TTP10-05 Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^$ in a General Gauge Theory

TTP10-05 Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^$ in a General Gauge Theory

We compute, for the first time, the order alpha_s^4
contributions to the Bjorken sum rule for polarized electron-nucleon scattering
and to the (non-singlet) Adler function for the case of a generic colour 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 \beta-function in quenched QED.
In particular, the appearance of an irrational contribution proportional
to zeta_3 in the latter quantity is confirmed.
We obtain the {\em commensurate} scale equation relating the effective
strong coupling constants as inferred from the Bjorken sum rule and from
the Adler function at order alpha_s^4.