Riemann ζ(4) function contributions to O(α_s⁵) terms of Adler D-function and Bjorken polarized sum rule in SU(N_c) QCD: results and consequences

2020/11/30 by Goriachuk, I. O., Kataev, A. L.
#FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2011.14746

Abstract

Two renormalization group invariant quantities in quantum chromodinamics (QCD), defined in Euclidean space,namely, Adler D-function of electron-positron annihilation to hadrons and Bjorken polarized deep-inelastic scattering sum rule, are considered. It is shown, that the 5-th order corrections to them in MS-like renormalization prescriptions, proportional to Riemann ζ-function ζ(4), can be restored by the transition to the C-scheme, with the β-function, analogous to Novikov, Shifman, Vainshtein and Zakharov exact β-function in N=1 supersymmetric gauge theories. The general analytical expression for these corrections in SU(N_c) QCD is deduced and their scale invariance is shown. The β-expansion procedure for these contributions is performed and mutual cancellation of them in the 5-th order of the generalized Crewther identity are discussed.

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