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arXiv · 2101.10922

The Gross-Llewellyn Smith sum rule up to ${\cal O}(\alpha_s^4)$-order QCD corrections

Xu-Dong Huang·Xing-Gang Wu·Qing Yu·Xu-Chang Zheng·Jun Zeng
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Abstract

In the paper, we analyze the properties of Gross-Llewellyn Smith (GLS) sum rule by using the $\mathcal{O}(\alpha_s^4)$-order QCD corrections with the help of principle of maximum conformality (PMC). By using the PMC single-scale approach, we obtain an accurate renormalization scale-and-scheme independent fixed-order pQCD contribution for GLS sum rule, e.g. $S^{\rm GLS}(Q_0^2=3{\rm GeV}^2)|_{\rm PMC}=2.559^{+0.023}_{-0.024}$, where the error is squared average of those from $\Delta\alpha_s(M_Z)$, the predicted $\mathcal{O}(\alpha_s^5)$-order terms predicted by using the Pad\'{e} approximation approach. After applying the PMC, a more convergent pQCD series has been obtained, and the contributions from the unknown higher-order terms are highly suppressed. In combination with the nonperturbative high-twist contribution, our final prediction of GLS sum rule agrees well with the experimental data given by the CCFR collaboration.

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Xu-Dong Huang, Xing-Gang Wu, Qing Yu, Xu-Chang Zheng, Jun Zeng. 2021-01-26. The Gross-Llewellyn Smith sum rule up to ${\cal O}(\alpha_s^4)$-order QCD corrections. https://doi.org/10.1016/j.nuclphysb.2021.115466

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