We have discovered 7 intimate connections between the published results for the radiative corrections, C K , to the Gross-Llewellyn Smith (GLS) sum rule, in deepinelastic lepton scattering, and the radiative corrections, C R , to the Adler function of the flavour-singlet vector current, in e + e − annihilation. These include a surprising relation between the scheme-independent single-electron-loop contributions to the 4-loop QED β-function and the zero-fermion-loop abelian terms in the 3-loop GLS sum rule. The combined effect of all 7 relations is to give the factorization of the 2-loop β-function in INR-820/93 OUT-4102-45 1 ) In memoriam Sergei Grigorievich Gorishny, 1958-1988 2 ) D.Broadhurst@open.ac.uk 3 ) Kataev@inucres.msk.su
We present the attempt to study the problem of the estimates of higher-order perturbative corrections to physical quantities in the Euclidean region. Our considerations are based on the application of the scheme-invariant methods, namely the principle of minimal sensitivity and the effective charges approach. We emphasize, that in order to obtain the concrete results for the physical quantities in the Minkowskian region the results of application of this formalism should be supplemented by the explicite calculations of the effects of the analytical continuation. We present the estimates of the order O(α The problem of the fixation of the uncertainties due to the O(α 5 s ) corrections to the considered quantities is also discussed.
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