A measurement of $alpha_s(Q^2)$ from the Gross-Llewellyn Smith Sum Rule

Abstract

We extract a set of values for the Gross-Llewellyn Smith sum rule at different values of 4-momentum transfer squared ($Q^{2}$), by combining revised CCFR neutrino data with data from other neutrino deep-inelastic scattering experiments for $1 < Q^2 < 15 GeV^2/c^2$. A comparison with the order $\alpha^{3}_{s}$ theoretical predictions yields a determination of $\alpha_{s}$ at the scale of the Z-boson mass of $0.114 \pm^{.009}_{.012}$. This measurement provides a new and useful test of perturbative QCD at low $Q^2$, because of the low uncertainties in the higher order calculations.