Four-loop non-singlet splitting functions in QCD are computed analytically for the first time, with numerical representations provided.
The Three-Loop Splitting Functions in QCD: The Singlet Case
12 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We compute the next-to-next-to-leading order (NNLO) contributions to the splitting functions governing the evolution of the unpolarized flavour-singlet parton densities in perturbative QCD. The exact expressions are presented in both Mellin-N and Bjorken-x space. We also provide accurate parametrizations for practical applications. Our results agree with all partial results available in the literature. As in the non-singlet case, the correct leading logarithmic predictions for small momentum fractions x do not provide good estimates of the respective complete splitting functions. We investigate the size of the corrections and the stability of the NNLO evolution under variation of the renormalization scale. The perturbative expansion appears to converge rapidly at x >~ 10^-3. Relatively large third-order corrections are found at smaller values of x.
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Four-loop non-singlet QCD splitting functions are verified for consistency and used to finalize analytical forms for the gluon virtual anomalous dimension and N^4LL threshold resummation coefficients, revealing a new small-x logarithmic structure.
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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.
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.
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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.
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.
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