Andrzej J. Buras

We review the present status of QCD corrections to weak decays beyond the leading-logarithmic approximation, including particle-antiparticle mixing and rare and $\mathrm{CP}$-violating decays. After presenting the basic formalism for these calculations we discuss in detail the effective Hamiltonians of all decays for which the next-to-leading-order corrections are known. Subsequently, we present the phenomenological implications of these calculations. The values of various parameters are updated, in particular the mass of the newly discovered top quark. One of the central issues in this review are the theoretical uncertainties related to renormalization-scale ambiguities, which are substantially reduced by including next-to-leading-order corrections. The impact of this theoretical improvement on the determination of the Cabibbo-Kobayashi-Maskawa matrix is then illustrated. [S0034-6861(96)00304-2]

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%.

The present status of quantum chromodynamics formalism for inclusive deep-inelastic scattering is reviewed. Leading-order and higher-order asymptotic freedom corrections are discussed in detail. Both the formal language of operator product expansion and renormalization group and the intuitive parton model picture are used. Systematic comparison of asymptotic freedom predictions with deep-inelastic data is presented. Extensions of asymptotic freedom ideas to other processes such as massive $\ensuremath{\mu}$-pair production, semi-inclusive deep-inelastic scattering, ${e}^{+}{e}^{\ensuremath{-}}$ annihilation, and photon-photon scattering are briefly discussed. The importance of higher-order corrections is emphasized.