Search for CP violation in Z0 → τ + τ − and an upper limit on the weak dipole moment of the τ lepton

An improved test of invariance in the reaction e⁺e^? τ ⁺ τ ^? on the Z0 peak is performed using the data sample recorded between 1991 and 1995 with the OPAL detector at LEP. Optimal observables, requiring the reconstruction of the τ flight direction and spin, have been used for different final state topologies. From the non-observation of violation we derive 95% confidence level upper limits on the real and imaginary parts of the weak dipole moment of the τ lepton of |Re(d _τ ^w (m _Z ² | < 5.6 × 10^?18 e cm and |Im(d _τ ^w (m _Z ² ))| < 1.5 × 10^?17 e cm, respectively.     

Neutron-rich hypernuclei in the chiral soliton model

The binding energies of neutron-rich strangeness S = ?1 hypernuclei are estimated in the chiral soliton approach using the bound state rigid oscillator version of the SU(3) quantization model. Additional binding of strange hypernuclei in comparison with nonstrange neutron-rich nuclei takes place at not large values of atomic (baryon) numbers, A = B ?? ??10. This effect becomes stronger with increasing isospin of nuclides, and for the ??nuclear variant?? of the model with rescaled Skyrme constant e. Binding energies of _?? ⁸ He and recently discovered _?? ⁶ H satisfactorily agree with data. Hypernuclei _?? ⁷ H, _?? ⁹ He are predicted to be bound stronger in comparison with their nonstrange analogues ⁷H, ⁹He; hypernuclei _?? ¹⁰ Li, _?? ¹¹ LI, _?? ¹² Be, _?? ¹³ Be, etc. are bound stronger in the nuclear variant of the model.     

Microscopic foundation of the interacting boson model in thes d-shell nuclei

Starting from an isospin invariant shell-model hamiltonian, we describe a method for deriving microscopically the IBM-hamiltonian appropriate to lights d-shell nuclei. The key ingredients of our approach are:a) the Belyaev-Zelevinsky-Marshalek (BZM) bosonization procedure;b) two successive unitary transformations that extract the “maximally decoupled” collective bosons with angular momentaJ=0(s _ππ ⁺ ,s _νν ⁺ ,s _πν ⁺ ) andJ =2(d _ππ ⁺ ,d _νν ⁺ ,d _πν ⁺ (T=0),d _πν ⁺ (T=1)). The method is applied to obtain the low-energy spectra and the electron scattering form factors for the 0 ₁ ⁺ →2 ₁ ⁺ transitions in²⁰Ne and²⁴Mg. Good agreement with the exact shell-model results is achieved. The inclusion of proton-neutron bosons (s _πν ⁺ ,d _πν ⁺ (T=1),d _πν ⁺ (T=0)), as well as the renormalization of boson parameters due to the non-collective degrees of freedom, are shown to play a crucial role.     

The decay of the Bethe-Salpeter kernel inP(ϕ)2 quantum field models

We extend methods of high temperature expansions to show that for even weakly coupledP(?)₂ quantum field models the Bethe-Salpeter kernel has 4 particle decay. More precisely ifK denotes the Euclidean Bethe-Salpeter kernel $$|K(x_1 ,x_2 ,x_3 ,x_4 )| \leqq Oe^{ - m_0 (1 - \varepsilon )d_2 } ,$$ wherex=(x ⁰,x ¹),d ₂=2|x ₁ ⁰ +x ₂ ⁰ ?x ₃ ⁰ ?x ₄ ⁰ |+|x ₁ ⁰ ?x ₂ ⁰ |+|x ₃ ⁰ ?x ₄ ⁰ | and ε(λ)→0 as λ→0. Our methods apply to otherr particle irreducible kernels.     

A new many-body solution of the Friedel resonance problem

It is numerically shown that the groundstate of the Friedel problem (consisting of a conduction band and a dresonance), occupied with (n+ 1) electrons, can be written as Ψ = (A a ₀ ^* +Bd*) Π _v=1 ⁿ a _v ^* Φ₀, where a ₀ ^* represents a localized conduction electron state, d* is the Friedel resonance state and Π _v=1 ⁿ a _v ⁸ Φ₀ is a Slater determinant of n single electron states a _t ^* , (Φ₀ is the vacuum state). The a _i ^* together with a ₀ ^* are part of a full ortho-normalized basis of the conductions band.     

