Fine Structure of Avalanches in the Abelian Sandpile Model

We study the two-dimensional Abelian Sandpile Model on a square lattice of linear size L. We introduce the notion of avalanche's fine structure and compare the behavior of avalanches and waves of toppling. We show that according to the degree of complexity in the fine structure of avalanches, which is a direct consequence of the intricate superposition of the boundaries of successive waves, avalanches fall into two different categories. We propose scaling ans\"{a}tz for these avalanche types and verify them numerically. We find that while the first type of avalanches has a simple scaling behavior, the second (complex) type is characterized by an avalanche-size dependent scaling exponent. This provides a framework within which one can understand the failure of a consistent scaling behavior in this model.Comment: 10 page

Avalanche Dynamics in Evolution, Growth, and Depinning Models

The dynamics of complex systems in nature often occurs in terms of punctuations, or avalanches, rather than following a smooth, gradual path. A comprehensive theory of avalanche dynamics in models of growth, interface depinning, and evolution is presented. Specifically, we include the Bak-Sneppen evolution model, the Sneppen interface depinning model, the Zaitsev flux creep model, invasion percolation, and several other depinning models into a unified treatment encompassing a large class of far from equilibrium processes. The formation of fractal structures, the appearance of $1/f$ noise, diffusion with anomalous Hurst exponents, Levy flights, and punctuated equilibria can all be related to the same underlying avalanche dynamics. This dynamics can be represented as a fractal in $d$ spatial plus one temporal dimension. We develop a scaling theory that relates many of the critical exponents in this broad category of extremal models, representing different universality classes, to two basic exponents characterizing the fractal attractor. The exact equations and the derived set of scaling relations are consistent with numerical simulations of the above mentioned models.Comment: 27 pages in revtex, no figures included. Figures or hard copy of the manuscript supplied on reques

Neutral-Current Four-Fermion Production in e+e- Interactions at LEP

Neutral-current four-fermion production, e+e- -> ffff is studied in 0.7/fb of data collected with the L3 detector at LEP at centre-of-mass energies root(s)=183-209GeV. Four final states are considered: qqvv, qqll, llll and llvv, where l denotes either an electron or a muon. Their cross sections are measured and found to agree with the Standard Model predictions. In addition, the e+e- -> Zgamma* -> ffff process is studied and its total cross section at the average centre-of-mass energy 196.6GeV is found to be 0.29 +/- 0.05 +/- 0.03 pb, where the first uncertainty is statistical and the second systematic, in agreement with the Standard Model prediction of 0.22 pb. Finally, the mass spectra of the qqll final states are analysed to search for the possible production of a new neutral heavy particle, for which no evidence is found

Measurement of the Cross Section of W-boson pair production at LEP

The cross section of W-boson pair-production is measured with the L3 detector at LEP. In a data sample corresponding to a total luminosity of 629.4/pb, collected at centre-of-mass energies ranging from 189 to 209 GeV, 9834 four-fermion events with W bosons decaying into hadrons or leptons are selected. The total cross section is measured with a precision of 1.4 % and agrees with the Standard Model expectation. Assuming charged-lepton universality, the branching fraction for hadronic W-boson decays is measured to be: Br(W-->hadrons) = 67.50 +- 0.42 (stat.) +- 0.30(syst.) %, in agreement with the Standard Model. Differential cross sections as a function of the W- production angle are also measured for the semi-leptonic channels qqev and qqmv

Determination of alphaS from Hadronic Event Shapes in e+e- Annihilation at 192 < sqrt(s) < 208 GeV

Results are presented from a study of the structure of high energy hadronic events recorded by the L3 detector at sqrt(s)>192 GeV. The distributions of several event shape variables are compared to resummed O(alphaS^2) QCD calculations. We determine the strong coupling constant at three average centre-of-mass energies: 194.4, 200.2 and 206.2 GeV. These measurements, combined with previous L3 measurements at lower energies, demonstrate the running of alphaS as expected in QCD and yield alphaS(mZ) = 0.1227 +- 0.0012 +- 0.0058, where the first uncertainty is experimental and the second is theoretical

Measurement of the Tau Branching Fractions into Leptons

Using data collected with the L3 detector near the Z resonance, corresponding to an integrated luminosity of 150pb-1, the branching fractions of the tau lepton into electron and muon are measured to be B(tau->e nu nu) = (17.806 +- 0.104 (stat.) +- 0.076 (syst.)) %, B(tau->mu nu nu) = (17.342 +- 0.110 (stat.) +- 0.067 (syst.)) %. From these results the ratio of the charged current coupling constants of the muon and the electron is determined to be g_mu/g_e = 1.0007 +- 0.0051. Assuming electron-muon universality, the Fermi constant is measured in tau lepton decays as G_F = (1.1616 +- 0.0058) 10^{-5} GeV^{-2}. Furthermore, the coupling constant of the strong interaction at the tau mass scale is obtained as alpha_s(m_tau^2) = 0.322 +- 0.009 (exp.) +- 0.015 (theory)

Measurement of the Topological Branching Fractions of the tau lepton at LEP

Using data collected with the L3 detector at LEP from 1992 to 1995 on the Z peak, we determine the branching fractions of the tau lepton into one, three and five charged particles to be: B(tau->(1-prong)) = 85.274 +- 0.105 +- 0.073 %, B(tau->(3-prong)) = 14.556 +- 0.105 +- 0.076 %, B(tau->(5-prong)) = 0.170 +- 0.022 +- 0.026 %. The first uncertainties are statistical and the second systematic. The accuracy of these measurements alone is similar to that of the current world average

Study of Inclusive Strange-Baryon Production and Search for Pentaquarks in Two-Photon Collisions at LEP

Measurements of inclusive production of the Lambda, Xi- and Xi*(1530) baryons in two-photon collisions with the L3 detector at LEP are presented. The inclusive differential cross sections for Lambda and Xi- are measured as a function of the baryon transverse momentum, pt, and pseudo-rapidity, eta. The mean number of Lambda, Xi- and Xi*(1530) baryons per hadronic two-photon event is determined in the kinematic range 0.4 GeV < pt< 2.5 GeV, |eta| < 1.2. Overall agreement with the theoretical models and Monte Carlo predictions is observed. A search for inclusive production of the pentaquark theta+(1540) in two-photon collisions through the decay theta+ -> proton K0s is also presented. No evidence for production of this state is found

Measurement of the Lifetime of the Tau Lepton

The tau lepton lifetime is measured with the L3 detector at LEP using the complete data taken at centre-of-mass energies around the Z pole resulting in tau_tau = 293.2 +/- 2.0 (stat) +/- 1.5 (syst) fs. The comparison of this result with the muon lifetime supports lepton universality of the weak charged current at the level of six per mille. Assuming lepton universality, the value of the strong coupling constant, alpha_s is found to be alpha_s(m_tau^2) = 0.319 +/- 0.015(exp.) +/- 0.014 (theory)

Measurement of W Polarisation at LEP

The three different helicity states of W bosons produced in the reaction e+ e- -> W+ W- -> l nu q q~ at LEP are studied using leptonic and hadronic W decays. Data at centre-of-mass energies \sqrt s = 183-209 GeV are used to measure the polarisation of W bosons, and its dependence on the W boson production angle. The fraction of longitudinally polarised W bosons is measured to be 0.218 \pm 0.027 \pm 0.016 where the first uncertainty is statistical and the second systematic, in agreement with the Standard Model expectation