arXiv subjects
Publications and source records attributed to J. H. Kühn.
A systematic theoretical evaluation of the cross section for hadron production in electron-positron collisions in the energy range just below the $B$ meson threshold is presented which includes charm and bottom mass effects and is accurate to order $\as^3$. The corresponding measurement in the energy region several $GeV$ above the threshold is also discussed.
The rate for the production of massive fermions radiated off a pair of massless fermions is calculated analytically. Combined with the analytic calculation of the corresponding virtual contribution one obtains the order $α^2$ correction to the cross section which is induced by the real and virtual radiation of a pair of massive fermions by massless fermions. Approximations valid for large and for small masses are derived and shown to agree with earlier calculations.
Radiative QCD corrections significantly influence the theoretical predictions for the decay rates of the $Z$ and the Higgs boson. The status of the QCD calculations to the hadronic $Z$ width is reviewed. The role of mass corrections from bottom quark final states is emphasized. An estimate of the theoretical uncertainties is given. New results for quartic mass terms of order ${\cal O}(α_s^2)$ are presented. The impact of secondary radiation of bottom quarks on the determination of $Γ(Z\rightarrow b\bar{b})$ is discussed. Second order QCD corrections to the partial decay rate $Γ(H\rightarrow b\bar{b})$ are also presented in this talk. A recent result for the flavour singlet contribution to this quantity is presented. It includes quark mass effects and completes the otherwise massless calculations of order $\ordas^2)$.
The influence of nonvanishing quark masses on the total cross section in electron positron collisions and on the $Z$ decay rate is calculated. The corrections are expanded in $m^2/s$ and $\as$. Methods similar to those applied for the quadratic mass terms allow to derive the corrections of order $\as m^4/s^2$ and $\as^2m^4/s^2$. Coefficients which depend logarithmically on $m^2/s$ and which cannot be absorbed in a running quark mass arise in order $\as^2$. The implications of these results on electron positron annihilation cross sections at LEP and at lower energies in particular between the charm and the bottom threshold and for energies several GeV above the $b\bar b$ threshold are discussed.
The rate for the final state radiation of hadrons in leptonic $Z$ decays is evaluated, using as input experimental data for $σ(e^+e^-\to hadrons)$ 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 $Γ_{l\bar l had}/Γ_{l\bar l}=6.3\times 10^{-4}$ 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.
Angular-energy distributions are studied for charged leptons and neutrinos from the decays of polarised top quarks. A small admixture of V+A interactions is incorporated. The polarisation dependent part of the neutrino distribution which can be measured experimentally through the missing momentum is particularly sensitive towards deviations from the V-A structure. This result remains unaffected by QCD corrections which, however, cannot be neglected in a quantitative analysis.
Distributions of charged leptons in semileptonic $Λ_c$ and $Λ_b$ decays can be used as spin analysers for the corresponding charm and bottom quarks. QCD corrections to the energy spectra of charged leptons have been given in the literature as well as the corrections to the angular dependence for polarised up-type quarks. The analogous formulae are derived also for polarised down-type quarks. These results are applied to the decays of polarised charm and bottom quarks. The corrections to the asymmetries are found to be small for charm decays. For bottom decays they exhibit a non-trivial dependence on the energy of the charged lepton.
The behavior of the momentum distribution of top quarks in the threshold region is investigated. The qualitative behavior, in particular the dependence of the average momentum on the strong coupling constant can be understood from analytical calculations for the Coulomb potential. Ambiguities in the relation between the excitation curve and the top mass are addressed.
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 $τ$ 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 $τ$ 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 $τ$ polarisation. Implications are considered for an experiment where the $τ$ 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 $τ$ and the missing neutrino momentum.
The momenta of $τ$ decay products in the reaction $e^+e^-\toτ^+τ^-$ do not constrain the $τ$ direction unambiguously. It is shown how the measurement of tracks of hadrons from semileptonic $τ$ decays, in particular their relative impact parameters, allows to resolve this ambiguity.
A critical assessment of the available calculations of the top quark width is presented. QCD corrections, the finite mass of the $b$ quark and the effect of the $W$ width are included as well as the electroweak corrections. The relative importance of these corrections is demonstrated for the realistic range of top masses. For the QCD corrected decay rate we use the formulae from \cite{JK1} and include the electroweak correction taken from \cite{DS}. Our results differ from those available in the literature because all the later calculations ignored the effect of W width discussed earlier in \cite{JK1}~. This leads to an effect comparable in size to the electroweak correction.