The Virtual Compton Amplitude in the Generalized Bjorken Region: Twist--2 Contributions
J. Blümlein, B. Geyer, D. Robaschik
TL;DR
The paper develops twist-2 QCD evolution for quark and gluon light-ray operators in the generalized Bjorken region, using a non-local light-cone expansion to derive two-variable distribution amplitudes and their RG evolution. It provides explicit anomalous dimensions at ${\cal O}(\alpha_s)$, establishes relations between non-local and local operators, and constructs evolution kernels in both two- and one-variable representations, unifying forward and deeply virtual Compton scattering and vacuum-meson transitions. Special limits recover standard forward DIS results (Callan-Gross, WW, AP) and the Brodsky-Lepage framework, while solutions via Mellin and Gegenbauer methods yield the evolution of singlet and non-singlet sectors. The framework yields a coherent, process-independent description of scaling violations in non-forward Compton scattering.
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.