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28 March 2024
 
  » arxiv » 2010.08910

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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
AbstractIn 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
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