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

TL;DR

This paper calculates anomalous dimensions of twist-2 light-ray operators in QCD at order alpha_s, deriving evolution equations for various functions and extending known solutions from non-singlet to singlet cases.

Contribution

It provides new calculations of anomalous dimensions and extends Radyushkin's solution to the singlet case, enhancing understanding of evolution equations in QCD.

Findings

Calculated non-singlet and singlet anomalous dimensions at O(α_s)

Derived evolution equations for structure functions and wave functions

Extended Radyushkin's solution to the singlet case

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.