Conformal symmetry limit of QED and QCD and identities between perturbative contributions to deep-inelastic scattering sum rules

TL;DR

This paper derives conformal symmetry-based relations between perturbative QED and QCD contributions to key deep-inelastic scattering sum rules and Adler functions, providing all-order identities and approximations relevant for theoretical analyses.

Contribution

It introduces new conformal symmetry-based identities linking perturbative contributions across different sum rules and Adler functions in QED and QCD, valid under specific symmetry conditions.

Findings

Derived all-order perturbative identities for sum rules and Adler functions.

Provided analytical and numerical conformal symmetry-based approximations up to O(α^4) and O(α_s^2).

Discussed conditions for conformal symmetry validity in gauge models.

Abstract

Conformal symmetry-based relations between concrete perturbative QED and QCD approximations for the Bjorken, the Ellis-Jaffe sum rules of polarized lepton- nucleon deep-inelastic scattering (DIS), the Gross-Llewellyn Smith sum rules of neutrino-nucleon DIS, and for the Adler functions of axial-vector and vector channels are derived. They result from the application of the operator product expansion to three triangle Green functions, constructed from the non-singlet axial-vector, and two vector currents, the singlet axial-vector and two non-singlet vector currents and the non-singlet axial-vector, vector and singlet vector currents in the limit, when the conformal symmetry of the gauge models with fermions is considered unbroken. We specify the perturbative conditions for this symmetry to be valid in the case of the $U(1)$ and $SU(N_c)$ models. The all-order perturbative identity following from the conformal invariant limit between the concrete contributions to the Bjorken, the Ellis-Jaffe and the Gross-Llewellyn Smith sum rules is proved. The analytical and numerical $O(\alpha^4)$ and $O(\alpha_s^2)$ conformal symmetry based approximations for these sum rules and for the Adler function of the non-singlet vector currents are summarized. Possible theoretical applications of the results presented are discussed.