Conformal symmetry based relation between Bjorken and Ellis-Jaffe sum rules

Abstract

The identity between expressions for the coefficient functions of the Bjorken and Ellis-Jaffe sum rules is derived in the conformal invariant limit of massless U(1) theory, namely in the perturbative quenched QED model, and in the same limit of the massless $SU(N_c)$ gauge theory with fermions. The derivation is based on the comparison of results of application of the operator product expansion approach to the dressed triangle Green functions of singlet Axial vector- Vector-Vector and non-singlet Axial vector-Vector-Vector fermion currents in the limit, when the conformal symmetry is not violated. The expressions for the $O(\alpha_s^3)$ approximation of the non-singlet coefficient function, derived in the conformal invariant limit of $SU(N_c)$ group, is reminded. Its possible application in the phenomenological analysis of the experimental data for the Bjorken polarized sum rule is outlined.