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.
We have found 122 charmed-particle decays among 3855 neutrino interactions located in the fiducial volume of a hybrid emulsion spectrometer installed in the Fermilab wide-band neutrino beam. We obtain an average relative charmed-particle production cross section of σ(ν μ → c μ − ) σ(ν μ →μ − ) =4.9 −0.6 +0.7 % , at an average neutrino energy of 22 GeV. We also obtain a production rate of σ(ν μ → c c ν μ ) σ(ν μ →ν μ ) =0.13 −0.11 +0.31 % , if we assume that there was an undetected muon, a limit of σ(ν μ → c c μ − ) σ(ν μ → c μ − )<3% (90% CL ) can be obtained. Other cross section ratios and limits are also presented.
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