Polarization in Top Quark Pair Production near Threshold

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.Comment: 11 pages, LaTex (uses epsf.sty, 3 ps-figures appended as extra uuencoded file). The complete paper, including figures, is also available via anonymous ftp at ftp://ttpux2.physik.uni-karlsruhe.de/ttp94-28/ttp94-28.ps, or via www at http://ttpux2.physik.uni-karlsruhe.de/preprints.htm

Electroweak corrections to the toponium decay width

We discuss one-loop electroweak corrections to the decay width of toponium. We calculate the energy-level shifts by expanding around the solution of the Bethe-Salpeter equation in the instantaneous approximation, in analogy with the positronium case. We show that first-order electroweak effects are suppressed by at least four powers of the strong coupling constant, and are therefore negligible compared with QCD corrections. The calculation is manifestly gauge invariant and takes into account the contributions to the decay rate due to both Coulomb enhancement and phase space reduction effects.Comment: to be published in Phys. Lett. B, 9 pages LaTeX (incl. 3 figures) uses feynman, epic and eepi

Momentum Distributions in ttˉt\bar t

We apply the Green function formalism for $t-\bar t$ production and decay near threshold in a study of the effects due to the momentum dependent width for such a system. We point out that these effects are likely to be much smaller than expected from the reduction of the available phase space. The Lippmann--Schwinger equation for the QCD chromostatic potential is solved numerically for $S$ partial wave. We compare the results on the total cross section, top quark intrinsic momentum distributions and on the energy spectra of $W$ bosons from top quark decays with those obtained for the constant width.Comment: 12 pages (without figures) (11 (sub)figures available on request), Karlsruhe preprint TTP93-11, hep-ph/yymmnn

Polarization of tau leptons in semileptonic B decays

Analytic formulae for the one-loop order QCD corrections to the differential width of the semileptonic b decay are given with the tau polarization taken into account. Thence the polarization of tau is expressed by its energy and the invariant mass of the tau + antineutrino system. The non-perturbative corrections by Falk et al. are incorporated in the calculation.Comment: one footnote and one reference have been added; the paper is going to be published in Nucl. Phys.

Seesaw mechanism and the neutrino mass matrix

The seesaw mechanism of neutrino mass generation is analysed under the following assumptions: (1) minimal seesaw with no Higgs triplets, (2) hierarchical Dirac masses of neutrinos, (3) large lepton mixing primarily or solely due to the mixing in the right-handed neutrino sector, and (4) unrelated Dirac and Majorana sectors of neutrino masses. It is shown that large mixing governing the dominant channel of the atmospheric neutrino oscillations can be naturally obtained and that this constrained seesaw mechanism favours the normal mass hierarchy for the light neutrinos leading to a small $U_{e3}$ entry of the lepton mixing matrix and a mass scale of the lightest right handed neutrino $M\simeq 10^{10} - 10^{11}$ GeV. Any of the three main neutrino oscillation solutions to the solar neutrino problem can be accommodated. The inverted mass hierarchy and quasi-degeneracy of neutrinos are disfavoured in our scheme.Comment: LaTeX, 3 pages, no figures. Talk given at 6th International Workshop on Topics in Astroparticle and Underground Physics (TAUP 99), September 6-10, 1999, Paris, Franc

Relativistic Bound State Equation for Unstable Fermions and the Toponium Width

The bound state problem for a fermion-antifermion system is considered taking into account a finite decay width of the constituents. We propose an exactly solvable relativistic zero order equation similar to that of Barbieri and Remiddi, but including a constant width. We focus especially on the $t\bar{t}$ system for which we reconsider our recent calculation of the bound state corrections to the toponium width, which was performed in the narrow width approximation and needed the use of second order Bethe-Salpeter perturbation theory. We show that one obtains the same result already in first order BS perturbation theory if one uses our present approach. Furthermore the large cancellations of gauge dependent terms is demonstrated to be a consequence of a Ward identity. This cancellation mechanism is shown to be valid for general fermion-antifermion systems.Comment: 12 pages, latex, 3 eps figures

Final-State Interactions in e^+e^- -> t\bar{t} -> b l^+ \nu \bar{b} W^- Near Top Quark Threshold

We calculate final-state interaction corrections to the energy-angular distribution of l^+ in semi-leptonic top quark decay, where the parent top quark is produced via e^+e^- -> t\bar{t} near threshold. These are the corrections due to gluon exchange between t and \bar{b} (\bar{t} and b) and between b and \bar{b}. Combining with previously known other corrections, we explicitly write down the l^+ energy-angular distribution including the full O(alpha_s)=O(beta) corrections near t\bar{t} threshold. Numerical analyses of the final-state interaction corrections are given. We find that they deform the l^+ distribution typically at the 10% level. We also find that all qualitative features of the numerical results can be understood from intuitive pictures. The mechanisms of various effects of the final-state interactions are elucidated. Finally we define an observable which is proper to the decay process of the top quark (dependent only on d\Gamma_{t -> b l^+ \nu}/ dE_l d\Omega_l of a free polarized top quark) near t\bar{t} threshold. Such a quantity will be useful in extracting the decay property of the top quark using the highly polarized top quark samples.Comment: Section 6 is enlarged substantially and a paragraph is added to Section 8 correspondingly. Reference list is also improved. (27 pages including figures, LaTeX

V-a Tests Through Leptons from Polarised Top Quarks

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.Comment: 10 pages, LaTex (uses epsf.sty, 2 figures appended as uuencoded ps files). A complete postscript file, including figures, is available via anonymous ftp at ttpux2.physik.uni-karlsruhe.de (129.13.102.139) as /ttp94-4/ttp94-4.ps, Local preprint# TTP94-

Neutrino Masses and Bimaximal Mixing

Solar and atmospheric neutrino anomalies are described by bimaximal mixing of three neutrinos. Neutrino oscillations in appearance nu_e nu_mu,nu_tau and in disappearance nu_e long baseline and atmospheric experiments are sensitive to deviations from the ideal bimaximal mixing. It is suggested that these deviations may be dominated by a rotation in the electron--muon plane of the generation space. Simple seesaw models are described supporting this idea. The rotation angle is estimated from Fritzsch's relation. Predictions are presented for oscillations in long baseline experiments, for solar neutrinos, and for the rates of neutrinoless double beta decays.Comment: Latex, 13 p., no figure