Conserved-vector-current hypothesis and the\bar v_e e^ - \to \pi ^ - \pi ^0 process

Based on the conserved-vector-current (CVC) hypothesis and a four-ρ-resonance unitary and analytic VMD model of the pion electromagnetic form factor, theσ _tot(E _v ^lab ) and dσdE _π ^lab of the weak \(\bar v_e e^ - \to \pi ^ - \pi ^0\) process are predicted theoretically for the first time. Their experimental approval could verify the CVC hypothesis for all energies above the two-pion threshold. Since, unlike the electromagnetic e⁺e^?→π⁺π^? process, there is no isoscalar vector-meson contribution to the weak \(\bar v_e e^ - \to \pi ^ - \pi ^0\) reaction, accurate measurements of theσ _tot(E _v ^lab ) that moreover is strengthened with energyE _v ^lab linearly could solve now a widely discussed problem of the mass specification of the first excited state of theρ(770) meson. As a by-product, an equality \(\sigma _{tot} (\bar v_e e^ - \to \pi ^ - \pi ^0 ) = \sigma _{tot} (e^ + e^ - \to \pi ^ - \pi ^0 )\) is predicted for \(\sqrt s \approx 70 GeV\) .     

Ground-state energy of quantum liquids

The kinetic (K ₄ ⁰ (n) and K ₃ ⁰ (n)) and potential (V ₄ ⁰ (n) and V ₃ ⁰ (n)) energies of ⁴He and ³He atoms have been found from the law of corresponding states and the experimental data on the dependence of the ground-state energies E ₄ ⁰ (n) and E ₃ ⁰ (n) on the density of the isotopes ⁴He and ³He. In the approximation of structureless quantum liquid, the potential energies are equal, V ₄ ⁰ V ₃ ⁰ (n) = (n), and the kinetic energies are inversely proportional to the atomic mass, $K_4^0 (n) = \frac{3} {4}K_3^0 (n)$ . The potential energy given by the expression V ⁰ = 4E ₄ ⁰ ? 3E ₃ ⁰ to a high accuracy is linear in the density n, which is associated with nearly an absence of short-range order in liquid helium. The kinetic energy of liquid ⁴He is given by the expression K ₄ ⁰ = 3(E ₃ ⁰ ? E ₄ ⁰ ), which agrees with the experimental data on neutron scattering in liquid ⁴He. The quantities K ₄ ⁰ (n) and K ₃ ⁰ (n) determine the scale of all thermodynamic characteristics in the temperature range where the effects of the particle statistics can be neglected.     

Charge radii and magnetic moments of odd- A 183-189Pb isotopes

Unexpected features of the BaBar data on e ⁺ e ^- $ \rightarrow$ B $ \overline{{B}}$ cross-sections (B stands for baryon) are discussed. These data have been collected, with unprecedented accuracy, by means of the initial-state radiation technique, which is particularly suitable in giving good acceptance and energy resolution at threshold. A striking feature observed in the BaBar data is the non-vanishing cross-section at threshold for all these processes. This is the expectation due to the Coulomb enhancement factor acting on a charged fermion pair. In the case of e ⁺ e ^- $ \rightarrow$ p $ \overline{{p}}$ it is found that Coulomb final-state interactions largely dominate the cross-section and the form factor is | G ^p(4M ² _p)| ～ 1 , which could be a general feature for baryons. In the case of neutral baryons an interpretation of the non-vanishing cross-section at threshold is suggested, based on quark electromagnetic interaction and taking into account the asymmetry between attractive and repulsive Coulomb factors. Besides strange baryon cross-sections are compared to U -spin invariance predictions.     

Anomalous magnetic moment of theW-bosons and non-standardZ 0 W + W − coupling in polarizede − e + collisions

We study quantitatively the reactions \(e^ + e^ - \to W^ + e\bar \nu _e \) ,e _R ^? e ⁺ and the rare decay \(Z^0 \to W^ \pm l^ \mp \mathop {\nu _e }\limits^{( - )} \) forl=e, μ and τ, as a test for anomalous γW ⁺ W ^? andZ ⁰ W ⁺ W ^? structure. If κ denotes the anomalous magnetic moment of theW-boson and ω its anomalous coupling to theZ ⁰, values of |ω|>2.5 and |κ|>1.5 can be ruled out at LEP and SLC rather easily. This will put constraints on composite model building.     

Description of the properties of the low-lying energy states in 100Mo with IBM2

The properties of the low-lying energy states for the 100Mo isotope is investigated within the framework of the proton-neutron interacting model IBM2.By considering the relative energy of the d proton boson to be diferent from that of the neutron boson and taking into account the dipole interacting among like-boson LπLπand LνLν,the low-lying energy spectrum is reproduced well.Particularly,the relative position of the energies for 2+1,0+2,2+2 and 4+1states shifted correctly fit the experimental data.The electromagnetic properties,including the key observable B(E2)reduced transition branching ratios and the E2 reduced matrix elements of the experimental data,are well described.Our calculations show possible shape coexistence in the 100Mo nucleus.     

