The tau weak-magnetic dipole moment

We calculate the prediction for the anomalous weak-magnetic form factor of the tau lepton at q² = M² within the Standard Model. With all particles on-shell, this is an electroweak gauge-invariant quantity. Its value is a_τ^w(M_Z²)= − (2.10+0.61 i) × 10⁻⁶. We show that the transverse and normal components of the single-tau polarization of tau pairs produced at e⁺e⁻ unpolarized collisions are sensitive to the real and absorptive parts of the anomalous weak-magnetic dipole moment of the tau. The sensitivity one can achieve at LEP in the measurement of this dipole moment is discussed.     

Polarization amplitudes fore + e − →W + W − ande + e − →ZZ

The main purpose of this work is to study the three weak boson vertex. We give explicit formulae for all polarization amplitudes of the processese ⁺ e ^? →W ⁺ W ^? ande ⁺ e ^? →ZZ, with arbitrary couplings between the various intermediate vector bosons. Using these expressions we discuss possible signatures ofC, P andT violation in the three vector boson coupling, as well as the effects of anomalous magnetic dipole and electric quadrupole moments ofW ^±. The amplitudes for the above processes in any SU(2) × U(1) and SU(2)_L × SU(2)_R × U(1) gauge theory are also given, while the special case of the Weinberg-Salam model is studied in detail.     

Loop corrections to the ϱ-parameter; the magnetic moment of the W± and e+e−→W+W−

Vector-boson loop corrections to the ϱ-parameter are considered for vector-boson self-interactions following from global SU(2)_WI broken by electromagnetism. Minimizing the degree of divergence of the ϱ-parameter restricts the free trilinear vector-boson self-couplings to a single one, the anomalous magnetic dipole moment, κ, of the W^+-. The analysis of e⁺e⁻ → W⁺W⁻ shows that this process is well suited for accurately determining this remaining free parameter, κ.     

On the magnetic moment inZ→ττ

Together with the vector and axial vector couplings, the general Lorentz structure of leptonicZ decays,Z→l ⁺ l ^?, allows for two types of interactions which correspond to weak magnetic and electric dipole moments. A way to measure the anomalous weak magnetic moment in the reactionZ→τ ⁺ τ ^? is described. This measurement may be performed at LEP and the SLC.     

Predictions for anomalous τ+τ−γ production at LEP 1

We calculate distributions for τ⁺τ^?γ production at LEP 1 taking into account a potentially existing anomalous magnetic moment a _τ of the τ lepton. The existing upper limits for ¦a _τ¦ are known from the dependence of the decay Z ⁰ → τ⁺τ^?γ on a _τ ² and are of the order of (1–5)%. We show that such limits are also sensitive to linear terms in a _τ, which are of equal importance at ¦a _τ¦ ～ (1–2)% and dominate below this value. Contributions from an electric dipole moment dτ do not interfere with the electromagnetic vertex or with the anomalous magnetic moment. Appropriate formulae are derived.     

Anomalous moments of heavy charged leptons

If leptons and quarks are composite particles we expect them to have anomalous moments: an anomalous magnetic moment and an analogue of this with respect to the weak neutral current. If these moments are suppressed by chiral symmetry they will have sizeable values only for heavy fermions, e.g. for fermions of the fourth generation. The forward-backward asymmetry of e⁺e⁻ → f̄f on the Z⁰ resonance is particularly suited for detecting the anomalous “weak magnetic” moment of f if f is the charged lepton of the fourth generation. Under favourable circumstances this moment may lead to a 10% effect.     

On W±, Z0, γ self-interactions: High energy behaviour and tree unitarity bounds

We analyze the high-energy behaviour of vector boson scattering amplitudes within the framework of a recently suggested lagrangian model based on global weak isospin symmetry broken by electromagnetism. Requiring vanishing of the most strongly (as s²) rising contribution to vector boson scattering amplitudes leads to vector boson self-interactions dependent on a single parameter, for which the anomalous W^± magnetic moment, κ, can be chosen. Tree unitarity is violated at about 2 TeV for arbitrary κ as in the SU(2)_L × U(1)_Y theory for m_H → ∞. The model is well suited for significant tests of the vector boson sector of the SU(2)_L × U(1)_Y electroweak theory in processes such as e⁺e⁻ → W⁺W⁻.     

The τ lepton as a laboratory for quantum chromodynamics

Decays of the τ lepton provide a clean environment to study hadron dynamics in an energy regime dominated by resonances. Inclusive spectral functions are the basis for quantum chromodynamics (QCD) analyses, providing a most accurate determination of the strong coupling constant and quantitative information on nonperturbative contributions. The τ vector spectral function is used together with e⁺e⁻ data in order to compute vacuum polarization integrals arising in the calculations of the anomalous magnetic moment of the muon and the running of the electromagnetic coupling constant. To cite this article: M. Davier, A. Höcker, C. R. Physique 3 (2002) 1223–1233.     

