We analyze the prospects of measuring the parity of Higgs particles in the Standard Model and its supersymmetric extensions. Higgs decays are discussed in this context as well as production processes including, in particular, the fusion of Higgs particles in linearly polarized photon–photon collisions.

The rate for the final state radiation of hadrons in leptonic $Z$ decays is evaluated, using as input experimental data for $\sigma (e^+e^-\to hadrons)$ in the low energy region. Configurations with a lepton pair of large and a hadronic state of low invariant mass are dominant. A relative rate $\Gamma_{l\bar l had}/\Gamma_{l\bar l}=6.3\times 10^{-4}$ is calculated. This result is about twice the prediction based on a parton model calculation with a quark mass of $300$ MeV. The rate for secondary production of heavy quarks is calculated in the same formalism.

Within the framework of pertubative QCD we calculate inclusive $\Jpsi$ production using the ``color singlet model'' (CSM). Predictions for the total cross section including the leading corrections from initial state radiation and the $\psi'$ contribution are given. We analyze the production and decay properties by considering suitable lepton-hadron correlations. It is shown that the production and the decay process of an $\Jpsi$ are described by four structure functions, respectively. We give analytical expressions for these

structure functions

and suggest energy dependent coefficients of angular distributions as a test for the model. Finally we give detailed predictions for an energy of 10.5 GeV that could be tested at the CLEO-II experiment.

The effect of arbitrarily polarized electron/positron beams is included.

Theoretical results for top quark physics at a linear electron positron collider will be presented. The predictions for the top quark decay rate and distributions are described, including the influence of radiative corrections and of extensions of the Standard Model. The production cross section for top quarks through electron positron annihilation and photon photon fusion is large throughout, which may allow an accurate determination of the top magnetic moment as well as interesting measurement of CP violating observables. The cross section in the threshold region as well as the momentum distribution of top quarks and their decay products will lead to an accurate determination of the top quark mass, the interquark potential, and eventually even of the Yukawa coupling to the Higgs boson. It is shown that higher order corrections through final state interaction and relativistic corrections are small and sufficiently under control.

Toponium and open top production are strongly enhanced by the exchange of a light Higgs boson. This enhancement exhibits a rapid energy variation. It is shown that the leading energy dependent term can be absorbed in an instantaneous Yukawa potential. The remainder can again be evaluated in the static limit.

The status of top quark searches will be briefly reviewed. Theoretical predictions for the top quark decay rate are presented including QCD and electroweak radiative corrections. The possibilities for quarkonium searches at an hadron collider will be discussed. The perspectives for top production at an electron positron collider will be described in detail with emphasis on the behavior of the cross section and decay distribution in the threshold region.

Semileptonic decays of polarised $\tau$ leptons are investigated. Predictions for the rate, based on CVC and chiral Lagrangians, are contrasted with experiments. Predictions for the angular distributions of three meson final states are given. Emphasis is put on studies in electron-positron annihilation where the neutrino escapes detection and the $\tau$ restframe cannot be reconstructed. It is shown that the form factors can be measured in ongoing high statistics experiments. Of particular interest for the three meson case are the distribution of the normal to the Dalitz plane and the distribution around this normal. At LEP these distributions allow for an improved measurement of the $\tau$ polarisation. Implications are considered for an experiment where the $\tau$ restframe is reconstructed. It is shown that the measurement of impact parameters with the help of vertex detectors allows a full kinematic reconstruction, including the direction of the $\tau$ and the missing neutrino momentum.

The partial decay rate \mbox{$\Gamma(Z\rightarrow b\bar{b})$} of

the $Z$-boson is significantly affected by 

higher order QCD corrections. Of particular interest is the influence of the non-\ vanishing bottom quark mass. Radiative corrections to the quadratic mass term of the partial $Z$-width are computed in perturbative QCD.

The calculation of the third order  

${\cal O}(\alpha_s^3 m_b^2/M_Z^2)$ contribution for the vector induced rate and of the second order ${\cal O}(\alpha_s^2 m_b^2/M_Z^2)$ correction for the axial induced rate is described. The numerical influence of the results and the theoretical uncertainties are discussed.

The momenta of $\tau$ decay products in the reaction $e^+e^-\to\tau^+\tau^-$ do not constrain the $\tau$ direction unambiguously. It is shown how the measurement of tracks of hadrons from semileptonic $\tau$ decays, in particular their relative impact parameters, allows to resolve this ambiguity.

The order ${\cal O} (\alpha\as m_t^2/M_W^2)$ corrections to the partial decay rate of $\Gamma(Z\rightarrow b\bar{b})$ are computed using the heavy top mass expansion. They are given by the absorptive part of the corresponding three loop $Z$-self energy diagrams. Our method provides an independent way to calculate the QCD corrections to the electroweak one loop result for $\Gamma(Z\rightarrow b\bar{b})$ and our result represents another confirmation of the one recently published by Fleischer et al.

Hadronic production of nonrelativistic boundstates of $b^{\prime}$ or isosinglet quarks D with suppressed weak decays is investigated for LHC and SSC energies. QCD corrections to production and decay rates are incorporated. Large rates for final states from $\eta_{b^{\prime}}\rightarrow HZ$ are predicted.

In this note radiative corrections to the total hadronic decay rate of the $\tau$-lepton are studied employing perturbative QCD and the operator product expansion. We calculate quadratic quark mass corrections to the decay rate ration $R_{\tau}$ to the order ${\cal O}(\alpha_s^2 m^2)$ and find that they contribute appreciably to the Cabbibo supressed decay modes of the $\tau$-lepton. We also discuss corrections of mass dimension $D=4$, where we emphasize the need of a suitable choice of the renormalization scale of the quark and gluon condensates.

The axial part of the Z decay rate into hadrons ($\G^A_Z$) gets extra singlet contributions due to the huge splitting between top and bottom quark masses. By treating the axial neutral current in the large top-mass limit we partially re-derive in a systematic manner the known results on the contribution of the $\as^2$ order anomalous “double triangle” diagrams to $\G^A_Z$ and resolve an ambiguity concerning the scale at which the strong coupling constant $\alpha_s$ is to be taken in these diagrams. We evaluate and sum all leading log and next to leading log QCD corrections of orders $\as^{1+n}(\ln(M_Z/4m^2_t))^n$ and $\as^{2+n}(\ln(M_Z/4m^2_t))^n$ respectively.

We examine the sensitivity of our results to a change of the renormalization scales to estimate the size of yet unknown corrections of order $\alpha_s^3$ to $\G^A_Z$. The analysis implies that the corrections might change the magnitude of the singlet term by up to 30\% while they hardly might be of noticeable numerical significance in comparison with the total contribution from non-singlet terms.

We use a simple renormalization group argument to demonstrate that the large top mass limit of the axial neutral current in QCD is unambiguously determined by the renormalization of the singlet axial current and suggests a natural scheme independent normalization condition for the latter. By calculating the anomalous dimension of the singlet axial current at three-loop level in the $\msbar$ scheme we derive the result for the top quark decoupling from the axial neutral current valid up to (and including) the terms of order $\as^2$.