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 — preprints:2010:ttp10-05 [2016/03/17 11:03] (current) Line 1: Line 1: + ====== TTP10-05 Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^$in a General Gauge Theory ====== + + + <​hidden TTP10-05 ​ Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^$ 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. + ​ + |**P.A. Baikov, K.G. Chetyrkin and  J.H. K\"​uhn...** ​ | + |** Phys.Rev.Lett. 104 132004 2010  **  | + | {{preprints:​2010:​ttp10-05.pdf|PDF}} {{preprints:​2010:​ttp10-05.ps|PostScript}} [[http://​arxiv.org/​abs/​1001.3606|arXiv]] ​  | + | |