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The scheme-independent generalized Crewther relation in QCD using the single-scale approach of the principle of maximum conformality | Xu-Dong Huang
; Xing-Gang Wu
; Qing Yu
; Xu-Chang Zheng
; Jun Zeng
; Jian-Ming Shen
; | Date: |
18 Oct 2020 | Abstract: | In the paper, we study the generalized Crewther Relation (GCR) between the
Adler function ($D$) and Gross-Llewellyn Smith sum rule for the polarized
deep-inelastic electron scattering ($C^{
m GLS}$) at the leading twist by
using the single-scale approach of the principle of maximum conformality (PMC).
The PMC adopts the renormalization group equation to set the correct running
behavior of the strong coupling constant for a pQCD approximant. After applying
the PMC, the perturbative series becomes scale independent, and a precise
fixed-order pQCD prediction can be achieved. We observe that the PMC conformal
series also leads to a scheme-independent GCR, or equivalently the commensurate
scale relation (CSR) between the effective charges of $D$ and $C^{
m GLS}$.
Similarly, we can obtain a CSR between the effective charges of $C^{
m GLS}$
and the $R$ ratio of $e^+e^-$ annihilation cross section, which is also
scheme-independent and allows us to fix the effective charge of $C^{
m GLS}$
from the $R$-ratio experimental data. Thus by using the PMC single-scale
approach, a precise test of QCD theory without renormalization scheme and scale
ambiguities can be achieved. | Source: | arXiv, 2010.08910 | Services: | Forum | Review | PDF | Favorites |
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