Light-Ray Operators and their Application in QCD

TL;DR

This paper explores light-ray operators in QCD, linking nonperturbative parton distributions to matrix elements, deriving evolution equations, and applying the operator product expansion to virtual Compton scattering.

Contribution

It introduces a generalized framework for light-ray operators, deriving evolution equations that unify various known kernels and applying the operator product expansion to new scattering processes.

Findings

Derived the Altarelli-Parisi kernel as a limit of the Brodsky-Lepage kernel.

Established evolution equations for generalized distribution amplitudes.

Applied the operator product expansion to virtual Compton scattering.

Abstract

The nonperturbative parton distribution and wave functions are directly related to matrix elements of light-ray (nonlocal) operators. These operators are generalizations of the standard local operators known from the operator product expansion. The renormalization group equation for these operators leads to evolution equations for more general distribution amplitudes which include the Altarelli-Parisi and the Brodsky-Lepage equations as special cases. It is possible to derive the Altarelli-Parisi kernel as a limiting case of the extended Brodsky-Lepage kernel. As new application of the operator product expansion the virtual Compton scattering near forward direction is considered.