Is it possible to check urgently the 5-loop analytical results for the $e^+e^-$-annihilation Adler function ?

Understand

Considering the results of recent distinguished analytical calculations of the 5-loop single-fermion loop corrections to the QED $\beta$-function we emphasize that to our point of view it is important to perform their independent cross-checks.

• We propose one of the ways of these cross-check.
• It is based on the application of the original Crewther relation.
• We derive the new analytical expressions for the $C_F^4\alpha_s^4$-contributions to the Bjorken polarized sum rule.