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arXiv · 1711.03997

The analytical $\mathcal{O}(a^4_s)$ expression for the polarized Bjorken sum rule in the miniMOM scheme and the consequences for the generalized Crewther relation

A. L. Kataev·V. S. Molokoedov
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Abstract

The analytical $\mathcal{O}(a^4_s)$ perturbative QCD expression for the flavour non-singlet contribution to the Bjorken polarized sum rule in the rather applicable at present gauge--dependent $\rm{miniMOM}$ scheme is obtained. For the considered three values of the gauge parameter, namely $\xi=0$ (Landau gauge), $\xi=-1$ (anti--Feynman gauge) and $\xi=-3$ (Stefanis--Mikhailov gauge), the scheme-dependent coefficients are considerably smaller than the gauge-independent $\rm{\overline{MS}}$ results. It is found that the fundamental property of the factorization of the QCD renormalization group $\beta$-function in the generalized Crewther relation, which is valid in the gauge-invariant $\rm{\overline{MS}}$ scheme up to $\mathcal{O}(a^4_s)$-level at least, is unexpectedly valid at the same level in the $\rm{miniMOM}$-scheme for $\xi=0$, and for $\xi=-1$ and $\xi=-3$ in part.

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A. L. Kataev, V. S. Molokoedov. 2017-11-10. The analytical $\mathcal{O}(a^4_s)$ expression for the polarized Bjorken sum rule in the miniMOM scheme and the consequences for the generalized Crewther relation. https://doi.org/10.1088/1742-6596%2F938%2F1%2F012050

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