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arXiv · 0808.3121

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

A. L. Kataev
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Abstract

Considering 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 $C_F^4α_s^4$-contributions to the Bjorken polarized sum rule. If results of possible direct calculations will agree with the presented expression, then the appearance of $ζ_3$-term in the 5-loop correction to the QED $β$-function and in the $C_F^4α_s^4$ 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".

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A. L. Kataev. 2008-08-22. Is it possible to check urgently the 5-loop analytical results for the $e^+e^-$-annihilation Adler function ?. https://doi.org/10.1016/j.physletb.2008.08.068

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