Conformal symmetry limit of QED and QCD and the identities between the concrete perturbative contributions to deep-inelastic scattering sum rules    [PDF]

A. L. Kataev
Conformal symmetry based relations between the concrete perturbative QED and QCD approximations of the polarized Bjorken, the Ellis-Jaffe, the Gross-Llewellyn Smith sum rules and of the Adler functions of the axial vector and vector channels are derived. They are based on application of the operator product expansion to three triangle AVV Green functions, constructed from the non-singlet axial vector-vector-vector currents, the {\it singlet} axial-vector and two {\it non-singlet} vector currents and the {\it non-singlet} axial-vector-vector and {\it singlet} vector currents, in the limit when the conformal symmetry of gauge models with fermions is unbroken. We specify the conditions when the conformal symmetry is valid in the U(1) and $SU(N_c)$ models. The identity between perturbative approximations of the Bjorken, Ellis-Jaffe and the Gross-Llewellyn Smith sum rules, which follow from this theoretical limit, is proved. The expressions for the $O(\alpha^4)$ and $O(\alpha_s^3)$ conformal symmetry based contributions for these sum rules and for the NS Adler function are considered. The differences between these terms and the similar corrections, obtained recently within the phenomenologically oriented generalization of the BLM-approach, which is based on the Principle of Maximal Conformality, are discovered. The necessity of careful study of the origin of this difference is discussed.
View original: http://arxiv.org/abs/1305.4605