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

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. $S^{\mathrm{GLS}}(Q_0^2=3{\mathrm{GeV}}^2){|}_{\mathrm{PMC}}=2.559_{-0.024}^{+0.023}$, 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 Padé 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.

6 pages, 5 figures

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• A new analysis of the pQCD contributions to the electroweak parameter $\rho$ using the single-scale approach of principle of maximum conformality