Towards the NNLO evolution of polarised parton distributions

Abstract

We report on the first calculation of the structure function g_1 in polarised deep-inelastic scattering to the third order in massless perturbative QCD. The calculation follows the dispersive approach already used for the corresponding unpolarised cases of F_2,L, but additionally involves higher tensor integrals and the Dirac matrix gamma_5 in D unequal 4 dimensions. Our results confirm all known two-loop expressions including the coefficient functions of Zijlstra and van Neerven not independently verified before. At three loops we extract the helicity-difference next-to-next-to-leading order (NNLO) quark-quark and gluon-quark splitting functions Delta P_qq and Delta P_qg. The results exhibit interesting features concerning sum rules and the momentum-fraction limits x to 1 and x to 0.

7 pages, LaTeX, 4 ps/eps-figures. Contribution to the proceedings of the workshops `Loops and Legs in Quantum Field Theory', April 2008, Sondershausen (Germany) and (shortened) DIS 2008, London, April 2008

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Cited by in corpus (33)

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• The Theory of Deeply Inelastic Scattering
• The three-loop unpolarized and polarized non-singlet anomalous dimensions from off shell operator matrix elements
• The three-loop polarized singlet anomalous dimensions from off-shell operator matrix elements
• The massless three-loop Wilson coefficients for the deep-inelastic structure functions $F_2,F_L,x{F}_3$ and $g_1$
• EKO: Evolution Kernel Operators
• The Polarized Three-Loop Anomalous Dimensions from On-Shell Massive Operator Matrix Elements
• QCD Spin Physics: Partonic Spin Structure of the Nucleon
• NNLO Global Analysis of Polarized Parton Distribution Functions
• Resummation of small-x double logarithms in QCD: inclusive deep-inelastic scattering
• The Polarized Two-Loop Massive Pure Singlet Wilson Coefficient for Deep-Inelastic Scattering
• Jet production in Polarized DIS at NNLO
• The Logarithmic Contributions to the Polarized and Operator Matrix Elements in Deeply Inelastic Scattering
• The spin-dependent quark beam function at NNLO
• Renormalization of the flavor-singlet axial-vector current and its anomaly in dimensional regularization
• On gamma_5 in higher-order QCD calculations and the NNLO evolution of the polarized valence distribution
• $O({\alpha }_s^2$) Polarized Heavy Flavor Corrections}to Deep-Inelastic Scattering at $Q^2\gg m^2$
• The full set of Polarized Deep Inelastic Scattering Structure Functions at NNLO accuracy
• The Spin Budget of the Proton at NNLO and Beyond
• Inclusive-jet and Di-jet Production in Polarized Deep Inelastic Scattering
• The Two-Loop Massless Off-Shell QCD Operator Matrix Elements to Finite Terms
• NNLO jet production in neutral and charged current polarized deep inelastic scattering
• Renormalization of the axial current operator in dimensional regularization at four-loop in QCD
• Parton-shower effects in polarized deep inelastic scattering
• Spin structure of the nucleon: QCD evolution, lattice results and models
• Dijet Production in Neutral Current and Charged Current Polarized Deep Inelastic Scattering
• A calculation of the three-loop helicity-dependent splitting functions in QCD
• The $\overline{\mathrm{MS}}$ renormalization constant of the singlet axial current operator at $\mathcal{O}({\alpha }_s^5)$ in QCD
• Illuminating the nucleon spin
• Proton Structure and PHENIX Experiment