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

TL;DR

This paper derives a conformal symmetry-based relation between the Bjorken and Ellis-Jaffe sum rules in massless gauge theories, providing a theoretical foundation that could aid in analyzing experimental data.

Contribution

It establishes a novel relation between the sum rules using conformal invariance in massless gauge theories, extending previous results to include higher-order approximations.

Findings

Derived the relation in conformal invariant limit of massless U(1) and SU(N_c) theories.

Presented the $O(eta^3)$ approximation of the non-singlet coefficient function.

Outlined potential applications in phenomenological analysis of experimental data.

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.