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We compute, for the first time, the order alpha_s^4 contributions to theBjorken sum rule for polarized electron-nucleon scattering and to the(non-singlet) Adler function for the case of a generic colour gauge group. Weconfirm at the same order a (generalized) Crewther relation which provides astrong test of the correctness of our previously obtained results: the QCDAdler function and the five-loop beta-function in quenched QED. In particular,the appearance of an irrational contribution proportional to zeta_3 in thelatter quantity is confirmed. We obtain the commensurate scale equationrelating the effective strong coupling constants as inferred from the Bjorkensum rule and from the Adler function at order alpha_s^4.

Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^4 in a General Gauge Theory