D. Muller et al., WAVE-FUNCTIONS, EVOLUTION-EQUATIONS AND EVOLUTION KERNELS FROM LIGHT-RAY OPERATORS OF QCD, Fortschritte der Physik, 42(2), 1994, pp. 101-141
The widely used nonperturbative wave functions and distribution functi
ons of QCD are determined as matrix elements of light-ray operators. T
hese operators appear as large momentum limit of non-local hadron oper
ators or as summed up local operators in light-cone expansions. Nonfor
ward one-particle matrix elements of such operators lead to new distri
bution amplitudes describing both hadrons simultaneously. These distri
bution functions depend besides other variables on two scaling variabl
es. They are applied for the description of exclusive virtual Compton
scattering in the Bjorken region near forward direction and the two me
son production process. The evolution equations for these distribution
amplitudes are derived on the basis of the renormalization group equa
tion of the considered operators. This includes that also the evolutio
n kernels follow from the anomalous dimensions of these operators. Rel
ations between different evolution kernels (especially the Altarelli-P
arisi and the Brodsky-Lepage kernels) are derived and explicitly check
ed for the existing two-loop calculations of QCD. Technical basis of t
hese results arc support and analytically properties of the anomalous
dimensions of light-ray operators obtained with the help of the alpha-
representation of Green's functions.