Correlations between D and [`(D)]{\overline D} mesons produced in 500 GeV/cπ?-nucleon interactions

We present a study of correlations between D and mesons produced in 500 GeV/cπ⁻-nucleon interactions, based on data from experiment E791 at Fermilab. We have fully reconstructed 791 ± 44 charm meson pairs to study correlations between the transverse and longitudinal momenta of the two D mesons and the relative production rates for different types of D meson pairs. We see slight correlations between the longitudinal momenta of the D and the , and significant correlations between the azimuthal angle of the D and the . The experimental distributions are compared to a next-to-leading-order QCD calculation and to predictions of the PYTHIA/JETSET Monte Carlo event generator. We observe less correlation between transverse momenta and different correlations between longitudinal momenta than these models predict for the default values of the model parameters. Better agreement between data and theory might be achieved by tuning the model parameters or by adding higher order perturbative terms, thus contributing to a better understanding of charm production.The relative production rates for the four sets of charm pairs, as calculated in the PYTHIA/JETSET event generator with the default parameters, agree with data as far as the relative ordering, but predict too many pairs and too few pairs.     

xF_3^{\gamma Z} in charged lepton scattering

Measurements of the structure function are now becoming available in charged lepton deep inelastic scattering at HERA. The correction factors which are necessary to compare these with measurements of in neutrino-nucleon scattering are deduced and a comparison is made between the H1 and the CCFR data. A sum rule is derived for the structure function measured in charged lepton scattering which is the analogue of the Gross Llewellyn-Smith sum rule for neutrino-nucleon scattering.     

Quantum Groups and Double Quiver Algebras

For a finite dimensional semisimple Lie algebra and a root q of unity in a field k, we associate to these data a double quiver . It is shown that a restricted version of the quantized enveloping algebras is a quotient of the double quiver algebra .*The author is partially supported by the National Science Foundation of China (Grant. 10271014) and Natural Science Foundation of Beijing City (grant. 1042001)     

Trigonometric Dynamical <Emphasis Type="Italic">r</Emphasis>-Matrices Over Poisson Lie Base

Let be a finite dimensional complex Lie algebra and a Lie subalgebra equipped with the structure of a factorizable quasitriangular Lie bialgebra. Consider the Lie group Exp with the Semenov-Tjan-Shansky Poisson bracket as a Poisson Lie manifold for the double Lie bialgebra . Let be an open domain parameterizing a neighborhood of the identity in Exp by the exponential map. We present dynamical r-matrices with values in over the Poisson Lie base manifold .*This research is partially supported by the Emmy Noether Research Institute for Mathematics, the Minerva Foundation of Germany, the Excellency Center Group Theoretic Methods in the study of Algebraic Varieties of the Israel Science foundation, and by the RFBR grant no. 03-01-00593.     

Differential Algebraicity of Multiple Sine Functions

The differential algebraicity of the multiple sine functions is investigated. The goal of the paper is to show the differential algebraicity of when the period is rational by using the classical theory due to Ostrowski.     

Improving bounds on flavor changing vertices in the two Higgs doublet model from B^0-\bar{B}^0 mixing

We find some constraints on the flavor changing vertices of the two Higgs doublet model, from the measurement. Although bounds from this observable have already been considered, this paper takes into account the role of a new operator not included previously, as well as the vertices , and . Using the Cheng–Sher parametrization, we find that for a relatively light charged Higgs boson (200–300 GeV), we obtain , while the parameter could have values up to about 50. In addition, we use bounds for and obtained from at next to leading order, and study the case where the only vanishing vertex factors are the ones involving quarks from the first family. We obtain that is not sensitive to the change of the parameter , while .     

Double Product Integrals and Enriquez Quantisation of Lie Bialgebras II: The Quantum Yang–Baxter Equation

For a Lie algebra with Lie bracket got by taking commutators in a nonunital associative algebra , let be the vector space of tensors over equipped with the Itô Hopf algebra structure derived from the associative multiplication in . It is shown that a necessary and sufficient condition that the double product integral satisfy the quantum Yang–Baxter equation over is that satisfy the same equation over the unital associative algebra got by adjoining a unit element to . In particular, the first-order coefficient r₁ of r[h] satisfies the classical Yang–Baxter equation. Using the fact that the multiplicative inverse of is where is the inverse of in we construct a quantisation of an arbitrary quasitriangular Lie bialgebra structure on in the unital associative subalgebra of consisting of formal power series whose zero order coefficient lies in the space of symmetric tensors. The deformation coproduct acts on by conjugating the undeformed coproduct by and the coboundary structure r of is given by where is the flip.Mathematical Subject Classification (2000). 53D55, 17B62     

