Operator product expansion in QCD in off-forward kinematics: Separation of kinematic and dynamical contributions

TL;DR

This paper develops a method to separate kinematic and dynamical contributions in QCD operator product expansion, providing tools for precise calculations in off-forward processes like deeply-virtual Compton scattering.

Contribution

It introduces projection operators to isolate kinematic parts of twist-four operators and derives comprehensive expressions for electromagnetic current products including these corrections.

Findings

Projection operators for kinematic contributions are established.

Complete expressions for electromagnetic current products with twist-four corrections.

Identification of twist-four operators sharing anomalous dimensions with leading twist.

Abstract

We develop a general approach to the calculation of target mass and finite t=(p'-p)^2 corrections in hard processes which can be studied in the framework of the operator product expansion and involve momentum transfer from the initial to the final hadron state. Such corrections, which are usually referred to as kinematic, can be defined as contributions of operators of all twists that can be reduced to total derivatives of the leading twist operators. As the principal result, we provide a set of projection operators that pick up the "kinematic" part of an arbitrary flavor-nonsinglet twist-four operator in QCD. A complete expression is derived for the time-ordered product of two electromagnetic currents that includes all kinematic corrections to twist-four accuracy. The results are immediately applicable to the studies of deeply-virtual Compton scattering, transition gamma^*-> M gamma form factors and related processes. As a byproduct of this study, we find a series of "genuine" twist-four flavor-nonsinglet quark-antiquark-gluon operators which have the same anomalous dimensions as the leading twist quark-antiquark operators.