Adler function, Bjorken Sum Rule and Crewther-Broadhurst-Kataev relation with generic fermion representations at order $O(\alpha^4_s)$

TL;DR

This paper calculates high-order QCD corrections to the Adler function and Bjorken sum rule for arbitrary fermion representations, confirming the Crewther-Broadhurst-Kataev relation at order $O(\alpha_s^4)$.

Contribution

It extends the calculation of QCD corrections to include arbitrary fermion representations at four-loop order, verifying the CBK relation in this context.

Findings

Confirmed the Crewther-Broadhurst-Kataev relation at $O(\alpha_s^4)$

Computed the nonsinglet Adler D-function at four-loop order

Calculated the Bjorken sum rule coefficient at four-loop order

Abstract

We compute the nonsinglet Adler $D$-function and the coefficient function for Bjorken polarized sum rules $S^{Bjp}$ at order $O(\alpha_s^4)$ in an extended QCD model with arbitrary number of fermion representations. The Crewther-Broadhurst-Kataev (CBK) relation in this order is confirmed.