The asymptotics of the evolution kernels P ab (z) of parton distributions is investigated as z→1. It is proven that to all orders of perturbative QCD, [Formula: see text] where [Formula: see text] is the cusp anomalous dimension of the contour functionals in the fundamental (α=“quark”) and adjoint (α=“gluon”) representations of gauge group and, to the lowest orders, C α are related to the anomalous dimension of a quark field in the axial gauge and the beta function of QCD by a simple equation.
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G.P. Korchemsky (1989) studied this question.