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

TL;DR

This paper calculates the alpha_s^4 order contributions to the Bjorken sum rule and Adler function for a general gauge group, confirming a generalized Crewther relation and providing new high-order QCD results.

Contribution

First computation of alpha_s^4 contributions to the Bjorken sum rule and Adler function in a general gauge theory, confirming the generalized Crewther relation at this order.

Findings

Confirmed the alpha_s^4 order contributions to the Bjorken sum rule and Adler function.

Validated the generalized Crewther relation at five-loop order.

Identified an irrational zeta_3 contribution in the QED Adler function.

Abstract

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 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.