New extended Crewther-type relation and the consequences of multiloop perturbative results

TL;DR

This paper explores an extended Crewther relation in QCD, analyzing multiloop perturbative results and their implications for conformal symmetry breaking, supported by high-order calculations and the $eta$-expansion formalism.

Contribution

It introduces a new form of the Crewther relation and examines its implications using multiloop perturbative QCD calculations and the $eta$-expansion approach.

Findings

Relations between 5-loop contributions to D-function and Bjorken sum rule are established.

Confirmation of high-order perturbative calculations through new theoretical relations.

Enhanced understanding of conformal symmetry breaking in QCD.

Abstract

We discuss the current status of the investigations of the conformal symmetry breaking contributions to three forms for the QCD generalizations of the Crewther relation. The new third form of the extension of this relation is considered in more detail. Particular attention is paid to the discussions of the applications of the $\beta$-expansion formalism proposed previously by one of us (SVM). Several relations between 5-loop contributions to the Adler D-function $D^{NS}_{A}$ and to the polarized Bjorken sum rule $S_\text{Bjp}$ are presented. One of them gives the additional confirmation of the correctness of the advanced analytical computer calculations of order $\alpha_s^4$ contributions to $D^{NS}_{A}$ and $S_\text{Bjp}$ in the general $SU(N_c)$ gauge group.