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 $\mathrm{\Delta }{\alpha }_s(M_Z)$, 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.

在本文中，我们通过使用以下公式来分析 Gross-Llewellyn Smith (GLS) 求和规则的性质 $\mathcal{哦}({\alpha }_{秒}^4)$借助最大保形原则 (PMC) 进行 - 阶 QCD 校正。通过使用 PMC 单尺度方法，我们为 GLS 求和规则获得了精确的重整化尺度和方案独立的固定阶 pQCD 贡献，例如${秒}^{\mathrm{GLS}}({问}_0^2=3{\mathrm{电子伏特}}^2){|}_{\mathrm{管理中心}}={2.559}_{-0.024}^{+0.023}$，其中误差是来自 $\mathrm{\Delta }{\alpha }_{秒}({米}_Z)$, 预测 $\mathcal{哦}({\alpha }_{秒}^5)$使用 Padé 近似方法预测的阶项。应用PMC后，得到了更收敛的pQCD级数，高度抑制了未知高阶项的贡献。结合非微扰高扭曲贡献，我们对 GLS 总和规则的最终预测与 CCFR 合作提供的实验数据非常吻合。