The Three-Loop Splitting Functions in QCD: The Helicity-Dependent Case

Abstract

We present the next-to-next-to-leading order (NNLO) contributions to the main splitting functions for the evolution of longitudinally polarized parton densities of hadrons in perturbative QCD. The quark-quark and gluon-quark splitting functions have been obtained by extending our previous all Mellin-N calculations to the structure function g_1 in electromagnetic deep-inelastic scattering (DIS). Their quark-gluon and gluon-gluon counterparts have been derived using third-order fixed-N calculations of structure functions in graviton-exchange DIS, relations to the unpolarized case and mathematical tools for systems of Diophantine equations. The NNLO corrections to the splitting functions are small outside the region of small momentum fractions x where they exhibit a large double-logarithmic enhancement, yet the corrections to the evolution of the parton densities can be unproblematic down to at least x about 10^{-4}.

52 pages, Latex, 10 figures. FORM and Fortran files of the main results available with the source

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Cited by in corpus (7)

• Four-Loop Non-Singlet Splitting Functions in the Planar Limit and Beyond
• Large-nf Contributions to the Four-Loop Splitting Functions in QCD
• Helicity Evolution at Small $x$: Flavor Singlet and Non-Singlet Observables
• The 3-Loop Non-Singlet Heavy Flavor Contributions to the Structure Function g_1(x,Q^2) at Large Momentum Transfer
• Absence of pi^2 terms in physical anomalous dimensions in DIS: verification and resulting predictions
• Study of spin-dependent structure functions of ${}^3\mathrm{He}$ and ${}^3\mathrm{H}$ at NNLO approximation and corresponding nuclear corrections
• The spin-dependent quark beam function at NNLO