Deep-inelastic scattering beyond the leading order in asymptotically free gauge theories

Abstract

We calculate the full order-${g}^{2}$ corrections to the coefficient functions which determine the ${Q}^{2}$ dependence of the moments of deep-inelastic structure functions. The calculation is performed in the minimal-subtraction scheme of 't Hooft. The results are combined with the recent two-loop calculations of anomalous dimensions by Floratos, Ross, and Sachrajda to give the full ${\overline{g}}^{2}$ corrections to the leading order of asymptotic freedom. We present results for ${C}_{n}(1,{\overline{g}}^{2})$ relevant for electroproduction and neutrino reactions for both nonsinglet and singlet combinations of the structure functions. Phenomenological consequences of the full ${\overline{g}}^{2}$ corrections to the nonsinglet structure function are discussed. The corrections to the Gross-Llewellyn Smith and Bjorken sum rules are estimated to be of the order of 15%.