New perturbation theory representation of the conformal symmetry breaking effects in gauge quantum field theory models

TL;DR

This paper introduces a new representation for conformal symmetry breaking in QCD's Crewther relation, validated up to four-loop order, and derives new relations between perturbative coefficients of key QCD observables.

Contribution

It proposes a detailed structure for the conformal symmetry breaking term in the Crewther relation within perturbative QCD and establishes its validity up to order , enabling new coefficient relations.

Findings

Validated the new representation at  order in  approximation.

Derived new relations between  coefficients of the Adler function and Bjorken sum rule.

Provided a theoretical check for recent high-order perturbative calculations.

Abstract

We propose a hypothesis on the detailed structure for the representation of the conformal symmetry breaking term in the basic Crewther relation generalized in the perturbation theory framework in QCD renormalized in the ${\rm \bar{MS}}$ scheme. We establish the validity of this representation in the $O(\alpha_s^4)$ approximation. Using the variant of the generalized Crewther relation formulated here allows finding relations between specific contributions to the QCD perturbation series coefficients for the flavor nonsinglet part of the Adler function $D^{ns}_A$ for the electron-positron annihilation in hadrons and to the perturbation series coefficients for the Bjorken sum rule $S_\text{Bjp}$ for the polarized deep-inelastic lepton-nucleon scattering. We find new relations between the $\alpha_s^4$ coefficients of $D^{ns}_A$ and $S_\text{Bjp}$. Satisfaction of one of them serves as an additional theoretical verification of the recent computer analytic calculations of the terms of order $\alpha_s^4$ in the expressions for these two quantities.