arXiv subjects
Publications and source records attributed to J. H. Kühn.
The dominant electroweak double logarithmic corrections to the process $e^+e^-\to f\bar f$ at high energy are found in all orders of perturbation theory. In contrast to results in simple Yang-Mills theories these corrections do not exponentiate.
An evaluation of the effective QED coupling at the scale M_Z is presented. It employs the predictions of perturbative QCD for the cross section of electron positron annihilation into hadrons up to order α_s^2, including the full quark mass dependence, and of order α_s^3 in the high energy region. This allows to predict the input for the dispersion relations over a large part of the integration region. The perturbative piece is combined with data for the lower energies and the heavy quark thresholds. The result for the hadronic contribution to the running of the coupling Δα^{(5)}_{\rm had}(M_Z^2)= (277.5 \pm 1.7)\times 10^{-4} leads to (α(M_Z^2))^{-1}=128.927 \pm 0.023. Compared to previous analyses the uncertainty is thus significantly reduced.
A sizeable difference in the differential production cross section of top and antitop quarks, respectively, is predicted for hadronically produced heavy quarks. It is of order $α_s$ and arises from the interference between charge odd and even amplitudes respectively. For the TEVATRON it amounts up to 15\% for the differential distribution in suitable chosen kinematical regions. The resulting integrated forward-backward asymmetry of 4--5\% could be measured in the next round of experiments. At the LHC the asymmetry can be studied by selecting appropriately chosen kinematical regions. Furthermore, a slight preference at LHC for centrally produced antitop is predicted, with top quarks more abundant at large positive and negative rapidities.
A sizeable difference in the differential production cross section of top and antitop quarks, respectively, is predicted for hadronically produced heavy quarks. It is of order $α_s$ and arises from the interference between charge odd and even amplitudes respectively. For the TEVATRON it amounts to approximately 5-10% in the region where the cross section is large and could therefore be measured in the next round of experiments. At the LHC the asymmetry can be studied by selecting appropriately chosen kinematical regions.
In this work radiative corrections in the total hadronic decay rate of the tau-lepton and some moments of its differential distributions are studied employing perturbative QCD and the operator product expansion. We calculate quadratic quark mass corrections in the strange mass to the decay rate ratio R_tau to the order O(α_s^3 m^2) and find that they contribute appreciably to the Cabibbo suppressed decay modes of the tau-lepton. Using the results of a recent experimental analysis, we obtain m_s(1 GeV) = 200 \pm 40_exp \pm 30_th MeV.
We analyze sum rules for the $Υ$ system with resummation of threshold effects on the basis of the nonrelativistic Coulomb approximation. We find for the pole mass of the bottom quark $m_b=4.75\pm 0.04 GeV$ and for the strong coupling constant $\al_s(M_Z)=0.118\pm 0.006$. The origin of the contradiction between two recent estimates obtained within the same formal framework is clarified.
Recent analytical and numerical results for the three-loop polarization function allow to present a phenomenological analysis of the cross section for massive quark production in electron positron annihilation to order $α_s^2$. Numerical predictions based on fixed order perturbation theory are presented for charm and bottom production above 5 and 11.5 GeV, respectively. The contribution from these energy regions to $α(M_Z^2)$, the running QED coupling constant at scale M_Z, are given. The dominant terms close to threshold, i.e. in an expansion for small quark velocity $β$, are presented.
In this paper the three-loop polarization functions Π(q^2) are calculated for the cases of an external vector, axial-vector, scalar or pseudo-scalar current. Results are presented for the imaginary part which directly leads to the cross section $σ(e^+e^- \to Z \to hadrons)$ and to the Higgs decay rates, respectively.
We present analytical calculation of the first seven moments of the heavy quark vacuum polarization function in the three-loop order. The obtained results are compared against the asymptotic formulas following from the threshold singularities. We also discuss the $μ$ dependence of the moments within the BLM procedure.
Recent analytic calculations on the rate for the production of a pair of massive fermions in $e^+ e^-$ annihilation plus real or virtual radiation of a pair of massless fermions are discussed. The contributions for real and virtual radiation are displayed separately. The asymptotic behaviour close to threshold is given in a compact form and an application to the angular distribution of massive quarks close to threshold is presented.
