A study of the decays of tau leptons produced on theZ resonance at LEP

From the analysis of a data sample corresponding to an integrated luminosity of 4.63 pb^–1 taken during the 1990 run of LEP at centre of mass energies between 88.2 GeV an 94.2 GeV, the tau decays and their charge conjugates have been studied. The following branching ratios have been measured; , , Br(^{– –} (K^–)v)=11.9±0.7±0.7%, BR (^{– –} v)= 22.4±0.8±1.3%, in good agreement with world averages. The measured electronic and muonic branching ratios lead to a measurement of the strong coupling constant, _s (m) = 0.26 _–0.12 ^+0.09 . Extrapolating the _s value fromm tom _Z yields _s (m_Z) = 0.109 _–0.028 ^+0.012 .The average polarizationP of taus produced in Z ^{s s} decays has also been measured using the above decay modes. The weighted mean of the polarizations obtained from the four decay modes isP =–0.24±0.07. This value ofP gives, in the improved Born approximation, a ratio between the axial and vector coupling constants of the tau of /a = 0.12 ± 0.04, and hence a value of the effective electroweak mixing parameter sin² _W(m _Z ² ).     

Tau decays into K* mesons

Using the ARGUS detector at the storage ring DORIS II we have measured decays into three charged mesons containingK ^* mesons. Exploiting the good particle identification capabilities of the detector we have determined the following branching ratios: ,B _r (^–K ^*0 K ^– v )= (0.20±0.05±0.04)%, andB _r (^–K ^*– X ⁰ v ) =(1.15±0.15_–0.18 ^+0.13)%.Supported by the German Bundesministerium für Forschung und Technologie, under contract number 054DO51P.     

CP-violating effects inZ decays to τ leptons

We calculate CP-odd correlations inZ decays to leptons, . These correlations are sensitive to the weak dipole moment of the . With 10⁷ producedZ particles and with observation of the decay channels and v we estimate that can be determined with an accuracy of about (1 s.d.).     

The Landau-Pomeranchuk effect and soft lepton-pair production in heavy ion collisions

The most general angular decay distribution of the hadronic system in the decay of a polarized into one pseudoscalar plus a vector is calculated. Emphasis is put on decays ine ⁺ e ^– experiments where the neutrino escapes detection and the restframe cannot be reconstructed. We propose a model for the decay intov involving both a vector- and a second class axial vector-current contribution. Then we present numerical results for this decay channel.     

Measurement of the decayτ? →ρ?ντ

An analysis of the decay ^--0 v has been performed using the ARGUS detector at the DORIS II storage ring. The branching ratio has been determined to be Br(^--0 v =(22.6±0.4±0.9)%. The shape of the ^-0 invariant mass spectrum is found to be in good agreement with the predictions obtained using the conserved vector current (CVC) hypothesis, suggesting that the ^-0 system is produced in aJ ^P=1^– state. An analysis of the measured decay angular distribution of the pions with respect to the flight direction of the ^-0 system demonstrates the vector nature of the coupling at the v vertex. With the assumption of zerov mass thev spin has been shown to be .Supported by the German Bundesministerium für Forschung und Technologie, under contract number 054DO51 P     

Infrared behaviour of metallic systems in one, two and three dimensions

A simple approximate expression for the electron lifetime() in metals is rederived and discussed for different dimensions. In the 3D-case we get the well known Drude behaviour, i.e. a constant. In one dimension() is strongly frequency-dependent in the IR. The 2D-case is intermediate to the preceding ones. These results are essentially due to the different form of the Fermi surface for an electron gas in one, two and three dimensions.     

