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

AbstractConsidering the results of recent distinguished analytical calculations of the 5-loop single-fermion loop corrections to the QED β-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 CF4αs4-contributions to the Bjorken polarized sum rule. If results of possible direct calculations will agree with the presented expression, then the appearance of ζ3-term in the 5-loop correction to the QED β-function and in the CF4αs4 contribution into the e+e− annihilation Adler function will get independent support and may be analysed within the framework of the recently introduced concept of “maximal transcendentality”