The analytical {\mathscr{O}}({a}_{s}^{4}) expression for the polarized Bjorken sum rule in the miniMOM scheme and the consequences for the generalized Crewther relation
Abstract
The analytical {\mathscr{O}}({a}s4) perturbative QCD expression for the flavour non-singlet contribution to the Bjorken polarized sum rule in the rather applicable at present gauge-dependent miniMOM scheme is obtained. For the considered three values of the gauge parameter, namely ξ = 0 (Landau gauge), ξ = -1 (anti-Feynman gauge) and ξ = -3 (Stefanis-Mikhailov gauge), the scheme-dependent coefficients are considerably smaller than the gauge-independent {\overline{{MS}}} results. It is found that the fundamental property of the factorization of the QCD renormalization group β-function in the generalized Crewther relation, which is valid in the gauge-invariant {\overline{{MS}}} scheme up to {\mathscr{O}}({a}s4)-level at least, is unexpectedly valid at the same level in the miniMOM-scheme for ξ = 0, and for ξ = -1 and ξ = -3 in part.
- Publication:
-
Journal of Physics Conference Series
- Pub Date:
- December 2017
- DOI:
- 10.1088/1742-6596/938/1/012050
- arXiv:
- arXiv:1711.03997
- Bibcode:
- 2017JPhCS.938a2050K
- Keywords:
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- High Energy Physics - Phenomenology;
- High Energy Physics - Lattice;
- High Energy Physics - Theory
- E-Print:
- 8 pages, 1 Table, proceedings of the XVII Workshop on High Energy spin Physics DSPIN-17 Dubna, Russia, September 11 - 15, 2017