Vector Measures on the Logic of <Emphasis Type="Italic">J</Emphasis>-projections of a Krein Space

Let be a Hilbert space with an inner product . In Jajte, R., and Paszkiewicz, A. (1978, Vector measure on the closed subspaces of a Hilbert space, Studia Mathematica 63, 229–251), the -measure on the logic of all orthogonal projections on H was studied. We examine the -measure on the hyperbolic logic of all J-projections on a Krein space. PACS: 03.65.Ta, 03.65.Db, 03.65.Ca.     

Finite State and Finite Stop Quantum Languages

We propose the concept of finite stop quantum automata (ftqa) based on Hilbert space and compare it with the finite state quantum automata (fsqa) proposed by Moore and Crutchfield (Theoretical Computer Science 237(1–2), 2000, 275–306). The languages accepted by fsqa form a proper subset of the languages accepted by ftqa. In addition, the fsqa form an infinite hierarchy of language inclusion with respect to the dimensionality of unitary matrices. We introduce complex-valued acceptance degrees and two types of finite stop quantum automata based on them: the invariant ftqa (icftq) and the variant ftqa (vcftq). The languages accepted by icftq form a proper subset of the languages accepted by vcftq. In addition, the icftq form an infinite hierarchy of language inclusion with respect to the dimensionality of unitary matrices. In this way, we establish two proper inclusion relations (fsqa) ⊂ (ftqa) and (icftq) ⊂ (vcftq), where the symbol means languages, and two infinite language hierarchies (fsqa) ⊂ (fsqa), (icftq) (icftq).     

Power Series for Solutions of the 3 {\mathcal D}-Navier-Stokes System on R 3

In this paper we study the Fourier transform of the -Navier-Stokes System without external forcing on the whole space R ³. The properties of solutions depend very much on the space in which the system is considered. In this paper we deal with the space of functions where and c (k) is bounded, . We construct the power series which converges for small t and gives solutions of the system for bounded intervals of time. These solutions can be estimated at infinity (in k-space) by .     

Prospects for B physics with the ATLAS and CMS detectors

The possibility of observing the radion using the ATLAS detector at the LHC is investigated. Studies on searches for the Standard Model Higgs with the ATLAS detector are re-interpreted to obtain limits on radion decay to γγ and ZZ^(*). The observability of radion decays into Higgs pairs, which subsequently decay into or is then estimated.     

Quantum Phase Dynamics of Interaction between Photon Field and Magnetic System: Effects of Magnetic Quantum Tunnelling

We investigate the dynamics of probability distributions of an initially one-mode coherent field interacting with a four-state molecular system, which is a single magnet with a tunneling across an anisotropic barrier, using a numerically exact approach. The population for each state, the phase properties of and , and ), the entropy are calculated for a model system. The model predicts that the molecule and field become asymptotically disentangled at half of the revival time, and that optical Schrödinger-cat and magnetic Schrödinger-cat states are generated.This paper was originally presented at the 5th International Conference on NEAR FIELD OPTICS and RELATED TECHNOLOGIES (NFO-5), which was held on December 6–10, 1998 at Coganoi Bay Hotel, Shirahama, Japan, in cooperation with the Japan Society of Applied Physics and Mombusho Grant-in Aid for Scientific Research on Priority Areas “Near-field Nano-optics” Project, sponsored by Japan Society for the Promotion of Science.     

Unitarily Inequivalent Representations in Algebraic Quantum Theory

It has been maintained that the physical content of a model of a system is completely contained in the C∗-algebra of quasi-local observables that is associated with the system. The reason given for this is that the unitarily inequivalent representations of are physically equivalent. But, this view is dubious for at least two reasons. First, it is not clear why the physical content does not extend to the elements of the von Neumann algebras that are generated by representations of . It is shown here that although the unitarily inequivalent representations of are physically equivalent, the extended representations are not. Second, this view detracts from special global features of physical systems such as temperature and chemical potential by effectively relegating them to the status of fixed parameters. It is desirable to characterize such observables theoretically as elements of the algebra that is associated with a system rather than as parameters, and thereby give a uniform treatment to all observables. This can be accomplished by going to larger algebras. One such algebra is the universal enveloping von Neumann algebra, which is generated by the universal representation of ; another is the direct integral of factor representations that are associated with the set of values of the global features. Placing interpretive significance on the von Neumann algebras mentioned earlier sheds light on the significance of unitarily inequivalent representations of , and it serves to show the limitations of the notion of physical equivalence.     

