On Connection between Coefficient Functions for Deep-Inelastic and Annihilation Processes

It has been shown that the one-loop behavior of the axial anomaly, occurring when the axial current is appropriately normalized, leads to the cancellation of the corrections of type $C_F^N{\bar α}_s^N,~~ (N\geq 1)$ in the Crewther relation for the coefficient functions of deep-inelastic and annihilation processes. The arguments in favour of the overall factorization of the factor $β({\bar α}_s)/ {\bar α}_s$ in all orders of perturbation theory in this relation are presented.

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