The generalized Crewther relation and V-scheme: analytic O(α⁴_s) results in QCD and QED

2023/02/07 by Kataev, A. L., Molokoedov, V. S.
#FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2302.03443

Abstract

Using the analytical \rmMS-scheme three-loop contribution to the perturbative Coulomb-like part of the static color potential of heavy quark-antiquark system, we obtain the analytical expression for the fourth-order β-function in the gauge-invariant effective V-scheme in the case of the generic simple gauge group. Also we present the Adler function of electron-positron annihilation into hadrons and the coefficient function of the Bjorken polarized sum rule in the V-scheme up to α⁴_s terms. We demonstrate that at this level of PT in this effective scheme the β-function is factorized in the conformal symmetry breaking term of the generalized Crewther relation, which connects the flavor non-singlet contributions to the Adler and Bjorken polarized sum rule functions. We prove why this relation will be true in other gauge-invariant renormalization schemes as well. The obtained results enable to reveal the difference between the V-scheme β-function in QED and the Gell-Man--Low Ψ-function. This distinction arises due to the presence of the light-by-light type scattering corrections first appearing in the static potential at the three-loop level.

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