Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order αs4 in a General Gauge Theory

We compute, for the first time, the order α_s⁴ contributions to the Bjorken sum rule for polarized electron-nucleon scattering and to the (nonsinglet) Adler function for the case of a generic color gauge group. We confirm at the same order a (generalized) Crewther relation which provides a strong test of the correctness of our previously obtained results: the QCD Adler function and the five-loop β function in quenched QED. In particular, the appearance of an irrational contribution proportional to ζ₃ in the latter quantity is confirmed. We obtain the commensurate scale equation relating the effective strong coupling constants as inferred from the Bjorken sum rule and from the Adler function at order α_s⁴.