A study of ultraviolet renormalon ambiguities in the determination of α s from τ decay

The divergent large-order behaviour of the perturbative series relevant for the determination of _s from decay is controlled by the leading ultraviolet (UV) renormalon. Even in the absence of the first infrared (IR) renormalon, an ambiguity of order ²/m ² is introduced. We make a quantitative study of the practical implications of this ambiguity. We discuss the magnitude of UV renormalon corrections obtained in the large-N _f limit, which, although unrealistic, is nevertheless interesting to some extent. We then study a number of improved approximants for the perturbative series, based on a change of variable in the Borel representation, such as to displace the leading UV renormalon singularity at a larger distance from the origin than the first IR renormalon. The spread of the resulting values of _s (m ²) obtained by different approximants, at different renormalization scales, is exhibited as a measure of the underlying ambiguities. Finally, on the basis of mathematical models, we discuss the prospects of an actual improvement, given the signs and magnitudes of the computed coefficients, the size of _s (m ²) and what is known of the asymptotic properties of the series. Our conclusion is that a realistic estimate of the theoretical error cannot go below _s (m ²)±0.060, or _s (m _Z ²)±0.006.On leave of absence from INFN, Sezione di Milano, Milan, Italy     

Determination of an upper limit for the mass of the τ-neutrino at LEP

An upper limit for the mass is determined through the kinematic reconstruction of the decay5 ^± in the OPAL detector at LEP. The limit is obtained using a new method based on the comparison of the two-dimensional distribution of energy and invariant mass of the five-pion system with expectations from different neutrino mass hypotheses. From a sample of five events surviving the selection criteria we obtain an upper limit of 74 MeV at 95% confidence level. It is the first measurement at LEP energies, where the larger average multiplicity of events makes the suppression of this background more robust compared to lower energies.     

Correlated angular distributions in τ+τ+ semileptonic decays

The spin correlated angular distribution for ⁺⁺ pairs at energies of theZ ⁰ resonance, both decaying semi-leptonically up to 3 hadrons in each final state, was derived assuming general vector and axial vector couplings. The use of these distributions to test the V-A structure of the -W-v vertex at LEP energies is analized.Partially supported by CONICET, Argentina     

Lifetime of charged and neutral B hadrons using event topology

The lifetimes of charged and neutral B hadrons have been measured using data collected by the DELPHI experiment at LEP between 1991 and 1993. B hadrons are tagged as jets with a secondary vertex and the charge of the B candidate is taken to be the sum of the charges of the particles in the secondary vertex. Approximately 1,434,000 multihadronic Z⁰ decays yielded 1817 B hadron candidates. The B purity was estimated to be around 99.1±0.3%, and 83% (70%) of the events measured as neutral (charged) came from neutral (charged) B's. The mean lifetimes of charged and neutral B hadrons were found to be 1.72±0.08 (stat.) ±0.06 (syst.) ps and 1.58±0.11 (stat.)±0.09 (syst.) ps respectively. The ratio of their lifertimes, _charged/_neutral, was 1.09 _–0.10 ^+0.11 (stat.)±0.08 (syst.). By making assumptions about the B _s ⁰ and _b ⁰ states, the B⁺ and B⁰ meson lifetimes were determined to be _B+ = 1.72 ± 0.08 (stat.) ±0.06 (syst.) ps and _B+ = 1.63 ± 0.14 (stat.)±0.13 (syst.) ps and the ratio of their lifetimes was:_B+/_B0 = 1.06 _–0.11 ^+0.13 ±0.10. The mean B lifetime was also deduced to be <> > = 1.64 ±0.06 (stat.)±0.04 (syst.) ps.     

A search for the lepton-flavour violating decays τ → eα, τ → μα

Lepton spectra in decays have been studied with the ARGUS detector at thee ⁺ e ^– storage ring DORIS II at DESY using the pseudo-rest-frame technique. We have improved upper limits for two-body -decays into a lepton and an unobservable particle.Supported by the German Bundesministerium für Forschung und Technologie, under contract number 054DO51P     

Instanton contribution toB→X s γ decay

We study instanton effects onBX _s decay using the heavy quark effective field theory and the operator product expansion. In the dilute gas approximation the effect is negligibly small. This is in contrast to the result of the instanton effect in inclusive semileptonicbu decay but similar to the inclusive hadronic decay. We discuss the similarities and differences of theBX _s decay compared to inclusive hadronic decay and semileptonicB decay.     

A matrix method for estimating the Liapunov exponent of one-dimensional systems

Let : [0, 1][0, 1] be a piecewise monotonie expanding map. Then admits an absolutely continuous invariant measure. A result of Kosyakin and Sandler shows that can be approximated by a sequence of absolutely continuous measures _n invariant under piecewise linear Markov maps _itn. Each _itn is constructed on the inverse images of the turning points of . The easily computable measures _n are used to estimate the Liapunov exponent of . The idea of using Markov maps for estimating the Liapunov exponent is applied to both expanding and nonexpanding maps.     