We review current issues in exclusive semileptonic tau decays. We present the formalism of structure functions, and then discuss predictions for final states with kaons, for decays into four pions and for radiative corrections to the decay into a single pion. Implications for testing the standard model at low energies are discussed.
Secondary radiation of hadrons from a tau pair produced in electron positron collisions may constitute an important obstacle for precision measurements of the production cross section and of branching ratios. The rate for real and virtual radiation is calculated and various distributions are presented. For Z decays a comprehensive analysis is performed which incorporates real and virtual radiation of leptons. The corresponding results are also given for primary electron and muon pairs. Compact analytical formulae are presented for entirely leptonic configurations. Measurements of $Z$ partial decay rates which eliminate all hadron and lepton radiation are about 0.3\% to 0.4\% lower than totally inclusive measurements, a consequence of the ${\cal O}(α^2)$ negative virtual corrections which are enhanced by the third power of a large logarithm.
The rate for the production of a pair of massive fermions in $e^+ e^-$ annihilation plus real or virtual radiation of a pair of massless fermions is calculated analytically. The contributions for real and virtual radiation are displayed separately. The asymptotic behaviour close to threshold and for high energies is given in a compact form. These approximations provide arguments for the appropriate choice of the scale in the ${\cal O}(α)$ result, such that no large logarithms remain in the final answer.
QCD corrections to the electron positron annihilation cross-section into hadrons and to the hadronic $Z$ boson decay rate are reviewed. Formal developments are introduced in a form particularly suited for practical applications. These include the operator product expansion, the heavy mass expansion, the decoupling of heavy quarks and matching conditions. Exact results for the quark mass depen- dence are presented whenever available, and formulae valid in the limit of small bottom mass ($m_{b}^2\ll s$) or of large top mass ($m_{t}^2\gg s$) are presen- ted. The differences between vector and axial vector induced rates as well the classification of singlet and nonsinglet rates are discussed. Handy formulae for all contributions are collected and their numerical relevance is investi- gated. Prescriptions for the separation of the total rate into partial rates are formulated. The applicability of the results in the low energy region, relevant for measurements around 10 GeV and below, is investigated and numerical predictions are collected for this energy region.
QCD corrections to all the allowed decays of superheavy groundstate quarkonia into electroweak gauge and Higgs bosons are presented. For quick estimates, approximations that reproduce the exact results within less than at worst two percent are also given.
The most general angular distribution of two or three meson final states from semileptonic decays $τ\rightarrow ππν$, $Kπν$, $πππν$, $Kππν$, $Kπν$, $KKKν$, $ηππν,\,\ldots{}$ of polarized $τ$ leptons can be characterized by 16 structure functions. Predictions for hadronic matrix elements, based on CVC and chiral Lagrangians and their relations to the structure functions are discussed. Most of them can be determined in currently ongoing high statistics experiments. Emphasis of the kinematical analysis is firstly put on $τ$ decays in $e^{+}e^{-}$ experiments where the neutrino escapes detection and the $τ$ rest frame cannot be reconstructed. Subsequently it is shown, how the determination of hadron tracks in double semileptonic events allows to fully reconstruct the $τ$ kinematics. The implications for the spin analysis are indicated.
The polarization dependent momentum distributions of top quarks and their decay products are calculated for $t\bar t$ production at future $e^+e^-$ colliders with polarized beams. The Green function formalism is applied to this reaction near energy threshold. The Lippmann--Schwinger equations for the $S$-wave and $P$-wave Green functions are solved numerically for the QCD chromostatic potential given by the two-loop formula at large momentum transfers and Richardson ansatz at intermediate and small ones. It is demonstrated that for the longitudinally polarized electron beam an optimally polarized sample of top quarks can be produced.
Theoretical results are presented for top quarks produced in annihilation of polarized electrons on positrons. Polarization studies for $t\bar t$ pairs near threshold are free from hadronization ambiguities. This is due to the short lifetime of the top quark. Semileptonic decays are discussed as well as their applications in studying polarization dependent processes involving top quarks. The Green function formalism is applied to $t\bar t$ production at future $e^+e^-$ colliders with polarized beams. Lippmann--Schwinger equation is solved numerically for the QCD chromostatic potential given by the two-loop formula at large momentum transfers and Richardson ansatz at intermediate and small ones. The polarization dependent momentum distributions of top quarks and their decay products are calculated.