Constraints on couplings of a fast decaying axion

Constraints are imposed on the couplings of an axion-like pseudoscalar particle φ that decays into e⁺e⁻ and γγ. The electron g−2 sets a severe bound not only on the φe⁺e⁻ coupling but also on the φγγ coupling. The most reliable bound on the φ coupling to the light quarks comes from the decay ∑⁺ → pe⁺e⁻ which was measured in a hydrogen bubble-chamber experiment with good sensitivity and resolution covering the entire range of e⁺e⁻ mass practically down to 2m_e. These upper bounds, together with a constraint from the decay K⁺→π⁺γγ, reinforce arguments against the particle-physics interpretation of the anomalous positrons in heavy-ion collisions, since the couplings are by orders of magnitude smaller than needed to produce e⁺e⁻ pairs at the observed level by known mechanisms.     

Measurements of tau decay modes and a precise determination of the mass

The cross sections for e⁺e^? → e⁺(μ⁺ + non showering track + any photons have been measured for cm energies between 3.1 GeV and 5.2 GeV. We observe τ-pair production below the thresholdfor charm production and determine the τ mass to be 1.807 ± 0.020 GeV from a fit to the energy dependence of the cross section. The ration of the leptonic branching ratios B_μ/B_e = 0.92 ± 0.32 is consistent with eμ-universality. The following branching ratios are determined for a V-A coupling: $\text{B(τ → ν}{}_{\mathrm{\tau }}\text{e}\text{ν}\text{) = B(τ → ν}{}_{\mathrm{\tau }}\text{μ}\text{ν}\text{) = 0.182 + 0.028}$. B(τ → ν_τ + charged hadron + any photons) = 0.29 ± 0.11, B(τ → ν_τ + three or more charged hadrons + any photons) = 0.35 ± 0.11.     

Limits on a lepton-number violating process from e+e− collisions

If a new hypothetical particle induces a lepton-number violating process, it could also affect the reactions e⁺e⁻→μ⁺μ⁻ and e⁺e⁻→τ⁺τ⁻ through the t-channel exchange of the particle. A fit of the cross sections and forward-backward asymmetries measured by experiments at PEP and PETRA yields the 90% confidence level limits on the coupling of the partile: G_eμ < 0.119G_F and G_eτ < 0.085G_F, where G_F is the Fermi coupling constant. These limits exclude certain regions of couplings allowed by other lepton-number violating searches.     

Search for the decay τ− → vτηπ−

We have searched for the decay τ⁻ → v_τηπ⁻ using data accumulated by the ARGUS detector at the e⁺e⁻ storage ring DORIS II at DESY. No η signal was found in the π⁺π⁻π⁰ subsystems of the decay τ⁻ →v_τπ⁻π⁻π⁺ π⁰. We obtain an upper limit for the branching ratio of the decay τ⁻ → v_τηπ⁻ of 1.3% at the 95% confidence level.     

Aspects of chiral pion-nucleon physics

The next-to-leading order chiral pion-nucleon Lagrangian contains seven finite low-energy constants. Two can be fixed from the nucleon anomalous magnetic moments and another one from the quark mass contribution to the neutron-proton mass splitting. We find a set of nine observables, which to one-loop order only depend on the remaining four dimension-two couplings. These are then determined from a best fit. We also show that their values can be understood in terms of resonance exchange related to Δ excitation as well as vector and scalar meson exchange. In particular, we discuss the role of the fictitious scalar-isoscalar meson. We also investigate the chiral expansion of the two P-wave scattering volumes P₁⁻ and P₂⁺ as well as the isovector S-wave effective range parameter b⁻. The one-loop calculation is in good agreement with the data. The difference P₁⁻ − P₂⁺ signals chiral loop effects in the πN P-waves. The calculated D- and F-wave threshold parameters compare well with the empirical values.     

Excited lepton production at LEP and HERA

General expressions for single and pair production cross sections of excited leptons (e ^*,µ^*,v ^*) are presented. Specific results are shown for a realisticSU(2)×U(1) invariant model. Pair production ine ⁺ e ^? annihilation can measure anomalous magnetic moments of excited leptons. Single production ofe ^* is dominated by thet-channel γ exchange contribution which makes its detection feasible up to masses just below thee ⁺ e ^? c.m. energy. Due to this small |t| enhancement effect, contributions from elastic and resonance scattering inep production ofe ^* are substantial. Realistic estimates of the excited lepton production cross section at HERA are given     

Finite temperature effects in quantum field theory

We consider quantum electrodynamics at finite temperatures. By making use of the real time formalism we compute, on the one-loop level, the finite-temperature correction to the mass of the electron and to the anomalous magnetic moment a_e^th. The gauge-invariant correction to the electron mass is found to be a ten percent effect at a temperature of the order of 2×10¹⁰ K. Some astrophysical implications of this result are briefly discussed. The leading temperature correction to the anomalous magnetic moment of the electron is, at a temperature of 300 K, found to be one order of magnitude smaller than the τ-lepton contribution to a_e^th.     

