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     

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 ).     

AssociateJ/ψ+γ production: a clean probe of gluon densities

Production of strange and charm particles by hadron-proton collisions is analyzed in terms of a fire-ball (FB) model assuming the multiplicity of secondaries of a given massm, to be proportional to the FB mass: n(m)M ^*, the FB kinematics being determined by the Feynman-Yang scaling, as in the case of production. It is found that (m)1/m ² and that, using this property together with the scaling, no-free-parameter fits to currently available data of strange and charm particles frompp and p collisions are satisfactory, as well as for the photoproduction of charm mesonD and charm hyperon _c .     

A theory of 1/f noise

Letu() be an absolutely integrable function and define the random process where thet _i are Poisson arrivals and thes _i, are identically distributed nonnegative random variables. Under routine independence assumptions, one may then calculate a formula for the spectrum ofn(t), S _n(), in terms of the probability density ofs, p_s(). If any probability density p_s() having the property p_s() I for small is substituted into this formula, the calculated S_n() is such that S_n() 1 for small . However, this is not a spectrum of a well-defined random process; here, it is termed alimit spectrum. If a probability density having the property p_s() for small , where > 0, is substituted into the formula instead, a spectrum is calculated which is indeed the spectrum of a well-defined random process. Also, if the latter p_s is suitably close to the former p_s, then the spectrum in the second case approximates, to an arbitrary, degree of accuracy, the limit spectrum. It is shown how one may thereby have 1/f noise with low-frequency turnover, and also strict 1/f ^1– noise (the latter spectrum being integrable for > 0). Suitable examples are given. Actually, u() may be itself a random process, and the theory is developed on this basis.     

Deep inelastic Compton scattering at theep collider HERA

Deep inelastic Compton scattering at HERA is investigated with the intention of determining the usefulness of this process in pinning down the photon and proton structure functions. We examine the contributions of the various _s and _s ² subprocesses that arise from the nonelementary structure of the photon atS _p =30000 GeV². An assessment is made of the sensitivity of this process to the various parton and photon structure functions presently available. In particular we study the possibility of directly measuring the gluon content of the proton and the photon as well as the quark fragmentation into a photon with this process. Theep laboratory frame helps to separate out the different contributions and in particular may allow a quantitative study of the box diagram term.     

Quantum Observables,Lie Algebra Homology and TQFT

Let us consider a Lie (super)algebra G spanned by T where T are quantum observables in BV formalism. It is proved that for every tensor c^... that determines a homology class of the Lie algebra G the expression c^...T...T is again a quantum observable. This theorem is used to construct quantum observables in the BV sigma model. We apply this construction to explain Kontsevich's results about the relation between homology of the Lie algebra of Hamiltonian vector fields and topological invariants of manifolds.     

On the Virial Theorem for the Relativistic Operator of Brown and Ravenhall,and the Absence of Embedded Eigenvalues

A virial theorem is established for the operator proposed by Brown and Ravenhall as a model for relativistic one-electron atoms. As a consequence, it is proved that the operator has no eigenvalues greater than max(2Z - )mc², where is the fine structure constant, for all values of the nuclear charge Z below the critical value Z_c: in particular, there are no eigenvalues embedded in the essential spectrum when Z 3/4 . Implications for the operators in the partial wave decomposition are also described.     

Singular Potentials and Inelasticity

We show that attractive singular potentials –_s/r^s, s 2, can be regularized by an infinitesimal imaginary addition to the interaction strength _s = Re _s±i0. Such a procedure enables the unique definition of the scattering observables and is equal to an absorption (creation) of the particles in the origin. We discuss the physical sense of such a regularization as well as a possible application of the developed formalism to the systems with a short-range annihilation.     

