The ${\rm{\bar{MS}}}$-scheme $\alpha_s^5$ QCD contributions to the Adler function and Bjorken polarized sum rule in the Crewther-type two-fold $\{\beta\}$-expanded representation
| Autor: | Goriachuk, I. O., Kataev, A. L., Molokoedov, V. S. |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/JHEP05(2022)028 |
| Popis: | We consider the two-fold expansion in powers of the conformal anomaly and of the strong coupling $\alpha_s$ for the non-singlet contributions to Adler $D$-function and Bjorken polarized sum rule calculated previously in the $\MSbar$-scheme at the four-loop level. This representation provides relations between definite terms of different loop orders appearing within the $\{\beta\}$-expansion of these quantities. Supposing the validity of this two-fold representation at the five-loop order and using these relations, we obtain some $\mathcal{O}(\alpha_s^5)$ corrections to the $D$-function, to the $R$-ratio of $e^+e^-$-annihilation into hadrons and to Bjorken polarized sum rule. These corrections are presented both analytically in the case of the generic simple gauge group and numerically for the $SU(3)$ color group. The arguments in the favor of validity of the two-fold representation are given at least at the four-loop level. Within the $\{\beta\}$-expansion procedure the analytical Riemann $\zeta_4$-contributions to the five-loop expressions for the Adler function and Bjorken polarized sum rule are also fixed for the case of the generic simple gauge group. Comment: 30 pages, 1 Figure, 6 Tables, text modified, the results unchanged, list of references modified, accepted for publication in JHEP |
| Databáze: | arXiv |
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