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.