Jet production rates at LEP and the scale of αs

We discuss the scale dependence of _s in connection with jet multiplicities on theZ pole in the framework of perturbative QCD. Several scale defining procedures are applied to jet fractions and compared to recent measurements at LEP.Dedicated to Prof. Dr. H.J. Mang on the occasion of his 60th birthday     

Alpha-decaying low-spin levels in155Lu and157Lu

Using an on-line mass separator, the -particle decays of¹⁵⁵Lu and¹⁵⁷Lu were investigated. A new -emitting level in¹⁵⁷Lu was identified [T_1/2=5.7(5) s,E =4924(20) keV]. In addition, a half-life of 140(20) ms was measured for the recently discovered second, low-lying, -decaying level [E =5579 (5)keV] in¹⁵⁵Lu.We wish to thank L.F. Archambault, R.B. Firestone, A.A. Shihab-Eldin, and A.A. Wydler for their contributions to this experimental program. We also express thanks to the staff of the SuperHILAC for providing smooth operation of the accelerator.     

Vacuum Einstein spaces with axial symmetry

Four classes of solutions are found to the equations R=–2_{; ;} and g _;=0 in three-dimensional space with metric gdxdx and signature (+ ––), equivalent to the Einstein equations R_ij=0 in a vacuum for the metric . The metric ds² assumes axial symmetry and symmetry with respect to the reflection .Translated from Izvestiya Uchebnykh Zavedenii, Fizika, No. 9, pp. 43–45, September, 1976.     

The Einstein 3-form Gα and its Equivalent 1-form Lα in Riemann–Cartan Space

We motivate the definition of the Einstein 3-form G by means of the contracted 2nd Bianchi identity. This definition contains the whole curvature 2-form. The L 1-form, defined via G = L ^*( ) ( is the Hodge-star, the coframe), is equivalent to the Einstein 3-form and contains all the information of the curvature 2-form relevant for the definition of the Einstein 3-form. A variational formula of Salgado on quadratic invariants of the L 1-form is discussed, generalized, and put into proper perspective.     

Perturbations of flows on Banach spaces and operator algebras

For automorphism groups of operator algebras we show how properties of the difference _t – ' _t are reflected in relations between the generators , . Indeed for a von Neumann algebraM with separable predual we show that if _t – '_t 0.28 for smallt, then = 0(+)°^-1 where is an inner automorphism ofM and is a bounded derivation ofM. If the difference _t – ' _t =O(t) ast ; 0, then = + and if _t – ' _t 0.28 for allt then =. We prove analogous results for unitary groups on a Hilbert space andC ₀,C ₀ ^* groups on a Banach space.This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität BielefeldWith partial support of the U.S. National Science Foundation     

High spin states in77Se populated by the74Ge(α,n γ) reaction

⁷⁷Se has been investigated by the reaction⁷⁴Ge(,n) at 14 MeV. Gamma singles spectra, gamma angular distributions and gamma-gamma coincidences have been taken. A level scheme has been established, spins and parities have been assigned. States of a rotational band on the 1/2^– ground state, a rotational band on the 5/2^– 249.7 keV state and an anormal band have been identified. Nuclear Reaction ⁷⁴Ge(,n )E =14 MeV; measuredE ,I ,--Coin.,-ang. distr.⁷⁷Se deduced levels,J, . Enriched target, Ge (Li).     

Static and stationary axially symmetric gravitational fields of bounded sources II. solutions obtainable from Weyl's class

This paper shows that a new class of axially symmetric static electrovacuum/magnetovacuum solutions is obtainable from Weyl's class of static vacuum solutions. The new class contains an infinite set of asymptotically flat solutions (in closed form) each of which involves an arbitrary set (d, _i) of parameters. These parameters have to be interpreted as functions of massm, chargee, and higher electric/magnetic multipole moments _i of the particle. The cased = 0, _i =0 leads to the Darmois solution and the cased = 0, _i 0 leads to the results of [1]. The case d=0, e=_i=0 leads to the Schwarzschild solution, the cased 0, _i =0,e 0 leads to the Reissner-Nordström solution. To get more general examples is a lengthy but straightforward exercise.     

Elastic scattering of α-particles on10B forEα = 5?50 MeV

Experimental data of the elastic scattering of-particles on¹⁰B forE = 30–50.6 MeV are presented. They are analysed together with the data of a previous measurement forE = 5–30 MeV in the frame of the optical model including spin-orbit coupling. The interaction radii of the-¹⁰B-systems are determined with the Inopin-Ericson model forE = 5–50 MeV. The mean free path of-particles in¹⁰B is calculated.     

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.