WAVE-FUNCTIONS, EVOLUTION-EQUATIONS AND EVOLUTION KERNELS FROM LIGHT-RAY OPERATORS OF QCD

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.