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Unpolarized Quark and Gluon TMD PDFs and FFs at N$^3$LO

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arxiv 2012.03256 v2 pith:EQRDS75N submitted 2020-12-06 hep-ph nucl-th

Ming-xing Luo , Tong-Zhi Yang , Hua Xing Zhu , Yu Jiao Zhu This is my paper · ORCID
classification hep-phnucl-th
keywords pdfsfunctionsgluonlogarithmicorderquantitiesquarkunpolarized
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

In this paper we calculate analytically the perturbative matching coefficients for unpolarized quark and gluon Transverse-Momentum-Dependent (TMD) Parton Distribution Functions (PDFs) and Fragmentation Functions (FFs) through Next-to-Next-to-Next-to-Leading Order (N$^3$LO) in QCD. The N$^3$LO TMD PDFs are calculated by solving a system of differential equation of Feynman and phase space integrals. The TMD FFs are obtained by analytic continuation from space-like quantities to time-like quantities, taking into account the probability interpretation of TMD PDFs and FFs properly. The coefficient functions for TMD FFs exhibit double logarithmic enhancement at small momentum fraction $z$. We resum such logarithmic terms to the third order in the expansion of $\alpha_s$. Our results constitute important ingredients for precision determination of TMD PDFs and FFs in current and future experiments.

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Cited by 4 Pith papers

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

  1. Impact of Z-boson transverse-momentum resummation on PDF determination

    hep-ph 2026-07 conditional novelty 6.0 of 10

    N3LL' resummation is required to reconcile the 13 TeV ATLAS Z-pT spectrum with global PDF fits, but lowering the pT cut below 30 GeV is not yet supported.

  2. Transverse Charge Distribution as a Probe of Nucleon Transversity

    hep-ph 2026-07 conditional novelty 6.0 of 10

    A charge-flow measurement built only from track angles and charge signs contains a leading-twist chiral-odd dipole that matches the charge-weighted Collins moment, giving enhanced transversity-sensitive asymmetries.

  3. Exploring nuclear modification using one-point energy correlator at the electron-ion collider

    hep-ph 2025-12 conditional novelty 6.0 of 10

    OPEC in e+A collisions factorizes in TMD QCD and predicts ~0.3–0.4 nuclear suppression at small angles, growing with angle, as a probe of cold-nuclear-matter broadening.

  4. Assessing the sensitivity of Energy-Energy Correlations in $e^+e^-$ annihilation to TMD dynamics

    hep-ph 2025-07 conditional novelty 6.0 of 10

    At N4LL accuracy, a global fit to all available e+e- energy-energy correlation data shows the data are insensitive to the Collins-Soper kernel and alpha_s, contradicting a recent extraction claim.

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