Riemann $\zeta(3)$- terms in perturbative QED series, conformal symmetry and the analogies with structures of multiloop effects in N=4 supersymmetric Yang-Mills theory

Understand

As was discovered recently, 5-loop perturbative quenched QED approximation to the QED $\beta$-function consist from the rational term and the term proportional to $\zeta(3)$-function.

• It is stressed, that this feature is also manifesting itself in the conformal invariant pqQED series for the 4-loop approximation to the anomalous mass dimension.
• The 4-loop pqQED expression for the singlet contribution into the Ellis-Jaffe polarized sum rule is obtained.
• It coincides with the similar approximation for the non-singlet coefficient function of Ellis-Jaffe sum rule and of Bjorken polarized sum rule.