Multiplicity with a thrust cut

We evaluate the multiplicity of hadrons in thee ⁺ e ^–-annihilation at a given thrustT in the modified leading-log approximation, including corrections. The calculation is done at a large value of =1–T by the use of the factorisation which takes place in the one-particle-inclusive cross section at a given . At a small , a different type of factorisation takes place, which also enable us to evaluate the multiplicity. Two approaches are compared numerically. Measuring this quantity near =1/3, we can determine the multiplicity ratio between a gluon-jet and a quark-jet.     

Macroscopic short-time electrodynamics for conductors

In the macroscopic electrodynamics (MED) of good conductors (metals) based on Ohm's law j=E, the momentum relaxation time =m/ne² of the electrons limits the application to electromagnetic (EM) processes with characteristic timest. An interesting physical difficulty occurs in MED since the EM field damping time _R=/ of metals is very small compared with the minimum macroscopic time scale, _R. Consequently, the damping and propagation of EM waves and pulses in good conductors cannot be correctly described within the frame of conventional MED. New hyperbolic EM wave equations with relaxation and memory are proposed, which no longer exhibit the _R deficiency. The latter is caused by Ohm's law, which breaks down for short-time processes, due to neglect of electron inertia. The advantages of the proposed and the disadvantages of the conventional EM wave equations for good conductors are discussed in applications.     

An Equilibrium Lattice Model of Wetting on Rough Substrates

We consider a semi-infinite 3-dimensional Ising system with a rough wall to describe the effect of the roughness r of the substrate on wetting. We show that the difference of wall free energies (r)= _AW(r)– _BW(r) of the two phases behaves like (r)r(1), where r=1 characterizes a purely flat surface, confirming at low enough temperature and small roughness the validity of Wenzel's law, cos (r)r cos (1), which relates the contact angle of a sessile droplet to the roughness of the substrate     

Enhancement of conductance fluctuations in two-dimensional mesoscopic electron systems with valley structures

Conductance fluctuations are studied in twodimensional mesoscopic electron system with a two-hold valley degeneracy (n _v =2), which corresponds to the inversion layer of Si-MOSFET formed in (1,0,0) plane. It is shown that the intervalley scattering modifies conductance fluctuations depending on the ratio, Min { _c , _T }/ _v , where _v = ( – 2)/2 and _c , _T , and are, respectively, system traversal time, thermal diffusion time, intervalley scattering time and total life time of electrons. Conductance fluctuations are no longer universal and vary from G _univ 0.862·e ²/h to {ie223-5} at low temperatures even for isotropic systems. The conductance fluctuations increase with decreasing system size, increasing electron density and increasing intervalley scattering time. The effect of intervalley scattering is essentially the same as that of intersubband scattering as previously reported. At finite temperatures where _{T c} , the intervalley scattering modifies the fluctuations through the change in the energy correlation range to results in the reduction of the conductance fluctuations. In Si-MOSFET formed in (1, 1, 1) plane, wheren _v =6, more enhanced fluctuations are expected. Experimental studies are desired on theoretically predicted points.     

Slowing down of retrieval in the hopfield model

The variation of the convergence time, as a function of the storage capacity is studied numerically for systems ranging in size fromN=1000 toN=16,000 neurons. is found to increase likeexp[–A(_c–)] as one nears the critical storage capacity _c =0.142=0.002.     

Polynomial τ-Functions of the NLS-Toda Hierarchy and the Virasoro Singular Vectors

A family of polynomial -functions for the NLS-Toda hierarchy is constructed. The hierarchy is associated with the homogeneous vertex operator representation of the affine algebra of type A ₁ ⁽¹⁾. These -functions are given explicitly in terms of Schur functions that correspond to rectangular Young diagrams. It is shown that an arbitrary polynomial -function which is an eigenvector of d, the degree operator of , is contained in the family. By the construction, any -function in the family becomes a Virasoro singular vector. This consideration gives rise to a simple proof of known results on the Fock representation of the Virasoro algebra with c = 1.