The closest elastic tensor of arbitrary symmetry to an elasticity tensor of lower symmetry

The closest tensors of higher symmetry classes are derived in explicit form for a given elasticity tensor of arbitrary symmetry. The mathematical problem is to minimize the elastic length or distance between the given tensor and the closest elasticity tensor of the specified symmetry. Solutions are presented for three distance functions, with particular attention to the Riemannian and log-Euclidean distances. These yield solutions that are invariant under inversion, i.e., the same whether elastic stiffness or compliance are considered. The Frobenius distance function, which corresponds to common notions of Euclidean length, is not invariant although it is simple to apply using projection operators. A complete description of the Euclidean projection method is presented. The three metrics are considered at a level of detail far greater than heretofore, as we develop the general framework to best fit a given set of moduli onto higher elastic symmetries. The procedures for finding the closest elasticity tensor are illustrated by application to a set of 21 moduli with no underlying symmetry.Comment: 48 pages, 1 figur

Measurement of the W+W-gamma Cross Section and Direct Limits on Anomalous Quartic Gauge Boson Couplings at LEP

The process e+e- -> W+W-gamma is analysed using the data collected with the L3 detector at LEP at a centre-of-mass energy of 188.6GeV, corresponding to an integrated luminosity of 176.8pb^-1. Based on a sample of 42 selected W+W- candidates containing an isolated hard photon, the W+W-gamma cross section, defined within phase-space cuts, is measured to be: sigma_WWgamma = 290 +/- 80 +/- 16 fb, consistent with the Standard Model expectation. Including the process e+e- -> nu nu gamma gamma, limits are derived on anomalous contributions to the Standard Model quartic vertices W+W- gamma gamma and W+W-Z gamma at 95% CL: -0.043 GeV^-2 < a_0/Lambda^2 < 0.043 GeV^-2 0.08 GeV^-2 < a_c/Lambda^2 < 0.13 GeV^-2 0.41 GeV^-2 < a_n/Lambda^2 < 0.37 GeV^-2

Production of Single W Bosons at \sqrt{s}=189 GeV and Measurement of WWgamma Gauge Couplings

Single W boson production in electron-positron collisions is studied with the L3 detector at LEP. The data sample collected at a centre-of-mass energy of \sqrt{s} = 188.7GeV corresponds to an integrated luminosity of 176.4pb^-1. Events with a single energetic lepton or two acoplanar hadronic jets are selected. Within phase-space cuts, the total cross-section is measured to be 0.53 +/- 0.12 +/- 0.03 pb, consistent with the Standard Model expectation. Including our single W boson results obtained at lower \sqrt{s}, the WWgamma gauge couplings kappa_gamma and lambda_gamma are determined to be kappa_gamma = 0.93 +/- 0.16 +/- 0.09 and lambda_gamma = -0.31 +0.68 -0.19 +/- 0.13

Search for an invisibly decaying Higgs boson in e^+e^- collisions at \sqrt{s} = 183 - 189 GeV

A search for a Higgs boson decaying into invisible particles is performed using the data collected at LEP by the L3 experiment at centre-of-mass energies of 183 GeV and 189 GeV. The integrated luminosities are respectively 55.3 pb^-1 and 176.4 pb^-1. The observed candidates are consistent with the expectations from Standard Model processes. In the hypothesis that the production cross section of this Higgs boson equals the Standard Model one and the branching ratio into invisible particles is 100%, a lower mass limit of 89.2 GeV is set at 95% confidence level

Search for Neutral Higgs Bosons of the Minimal Supersymmetric Standard Model in e+e- Interactions at \sqrt{s} = 189 GeV

A search for the lightest neutral scalar and neutral pseudoscalar Higgs bosons in the Minimal Supersymmetric Standard Model is performed using 176.4 pb^-1 of integrated luminosity collected by L3 at a center-of-mass energy of 189 GeV. No signal is observed, and the data are consistent with the expected Standard Model background. Lower limits on the masses of the lightest neutral scalar and pseudoscalar Higgs bosons are given as a function of tan(beta). Lower mass limits for tan(beta)>1 are set at the 95% confidence level to be m_h > 77.1 GeV and m_A > 77.1 GeV

Measurement of Bose-Einstein Correlations in e+e- -> W+W- at root(s)=189GeV

We investigate Bose-Einstein correlations (BEC) in W-pair production at root(s)=189GeV using the L3 detector at LEP. We observe BEC between particles from a single W decay in good agreement with those from a light-quark Z decay sample. We investigate their possible existence between particles coming from different W's. No evidence for such inter-W BEC 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)

Search for Extra Dimensions in Boson and Fermion Pair Production in e+e- Interactions at LEP

Extra spatial dimensions are proposed by recent theories that postulate the scale of gravity to be of the same order as the electroweak scale. A sizeable interaction between gravitons and Standard Model particles is then predicted. Effects of these new interactions in boson and fermion pair production are searched for in the data sample collected at centre-of-mass energies above the Z pole by the L3 detector at LEP. In addition, the direct production of a graviton associated with a Z boson is investigated. No statistically significant hints for the existence of these effects are found and lower limits in excess of 1 TeV are derived on the scale of this new theory of gravity

Measurement of the Photon Structure Function at High Q^2 at LEP

The structure functions of real and virtual photons are derived from cross section measurements of the reaction e^+e^ -> e^+e^- + hadrons at LEP. The reaction is studied at \sqrt{s} ~ 91 GeV with the L3 detector. One of the final state electrons is detected at a large angle relative to the beam direction, leading to Q^2 values between 40 GeV^2 and 500 GeV^2. The other final state electron is either undetected or it is detected at a four-momentum transfer squared P^2 between 1 GeV^2 and 8 GeV^2. These measurements are compared with predictions of the Quark Parton Model and other QCD based models