Decoupling of heavy quarks in quantum chromodynamics

Decoupling of heavy quarks in quantum chromodynamics (QCD) defined by mass-independent renormalization is investigated. The structure of the relations between the parameters of f flavour QCD and the parameters of the effective f ? 1 flavour QCD below a heavy-quark threshold is discussed to all orders in the loop expansion, and the relations are computed to two-loop approximation for the minimal subtraction schemes (MS) and to one-loop approximation for some Weinberg schemes. These matching relations can be used to systematically determine the renormalization group (RG)-invariant parameters of the effective theory in terms of the RG-invariant parameters of the theory which includes the heavy quark, or vice versa. For the $\text{MS}$ scheme the connection between Λ_{f ? 1} nad Λ_f to two and three loops is given as well as the two-loop connection between the RG-invariant mass parameters of the f ? 1 and f flavour theory. The effect of heavy quarks on the evolution of the QCD coupling is of significance for present QCD phenomenology based on next-to-leading-order perturbation theory. This is illustrated with a few examples within the $\text{MS}$ scheme.     

Semileptonic decays of top quarks

The lepton spectrum from the semileptonic decay of a heavy top quark is calculated, including the effect of the W propagator and QCD corrections. Lepton spectra from the decay of top quarks in toponium are affected by bound state effects, in particular by Fermi motion. Semileptonic decays may therefore probe the toponium wave function at very small distances.     

Semileptonic b-quark decay in quantum chromodynamics

We compute real and virtual one-gluon corrections to the charged lepton energy distribution in the following reaction: $\text{b}\text{→}\text{c}\text{+ ?}{}^{\mathrm{?}}\text{+}\text{v}{}_{\mathrm{?}}$ for arbitrary quark masses.     

Masses of light quarks in quantum chromodynamics

We try to determine light quark masses by considering sum rules for the vacuum expectation value of the time-ordered correlation function of two divergences of the axial vector current. The evaluation is carried out at momenta high enough for the non-perturbative contributions to be negligible. We find that the average mass of the up and down quark at a momentum of 1 GeV lies between 3.3 and 7.9 MeV while that for the strange quark lies between 84 and 212 MeV. The ranges of values reflect predominantly the uncertainty in the absorptive part in the low energy region (?1.7 GeV).     

Weak decays of heavy quarks

To investigate the role of real gluons in heavy meson weak decays, we compute the first-order QCD corrections to the total rate for the weak decay of a heavy quark. We find that to this order there are no leading log contributions. Furthermore, the first-order QCD corrections depress the total decay rate, although they provide an enhancement of the nonleptonic rate over the semileptonic rate. We discuss the relevance of our results to the usual picture of QCD enhancements based on short-distance expansions of weak decay amplitudes.     

Semileptonic decays of heavy to light mesons from an MIT bag model

Using the (modified) MIT bag model we calculated formfactors and decay widths for pseudoscalar-pseudoscalar and pseudoscalar-vector semileptonic decays of heavy to light mesons. We discuss the physical phenomena which are important in these processes and their influence on the measurable quantities. Our results are consistent with the available experimental data. A comparison with the results of other models is also given.Work supported by the KBN grant no. 2P30207607     

Semileptonic decays of pseudoscalar particles (M→M′+ℓ+νℓ) and short-distance behaviour of quantum chromodynamics

The form factors which govern the semileptonic decays of pseudoscalar particles (M→M′+?+ν_?) are constrained by the knowledge of the two-point function Π^μν(q) = i ∫ d⁴x e^iqx〈06TV^μ(x) V^ν+ (0)60〉 in the deep euclidean region, where V^μ(x) denotes the vector current responsible for the transition M→M′. We derive the precise constraints from a QCD calculation of Π^μν which includes perturbative contributions to two loops as well as leading non-perturbative contributions. Applications to π_?3, K_?3 and $\text{D}{}^{\mathrm{+}}\text{→}\text{K}{}^0\text{e}{}^{\mathrm{+}}\text{ν}{}_{\mathrm{<mtext>e</mtext>}}$ decays are discussed.     

Semileptonic decays of the B c meson

The semileptonic decays of the B _c meson into heavy quarkonia J/ψ(η_c) and a pair of leptons are investigated on the basis of three-point sum rules of QCD and nonrelativistic QCD (NRQCD). Calculations of analytic expressions for the spectral densities of QCD and NRQCD correlation functions with allowance for Coulomb-like α_s/v terms are presented. At recoil momenta close to zero, generalized relations due to the spin symmetry of NRQCD are derived for the B _c → J/ψ(η_c)/ν_l form factors, with l denoting one of the leptons (e, μ, or τ). This allows one to express all NRQCD form factors in terms of a single universal quantity, an analog of the Isgur-Wise function at the maximal lepton-pair invariant mass. The gluon-condensate corrections to three-point functions are calculated both in full QCD in the Borel transform scheme and in NRQCD in the moment scheme. This enlarges the parametric-stability region of the sum-rule method, thereby rendering the results of the approach more reliable. Numerical estimates of the widths for the transitions B _c → J/ψ(η_c)lν_l are presented.     

Effective gauge theory and the effect of heavy quarks in Higgs boson decays

A general framework is given for evaluating the contributions of as yet undiscovered heavy quarks to the gluonic decay rate of the Weinberg-Salam type Higgs boson. Since the Yukawa coupling of the Higgs boson to a quark pair is proportional to the quark mass, loop graphs involving heavy quarks have a non-vanishing effect on the gluonic decay width of the Higgs boson. This effect of heavy quarks with massesM _j(j=t,...) much greater than the Higgs boson massm _H is calculated in an effective gauge theory. The effects of two different kinds of large logarithms, lnM _j ² /μ m _h ² /μ ² are separated and summed up by the renormalization group method. It is found that the higher order QCD corrections are large and that the gluonic contribution to the hadronic decay width is significant if there are more than three generations. The Higgs decay width can therefore be used to probe the number of generations of heavy quarks.