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

Gluon Fragmentation into Heavy Quarkonium

The dominant production mechanism for heavy quark-antiquark bound states in very high energy processes is fragmentation, the splitting of a high energy parton into a quarkonium state and other partons. We show that the fragmentation functions $D(z,\mu)$ describing these processes can be calculated using perturbative QCD. We calculate the fragmentation functions for a gluon to split into S-wave quarkonium states to leading order in the QCD coupling constant. The leading logarithms of $\mu/m_Q$, where $\mu$ is the factorization scale and $m_Q$ is the heavy quark mass, are summed up using Altarelli-Parisi evolution equations.Comment: LateX 11 pages (3 figures available upon request). NUHEP-TH-92-2

Polarization in Top Quark Production and Decay near Threshold

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.Comment: 6 pages, LaTex (uses epsf.sty, 2 figures appended as uuencoded ps files). The complete paper, including figures, is also available via anonymous ftp at ttpux2.physik.uni-karlsruhe.de (129.13.102.139) as /ttp94-24/ttp94-24.ps, or via www at http://ttpux2.physik.uni-karlsruhe.de/preprints.html

Universality in Glassy Low-Temperature Physics

We propose a microscopic translationally invariant glass model which exhibits two level tunneling systems with a broad range of asymmetries and barrier heights in its glassy phase. Their distribution is qualitatively different from what is commonly assumed in phenomenological models, in that symmetric tunneling systems are systematically suppressed. Still, the model exhibits the usual glassy low-temperature anomalies. Universality is due to the collective origin of the glassy potential energy landscape. We obtain a simple explanation also for the mysterious {\em quantitative} universality expressed in the unusually narrow universal glassy range of values for the internal friction plateau.Comment: 4 pages, 5 figures, uses RevTeX

Electroweak effects in top-quark pair production at Hadron Colliders

Top-quark physics plays an important role at hadron colliders such as the Tevatron collider at Fermilab or the upcoming Large Hadron Collider (LHC) at CERN. Given the planned experimental precision, detailed theoretical predictions are mandatory. In this article we present analytic results for the complete electroweak corrections to gluon induced top-quark pair production, completing our earlier results for the quark-induced reaction. As an application we discuss top-quark pair production at Tevatron and at LHC. In particular we show that, although small for inclusive quantities, weak corrections can be sizeable for differential distribution

P-Wave Charmonium Production in B-Meson Decays

We calculate the decay rates of $B$ mesons into P-wave charmonium states using new factorization formulas that are valid to leading order in the relative velocity of the charmed quark and antiquark and to all orders in the running coupling constant of QCD. We express the production rates for all four P states in terms of two nonperturbative parameters, the derivative of the wavefunction at the origin and another parameter related to the probability for a charmed-quark-antiquark pair in a color-octet S-wave state to radiate a soft gluon and form a P-wave bound state. Using existing data on $B$ meson decays into $\chi_{c1}$ to estimate the color-octet parameter, we find that the color-octet mechanism may account for a significant fraction of the $\chi_{c1}$ production rate and that $B$ mesons should decay into $\chi_{c2}$ at a similar rate.Comment: 14 page

The Hofstadter Energy Spectrum for an Interacting 2DEG

We study the effects of the Coulomb interactions between electrons on the Hofstadter butterfly, which characterizes the subband structure of the Landau levels of a two-dimensional electron gas in a perpendicular homogeneous magnetic field and a periodic lateral superlattice potential. The interactions essentially preserve the intricate gap structure of the Hofstadter spectra, but with a lower symmetry that depends on the filling of the Landau bands. For short enough periods and strong enough modulation the miniband structure can be resolved in the thermodynamic density of states.Comment: LaTeX 4 pages with 3 PostScript figures, Contribution to EP2DSXI Nottingham August 95 to appear in Surface Scienc

Spectra of Modular and Small-World Matrices

We compute spectra of symmetric random matrices describing graphs with general modular structure and arbitrary inter- and intra-module degree distributions, subject only to the constraint of finite mean connectivities. We also evaluate spectra of a certain class of small-world matrices generated from random graphs by introducing short-cuts via additional random connectivity components. Both adjacency matrices and the associated graph Laplacians are investigated. For the Laplacians, we find Lifshitz type singular behaviour of the spectral density in a localised region of small $|\lambda|$ values. In the case of modular networks, we can identify contributions local densities of state from individual modules. For small-world networks, we find that the introduction of short cuts can lead to the creation of satellite bands outside the central band of extended states, exhibiting only localised states in the band-gaps. Results for the ensemble in the thermodynamic limit are in excellent agreement with those obtained via a cavity approach for large finite single instances, and with direct diagonalisation results.Comment: 18 pages, 5 figure