Twist-2 Light-Ray Operators: Anomalous Dimensions and Evolution Equations

Abstract

The non-singlet and singlet anomalous dimensions of the twist--2 light-ray operators for unpolarized and polarized deep inelastic scattering are calculated in $O({\alpha }_s)$. We apply these results for the derivation of evolution equations for partition functions, structure functions, and wave functions which are defined as Fourier transforms of the matrix elements of the light-ray operators. Special cases are the Altarelli-Parisi and Brodsky-Lepage kernels. Finally we extend Radyushkin's solution from the non-singlet to the singlet case.

14 pages latex, Contribution to the Proceedings of the Int. Workshop Deep Inelastic Scattering off Polarized Targets : Theory Meets Experiment, September 1--5, 1997, DESY--Zeuthen, Germany; 3 typos corrected