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

TL;DR

This paper refines the theoretical calculation of the Gross-Llewellyn Smith sum rule using high-order QCD corrections and the principle of maximum conformality, achieving better convergence and agreement with experimental data.

Contribution

It applies the PMC single-scale approach to compute the GLS sum rule at ${ m O}(\alpha_s^4)$, improving convergence and reducing scheme dependence in pQCD calculations.

Findings

The fixed-order pQCD contribution is precisely calculated as 2.559^{+0.023}_{-0.024}.

The PMC approach suppresses contributions from unknown higher-order terms.

The final prediction aligns well with CCFR experimental data.

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.