Statistics of the energy dissipation rate and local enstrophy in turbulent channel flow

Using high-resolution direct numerical simulations, the height and Reynolds number dependence of high-order statistics of the energy dissipation rate and local enstrophy are examined in incompressible, fully developed turbulent channel flow. The statistics are studied over a range of wall distances, spanning the viscous sublayer to the channel flow centerline, for friction Reynolds numbers Re_τ=180 and Re_τ=381. The high resolution of the simulations allows dissipation and enstrophy moments up to fourth order to be calculated. These moments show a dependence on wall distance, and Reynolds number effects are observed at the edge of the logarithmic layer. Conditional analyses based on locations of intense rotation are also carried out in order to determine the contribution of vortical structures to the dissipation and enstrophy moments. Our analysis shows that, for the simulation at the larger Reynolds number, small-scale fluctuations of both dissipation and enstrophy show relatively small variations for z⁺?100.     

Flavour-violating charged lepton decays in seesaw-type models

Analytic expressions of lepton-flavour- and lepton-number-violating decays of charged leptons are derived in the context of general SU(2)_L ⊗ U(1)_Y seesaw scenarios that are motivated by grand unified theories (GUT's) or superstring models, in which left-handed and/or right-handed neutral singlets are present. Possible constraints imposed by cosmology and low-energy data are briefly discussed. The violation of the decoupling theorem in flavour-dependent graphs due to the presence of heavy neutral leptons of Dirac or Majorana nature is emphasized. Numerical estimates reveal that the decays τ⁻ → e⁻ e⁻ e⁺or τ⁻ → e⁻ μ⁻ μ⁺ can be as large as ∼ 10⁻⁶, which may be observed in LEP experiments or other τ factories.     

Signal for intermittency in e+e− reactions obtained from negative binomial fits

With a simple relation between the parameter k of the negative binomial distribution and the factorial moments 〈Fⁱ〉 we reanalyse published data from e⁺e⁻ reactions at √s=29 GeV on multiplicity distributions in rapidity bins to show that there is a significant rise of the 〈Fⁱ〉 with decreasing bin size δy along the thrust axis. The rise for δy<1 can be regarded as a signal for intermittency. For further discussion we compare the data with the Lund shower Monte Carlo. We suggest a direct measurement of factorial moments in e⁺e⁻ jets.     

An upper limit on the tau neutrino mass from leptonic tau decays

The partial width of the τ → e ^- v _e v _τ can be calculated from the tau mass, lifetime and branching ratio. The increasing precision on these measurements is making the partial width sensitive to the mass of the tau neutrino. We present the tau neutrino mass dependence on the partial width and show that this leads to a limit of m _r < 71 MeV at the 95% confidence level. We show that the limit is determined by the uncertainty in the tau lifetime and τ → e?v _e v _τ branching ratio. Additional measurements of these values are expected in the next few years and we show that the limit could become competitive with the direct measurements.     

Anomalous magnetic moment of the muon in the left-right model

The effect of Higgs bosons on the anomalous magnetic moment of the muon is considered within the model that is based on the SU(2)_L×SU(2)_R×U(1)_B–L gauge group and which involves a bidoublet and two triplets of Higgs fields (left-right model). For the Yukawa coupling constants and the masses of Higgs bosons, the regions are found where the model leads to agreement with experimental results obtained at the Brookhaven National Laboratory (BNL) for the anomalous magnetic moment of the muon. In order to explore corollaries from the constraints obtained for the parameters of the Higgs sector, the processes e⁺e^? → μ⁺μ^?, τ⁺τ^? and μ⁺μ^? → μ⁺μ^?, τ⁺τ^? are considered both within the left-right model and within the model involving two Higgs doublets (two-Higgs-doublet model). It is shown that, if the mass of the lightest neutral Higgs boson does indeed lie in the range 3.1–10 GeV, as is inferred from the condition requiring the consistency of the two-Higgs-doublet model with the data of the BNL experiment, this Higgs boson may be observed as a resonance peak at currently operating e⁺e^? colliders (VEPP-4M, CESR, KEKB, PEP-II, and SLC). In order to implement this program, however, it is necessary to reduce considerably the scatter of energy in the e⁺ and e^? beams used, since the decay width of the lightest neutral Higgs boson is extremely small at such mass values. It is demonstrated that, in the case of the left-right model, for which the mass of the lightest neutral Higgs boson is not less than 115 GeV, the resonance peak associated with it may be detected at a muon collider.