K S 0 , Λ and ≡ production at intermediate to high pT from Au+Au collisions at \sqrt {s_{NN} } = 39, 11.5 and 7.7 GeV

We report on the p _T dependence of nuclear modification factors (R _CP) for K _S ⁰ , ??, ?? and the $\bar NK_S^0 $ ratios at mid-rapidity from Au+Au collisions at $\sqrt {s_{NN} } $ = 39, 11.5 and 7.7 GeV. At $\sqrt {s_{NN} } $ = 39 GeV, the R _CP data show a baryon/meson separation at intermediate p _T and a suppression for K _S ⁰ for p _T up to 4.5 GeV/c; the $\bar \Lambda K_S^0 $ shows baryon enhancement in the most central collisions. However, at $\sqrt {s_{NN} } $ = 11.5 and 7.7 GeV, R _CP shows less baryon/meson separation and $\bar NK_S^0 $ shows almost no baryon enhancement. These observations indicate that the matter created in Au+Au collisions at $\sqrt {s_{NN} } $ = 11.5 or 7.7 GeV might be distinct from that created at $\sqrt {s_{NN} } $ = 39 GeV.     

Form factor π0 → γ* + γ* at different photon virtualities

The π⁰ γγ vertex for virtual photons of squared masses q ₁ ² and q ₂ ² plays a vital rôle in several physical processes; for example for q ₁ ² < 0, q ₂ ² < 0, in the two-photon physics reaction e ⁺ e ^? → e ⁺ e ^?π⁰, and for q ₁ ² > 0, q ₂ ² > 0, in the annihilation process e ⁺ e ^? → π⁰ l ⁺l^?. It is also of interest because of its link to the axial anomaly. We suggest a new approach to this problem. We have obtained a closed analytic expression for the vertex in the limit in which at least one of ¦q ₁ ² ¦ and ¦q ₂ ² ¦ is large for arbitrary fixed values of the ratio q ₁ ² /q ₂ ² . We compare our results with those obtained previously by Brodsky and Lepage. It should be straightforward to test our predictions experimentally.     

Gaussian limit for critical oriented percolation in high dimensions

In this paper, we consider the spread-out oriented bond percolation models inZ ^d ×Z withd>4 and the nearest-neighbor oriented bond percolation model in sufficiently high dimensions. Let η _n ,n=1, 2, ..., be the random measures defined onR ^d by $$\eta _n (A) = \sum\limits_{x \in Z^d } {1_A (x/\sqrt n )1_{\{ (0,0) \to (x,n)\} } } $$ The mean of η _n , denoted by $\bar \eta _n $ , is the measure defined by $$\bar \eta _n (A) = E_p [\eta _n (A)]$$ We use the lace expansion method to show that the sequence of probability measures $[\bar \eta _n (R^d )]^{ - 1} \bar \eta _n $ converges weakly to a Gaussian limit asn→∞ for everyp in the subcritical regime as well as the critical regime of these percolation models. Also we show that for these models the parallel correlation length $\xi (p)~|p_c - p|^{ - 1} $ asp?p_c     

Vacuum energy ingϕ d /4 -theory forg→∞

In the nonlocalg? _d ^/4 (d≧1) and localg? ₂ ⁴ theory theS-matrix is obtained in a form of the functional integral which is proved to exist. The density of vacuum energy $$E(g) = - \mathop {\lim }\limits_{V \to \infty } \frac{1}{V}\ln \left\langle {0\left| {S_V (g)} \right|0} \right\rangle $$ is investigated. It is proved to be analytic through the whole complexg-plane except for the negative real axis and pointg=0. Its asymptotic behaviour forg→∞ is found.     

Hyperfine structure of the atomic osmium spectrum: Superposition of configurations and the effect of nucleus volume

The contributions of the superposition of configurations ns ²5d ⁷6s+ns5d ⁷6sn′s+ns5d ⁷6s ² (n=1–5, n′=7–10) to the parameters of the hyperfine structure a _5d ⁰¹ , a _5d ¹² , a _5d ¹⁰ , a _6s ¹⁰ in the spectrum of the osmium atom Os I are calculated. Nonzero contributions are shown to be made only to the parameters a _5d ¹⁰ and a _6s ¹⁰ . This fact justifies the inclusion of the parameter a _5d ¹⁰ in the semiempirical analysis of experimental values of magnetic dipole constants of the hyperfine structure of the 5d ⁷ s configuration in the spectrum of the osmium atom. The effect of nucleus volume on the parameters of the hyperfine structure in the spectra of osmium isotopes ¹⁸⁷Os and ¹⁸⁹Os is estimated.     

Hölder’s inequality for matrices

We prove that for arbitraryn×n matricesA ₁,A ₂,…,A _m and for positive real numbersp ₁,p ₂,…,p _m withp ₁ ^?1 +p ₂ ^?1 +…+p _m ^/?1 =1, the inequality 1 $$|Tr(A_1 A_2 ...A_m )^2 |< \mathop {II}\limits_{k = 1}^m [Tr(A_k^\dag A_k )^{p_k } ]P_k^{ - 1} $$ holds.     

