Is it possible to check urgently the 5-loop analytical results for the $e^{+}{e}^{-}$-annihilation Adler function ?

Abstract

Considering the results of recent distinguished analytical calculations of the 5-loop single-fermion loop corrections to the QED $\beta$-function we emphasize that to our point of view it is important to perform their independent cross-checks. We propose one of the ways of these cross-check. It is based on the application of the original Crewther relation. We derive the new analytical expressions for the $C_F^4{\alpha }_s^4$-contributions to the Bjorken polarized sum rule. If results of possible direct calculations will agree with the presented expression, then the appearance of ${\zeta }_3$-term in the 5-loop correction to the QED $\beta$-function and in the $C_F^4{\alpha }_s^4$ contribution into the $e^{+}{e}^{-}$ annihilation Adler function will get independent support and may be analysed within the framework of the recently introduced concept of "maximal transcendentality".

5 pages

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Cited by in corpus (13)

• Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^4 in a General Gauge Theory
• New perturbation theory representation of the conformal symmetry breaking effects in gauge quantum field theory models
• R(s) and hadronic tau-Decays in Order alpha_s^4: technical aspects
• Hadronic vacuum polarization function within dispersive approach to QCD
• Analytical five-loop expressions for the renormalization group QED $\beta$-function in different renormalization schemes
• Conformal symmetry limit of QED and QCD and identities between perturbative contributions to deep-inelastic scattering sum rules
• Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the $\beta$-factorization property?
• The absence of QCD $\beta$-function factorization property of the generalized Crewther relation in the 't Hooft $\overline{MS}$-based scheme
• Riemann $\zeta (3)$- terms in perturbative QED series, conformal symmetry and the analogies with structures of multiloop effects in N=4 supersymmetric Yang-Mills theory
• Inclusive tau lepton hadronic decay in vector and axial-vector channels within dispersive approach to QCD
• The analytical singlet ${\alpha }_s^4$ QCD contributions into the $e^{+}{e}^{-}$-annihilation Adler function and the generalized Crewther relations
• Dispersive approach to QCD: tau lepton hadronic decay in vector and axial-vector channels
• Hadronic contributions to electroweak observables within DPT