The Boltzmann Equation for Bose–Einstein Particles: Velocity Concentration and Convergence to Equilibrium

Long time behavior of solutions of the spatially homogeneous Boltzmann equation for Bose–Einstein particles is studied for hard potentials with certain cutoffs and for the hard sphere model. It is proved that in the cutoff case solutions as time converge to the Bose–Einstein distribution in L¹ topology with the weighted measure , where for temperature and for T<T_c. In particular this implies that if T<T_c then the solutions in the velocity regions (with ) converge to a unique Dirac delta function (velocity concentration). All these convergence are uniform with respect to the cutoff constants. For the hard sphere model, these results hold also for weak or distributional solutions. Our methods are based on entropy inequalities and an observation that the convergence to Bose–Einstein distributions can be reduced to the convergence to Maxwell distributions.     

Time dependent gravitational potential in the universe and some consequences

In this paper, assuming a linear change of the gravitational potential V in the universe, i.e. , some consequences are obtained. 1. The Hubble red shift is explained by the potential difference between the considered galaxy long time ago and the observer at this epoch. 2. The anomalous acceleration a _P from the spacecraft Pioneer 10 and 11 [1] is explained. 3. The deformations of the trajectories of planets are studied. It is shown that the planetary orbits are not axially symmetric and the angle from the perihelion to the aphelion is , while the angle from the aphelion to the perihelion is , where is the orbital period. There is no perihelion precession caused by the time dependent gravitational potential V. The quotient of two consecutive orbital periods ₁ and ₂ is equal to This formula is tested for the pulsars B1885+09 and B1534+12, and the results are good.This revised version was published online in April 2005. The publishing date was inserted.     

On the Product of Real Spectral Triples

The product of two real spectral triples and , the first of which is necessarily even, was defined by A.Connes as given by and, in the even-even case, by . Generically it is assumed that the real structure obeys the relations , , , where the -sign table depends on the dimension n modulo 8 of the spectral triple. If both spectral triples obey Connes' >-sign table, it is seen that their product, defined in the straightforward way above, does not necessarily obey this -sign table. In this Letter, we propose an alternative definition of the product real structure such that the -sign table is also satisfied by the product.     

Study of scalar top quarks in the neutralino and chargino decay channel at a future e + e − linear collider

The scalar top discovery potential has been studied with a full-statistics background simulation for s = 500GeV and = 500fb^–1. The simulation is based on a fast and realistic simulation of a TESLA detector. The large simulated data sample allowed the application of an Iterative Discriminant Analysis (IDA) which led to a significantly higher sensitivity than in previous studies. The effects of beam polarization on signal efficiency and individual background channels are studied using separate optimization with the IDA for both polarization states. The beam polarization is very important to measure the scalar top mixing angle and to determine its mass. Simulating a 180 GeV scalar top at minimum production cross section, we obtain m = 1GeV and cos = 0.009 in the neutralino decay channel, and m = 0.5 GeV and cos = 0.004 in the chargino decay channel.     

Narrow Escape, Part I

A Brownian particle with diffusion coefficient D is confined to a bounded domain Ω by a reflecting boundary, except for a small absorbing window . The mean time to absorption diverges as the window shrinks, thus rendering the calculation of the mean escape time a singular perturbation problem. In the three-dimensional case, we construct an asymptotic approximation when the window is an ellipse, assuming the large semi axis a is much smaller than ( is the volume), and show that the mean escape time is , where e is the eccentricity and is the complete elliptic integral of the first kind. In the special case of a circular hole the result reduces to Lord Rayleigh's formula , which was derived by heuristic considerations. For the special case of a spherical domain, we obtain the asymptotic expansion . This result is important in understanding the flow of ions in and out of narrow valves that control a wide range of biological and technological function. If Ω is a two-dimensional bounded Riemannian manifold with metric g and , we show that . This result is applicable to diffusion in membrane surfaces.