Direct analysis of scaling violations in large-Q2deep-inelastic neutrino and muon scattering

We have made an extensive analysis of all large-$Q^2$ deep-inelastic neutrino and muon scattering data using evolution equations to fit the scaling violations directly at fixed Bjorken $x$. We have included all higher-order corrections in both the nonsinglet and singlet cases. We find that the nonsinglet neutrino data give ${\Lambda }_{\overline{\mathrm{MS}}}\simeq 300\pm 80$ MeV but with systematic uncertainties of at least 100 MeV ($\overline{\mathrm{MS}}$ refers to the modified minimal-subtraction scheme). The singlet neutrino and muon data are equally consistent with either ${\Lambda }_{\overline{\mathrm{MS}}}\simeq 200\pm 100$ MeV and a soft gluon distribution or ${\Lambda }_{\overline{\mathrm{MS}}}\simeq 350\pm 100$ MeV and a hard gluon distribution. Values as low as ${\Lambda }_{\overline{\mathrm{MS}}}\simeq 100$ MeV found in previous analyses are likely to be spurious.