The virtual Compton amplitude in the generalized Bjorken region: Twist-2 contributions

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. Var ious representations of the anomalous dimensions are derived in the non-loc al and local light cone expansion and their properties are discussed in det ail. Evolution equations for these operators are derived using different re presentations. General two- and single-variable evolution equations are pre sented for the expectation values of these operators for non-forward scatte ring. The Compton amplitude is calculated in terms of these distribution am plitudes. In the limit of forward scattering a new derivation of the integr al relations between the twist-2 contributions to the structure functions i s given. Special limiting cases which are derived from the general relation s are discussed, as the forward case, near-forward scattering, and vacuum-m eson transition. Solutions of the two-variable evolution equations for non- forward scattering are presented. (C) 1999 Elsevier Science B.V. All rights reserved.