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Wave Functions, Evolution Equations and Evolution Kernels from Light‐Ray Operators of QCD
Author(s) -
Müller D.,
Robaschik D.,
Geyer B.,
Dittes F.M.,
Hořejši J.
Publication year - 1994
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190420202
Subject(s) - quantum chromodynamics , physics , light cone , parton , compton scattering , matrix (chemical analysis) , distribution (mathematics) , particle physics , momentum (technical analysis) , scattering , mathematical analysis , quantum mechanics , mathematics , materials science , finance , economics , composite material
The widely used nonperturbative wave functions and distribution functions of QCD are determined as matrix elements of light‐ray operators. These operators appear as large momentum limit of non‐local hadron operators or as summed up local operators in light‐cone expansions. Nonforward one‐particle matrix elements of such operators lead to new distribution amplitudes describing both hadrons simultaneously. These distribution functions depend besides other variables on two scaling variables. They are applied for the description of exclusive virtual Compton scattering in the Bjorken region near forward direction and the two meson production process. The evolution equations for these distribution amplitudes are derived on the basis of the renormalization group equation of the considered operators. This includes that also the evolution kernels follow from the anomalous dimensions of these operators. Relations between different evolution kernels (especially the Altarelli‐Parisi and the Brodsky‐Lepage kernels) are derived and explicitly checked for the existing two‐loop calculations of QCD. Technical basis of these results are support and analytically properties of the anomalous dimensions of light‐ray operators obtained with the help of the α‐representation of Green's functions.