurements: Foundations

    hep-ph 2026-07 accept novelty 1.0 of 10

    QCD collinear factorization, DGLAP evolution, and QT resummation, developed via DIS and Drell-Yan, form the calculational foundation for precision electroweak observables and new-physics searches.

  45. Parton Distribution Functions and their Generalizations

    hep-ph 2025-07 unverdicted novelty 1.0 of 10

    A textbook-style introduction to the definitions, QCD properties, experimental access, and current phenomenological status of PDFs and their generalizations.

  46. Energy Correlators: A Journey From Theory to Experiment

    hep-ph 2025-06 unverdicted novelty 1.0 of 10

    A review of energy correlators and their role in QCD, collider experiments, and formal quantum field theory.

  47. Mapping Parton Distributions of Hadrons with Lattice QCD

    hep-lat 2025-06 accept

    A review of lattice QCD methods and results for x-dependent parton distribution functions and generalized parton distributions of hadrons.

Pith tools