Weak decays beyond leading logarithms

TLDR

Theoretical uncertainties from renormalization‑scale ambiguities in weak decays are substantially reduced by including next‑to‑leading‑order QCD corrections. The review surveys QCD corrections to weak decays beyond leading logarithms, covering mixing, rare, and CP‑violating processes, and discusses their phenomenological implications. The authors present the formalism and effective Hamiltonians for next‑to‑leading‑order corrections, updating key parameters such as the top‑quark mass. These improvements sharpen the determination of the Cabibbo‑Kobayashi‑Maskawa matrix elements. S0034-6861(96)00304-2.

Abstract

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]