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]

Weak decays beyond leading logarithms

Heavy quark symmetry

Relativistic Quantum Fields

We calculate the leptonic decay constants of heavy-light pseudoscalar mesons with charm and bottom quarks in lattice quantum chromodynamics on four-flavor QCD gauge-field configurations with dynamical $u$, $d$, $s$, and $c$ quarks. We analyze over twenty isospin-symmetric ensembles with six lattice spacings down to $a\ensuremath{\approx}0.03\text{ }\text{ }\mathrm{fm}$ and several values of the light-quark mass down to the physical value $\frac{1}{2}({m}_{u}+{m}_{d})$. We employ the highly-improved staggered-quark (HISQ) action for the sea and valence quarks; on the finest lattice spacings, discretization errors are sufficiently small that we can calculate the $B$-meson decay constants with the HISQ action for the first time directly at the physical $b$-quark mass. We obtain the most precise determinations to-date of the $D$- and $B$-meson decay constants and their ratios, ${f}_{{D}^{+}}=212.7(0.6)\text{ }\text{ }\mathrm{MeV}$, ${f}_{{D}_{s}}=249.9(0.4)\text{ }\text{ }\mathrm{MeV}$, ${f}_{{D}_{s}}/{f}_{{D}^{+}}=1.1749(16)$, ${f}_{{B}^{+}}=189.4(1.4)\text{ }\text{ }\mathrm{MeV}$, ${f}_{{B}_{s}}=230.7(1.3)\text{ }\text{ }\mathrm{MeV}$, ${f}_{{B}_{s}}/{f}_{{B}^{+}}=1.2180(47)$, where the errors include statistical and all systematic uncertainties. Our results for the $B$-meson decay constants are three times more precise than the previous best lattice-QCD calculations, and bring the QCD errors in the standard model predictions for the rare leptonic decays $\overline{\mathcal{B}}({B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})=3.64(11)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$, $\overline{\mathcal{B}}({B}^{0}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})=\phantom{\rule{0ex}{0ex}}1.00(3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, and $\overline{\mathcal{B}}({B}^{0}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})/\overline{\mathcal{B}}({B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})=0.0273(9)$ to well below other sources of uncertainty. As a byproduct of our analysis, we also update our previously published results for the light-quark-mass ratios and the scale-setting quantities ${f}_{p4s}$, ${M}_{p4s}$, and ${R}_{p4s}$. We obtain the most precise lattice-QCD determination to date of the ratio ${f}_{{K}^{+}}/{f}_{{\ensuremath{\pi}}^{+}}=1.1950({\text{ }}_{\ensuremath{-}23}^{+16})\text{ }\text{ }\mathrm{MeV}$.

B- and D-meson leptonic decay constants from four-flavor lattice QCD

We compute on the lattice the ``bag'' parameters of the five ΔB = 2 operators of the supersymmetric basis, by combining their values determined in full QCD and in the static limit of HQET. The extrapolation of the QCD results from the accessible heavy-light meson masses to the B-meson mass is constrained by the static result. The matching of the corresponding results in HQET and in QCD is for the first time made at NLO accuracy in the (NDR) renormalization scheme. All results are obtained in the quenched approximation.

https://iopscience.iop.org/article/10.1088/1126-6708/2002/04/025/pdf

B-parameters of the complete set of matrix elements of (ΔB = 2) operators from the lattice

Sub-leading logarithmic mass-dependence in heavy-meson form-factors

The properties of the neutrino charge radius (NCR) and anapole moments (AM's) of elementary fermions, nucleons, and nuclei are discussed The dependence of these off-shell electromagnetic couplings on the weak gauge parameter is explicitly demonstrated by a calculation performed in the ${R}_{\ensuremath{\xi}}$ gauge The gauge dependence of the AM's and NCR implies that they cannot be observed in isolation from other second-order, electroweak effects It is shown, however, that the AM's of various hadronic systems having an $\mathrm{SU}{(2)}_{L}$ quantum number ${T}_{3}^{L}=0$ can be considered "observables" in certain formal, though unphysical, limits It is argued that, apart from these special limits, the AM is a physically meaningful entity only for heavy and/or nearly degenerate nuclei

Observability of the anapole moment and neutrino charge radius

https://scholarworks.umass.edu/cgi/viewcontent.cgi?article=1377&context=physics_faculty_pubs

M.J. Musolf

Papers

Sub-leading logarithmic mass-dependence in heavy-meson form-factors

Observability of the anapole moment and neutrino charge radius

Electroweak corrections to parity-violating neutral current scattering