The Virtual Compton Amplitude in the Generalized Bjorken Region: Twist--2 Contributions

TL;DR

This paper systematically derives the twist-2 anomalous dimensions of quark and gluon operators in the generalized Bjorken region, providing evolution equations and analyzing the Compton amplitude for both polarized and unpolarized scattering.

Contribution

It introduces new derivations of evolution equations and anomalous dimensions for twist-2 operators in non-forward scattering, expanding understanding of the generalized Bjorken region.

Findings

Derived twist-2 anomalous dimensions for quark and gluon operators.

Presented evolution equations for non-forward scattering.

Calculated the Compton amplitude in terms of distribution amplitudes.

Abstract

A systematic derivation is presented of the twist-2 anomalous dimensions of the general quark and gluon light-ray operators in the generalized Bjorken region in leading order both for unpolarized and polarized scattering. Various representations of the anomalous dimensions are derived both in the non-local and the local light cone expansion and their properties are discussed in detail. Evolution equations for these operators are derived using different representations. General two- and single-variable evolution equations are presented for the expectation values of these operators for non-forward scattering. The Compton amplitude is calculated in terms of these distribution amplitudes. In the limit of forward scattering a new derivation of the integral relations between the twist-2 contributions to the structure functions is given. Special limiting cases which are derived from the general relations are discussed, as the forward case, near-forward scattering, and vacuum-meson transition. Solutions of the two-variable evolution equations for non-forward scattering are presented.