Spin states of cobalt and the thermodynamics of Sm1 − x Ca x CoO3 − δ solid solutions

In the rare-earth SmCoO₃ perovskite, Co³⁺ ions at low temperatures appear to be in the low-spin state with S = 0, t _2g ² e _g ⁰ . If Ca²⁺ ions partially substitute Sm³⁺ ions, oxygen deficient Sm_{1 ? x} Ca _x CoO_{3 ? δ} solid solutions with δ = x/2 appear. The oxygen deficiency leads to the formation of pyramidally coordinated cobalt ions Co _pyr ³⁺ in addition to the existing cobalt ions Co _oct ³⁺ within the oxygen octahedra. Even at low temperatures, these ions have a magnetic state, either S = 1, t _2g ⁵ e _g ¹ or S = 2, t _2g ⁴ e _g ² . At low temperatures, the magnetization of Sm_{1 ? x} Ca _x CoO_{3 ? δ} is mainly determined by the response of Co _pyr ³⁺ ions. Owing to the characteristic features of the crystal structure of the oxygen deficient perovskite, these ions form a set of nearly isolated dimers. At high temperatures, the magnetization of Sm_{1 ? x} Ca _x CoO_{3 ? δ} is mainly determined by the response of Co _oct ³⁺ ions, which exhibit a tendency to undergo the transition from the S = 0, t _2g ⁶ e _g ⁰ state to the S = 1, t _2g ⁵ e _g ¹ or S = 2, tt _2g ⁴ e _g ² state. In addition, the magnetization and specific heat of the solid solutions under study include the contribution from the rare-earth subsystem, which undergoes a magnetic ordering at low temperatures.     

Pulsed ESR on the organic ion radical salt: 3,3′-diethyl-4,4′-dimethyl-2,2′-thiazolocyanine-[TCNQ]2

We present firstT _1e ^?1 andT _2e ^?1 measurements on the organic ion radical salt 3,3′-diethyl-4,4′-dimethyl-2,2′-thiazolocyanine-(TCNQ)₂ as function of temperature and of orientation. The electronic spin diffusion constant could be determined directly by the electron spin echo field gradient technique:D (300 K)=0.03±0.02 cm²/sec. Pulsed ESR experiments have — in comparison to conventional cw-ESR — the advantage to monitor viaT _1e ^?1 andT _2e ^?1 the spectral density of dynamical processes at different frequencies. This is shown in a general manner on 3,3′-diethyl-4,4′-dimethyl-2,2′-thiazolocyanine-(TCNQ)₂. Between 300 and 60 K,T _1e ^?1 andT _2e ^?1 are close in amplitude and have a similar temperature dependence. At 60 K their degeneracy is lifted, yielding a quantitative value for the effective spin exchange between localized spinsτ _ex ^?1 sec^?1 and via the absolute value of the relaxation an average distance of the localized centers of about 12 Å. The dynamical data as evaluated above cannot be correlated with the conductivity, clearly indicating that the conduction electrons are a minority, not being monitored by the ESR-experiments.     

151,153Eu electron paramagnetic resonance in SrMoO4 and determination of signs of spin Hamiltonian parameters at different temperatures

The electron paramagnetic resonance (EPR) spectra of Eu²⁺ impurity centers in SrMoO₄ crystals have been studied in the temperature range of 1.8, 100–300 K. A hyperfine structure has been simulated for ^151,153Eu of different EPR transitions observed experimentally at different temperatures and external magnetic field orientations. A unique set of all parameters of the spin Hamiltonian for the known sign of the hyperfine interaction parameters A _i has been determined. It has been found that the diagonal parameters |b _n ⁰ | of the spin Hamiltonian decrease with increasing temperature; however, the parameter b ₄ ⁴ increases. The results of the study have demonstrated that |b ₂ ⁰ (T)/P ₂ ⁰ (T)| ～ const for ^151,153Eu in this single crystal.     

Statistical mechanism of the formation of the energy spectra of sputtered molecular clusters

The energy spectra of Si _n O _m ^? clusters sputtered from Si targets by Xe⁺ ions with O₂ pumping onto a bombarded surface, as well as by O ₂ ⁺ ions, are studied. It is shown that the form of the Si _n O _2n+1 ^? energy distributions does not depend on the experimental conditions. Significant differences in the energy spectra of O and Si monomers as compared to Si _n O _2n+1 ^? clusters are revealed. The mentioned features of the energy distribution of Si _n O _m ^? clusters are explained within the framework of the statistical recombination mechanism of their formation in combinatorial synthesis processes.