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

Abstract

In the paper, we reanalyze the properties of Gross-Llewellyn Smith (GLS) sum rule by using the O(α 4 s )-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 pQCD contribution for GLS sum rule, e.g. S GLS (Q 2 0 = 3GeV 2 )|PMC = 2.559 +0.023 −0.024 , where the error is squared average of those from ∆αs(MZ ), the predicted O(α 5 s )-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.

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

“…In the PMC single-scale method, the unknown magnitude of the uncalculated even higher-order terms is called as the newly second kind of residual scale dependence [42]. In the literature, the Padé approximation approach (PAA) [34][35][36] is one of the approaches for estimating the unknown (n + 1) th -order coefficient from a given n th -order perturbative series.…”

“…It works effectively when we have known enough perturbative terms, and the renormalization scheme-and-scale independent conformal series is helpful for predicting the magnitudes of higherorder terms. Many successful applications by using PAA together with the PMC conformal series have been done in the literature [29,30,37,[40][41][42].…”