Conformal invariance and the expressions for $C_F^4{\alpha }_s^4$ contributions to the Bjorken polarized and the Gross-Llewellyn Smith sum rules

Abstract

Considering massless axial-vector-vector triangle diagram in the conformal invariant limit and the the results of recent distinguished analytical calculations of the 5-loop single-fermion loop corrections to the QED $\beta$-function, we derive the analytical expressions for the $C_F^4{\alpha }_s^4$-contributions to the Bjorken polarized and Gross-Llewellyn Smith sum rule. This visible in future evaluation can shed extra light on the reliability of the appearance of ${\zeta }_3$-term in the explicitly known part of 5-loop corrections to the QED $\beta$-function which are proportional to the conformal invariant set of $C_F^4{\alpha }_s^4$ -contributions into to the $e^{+}{e}^{-}$- annihilation Adler function.

Comments: Based on the Talk at the 15th International Seminar on High Energy Physics "QUARKS-2008", Sergiev Posad, Russia, 23-29 May, 2008 More detailed presentation, clarification in the abstract made, references added, special Acknowledgements added. Conclusions not changed