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     

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).     

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.     

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 .     

Twist-3 distribution amplitudes of the pion and kaon from the QCD sum rules

Twist-3 distribution amplitudes of the pion and kaon are studied in this paper. We calculate the first several moments for the twist-3 distribution amplitudes ( and ) of the pion and kaon by applying the QCD sum rules. Our results show that (i) the first three moments of and the first two moments of and of the pion and kaon can be obtained with 30 uncertainty; (ii) the fourth moment of the and the second moment of the can be obtained when the uncertainty are relaxed to 35 ; (iii) the fourth moment of the can be obtained only when the uncertainty are relaxed to 40 ; (iv) we have and after including the -corrections to the perturbative part. These moments will be helpful for constructing the twist-3 wave functions of the pion and kaon.Received: 6 January 2005, Revised: 29 March 2005, Published online: 22 June 2005PACS: 13.20.He, 11.55.Hx     

Exclusive semileptonic rare decays $B \to K^{(*)} l^ + l^-$ in a SUSY SO(10) GUT

In the SUSY SO(10) GUT context, we study the exclusive processes . Using the Wilson coefficients of the relevant operators including the new operators which are induced by neutral Higgs boson (NHB) penguins, we evaluate some possible observables associated with these processes like the invariant mass spectrum (IMS), lepton pair forward-backward asymmetry (FBA), lepton polarization asymmetries etc. In this model the contributions from Wilson coefficients , among new contributions, are dominant. Our results show that the NHB effects are sensitive to the FBA, , and of decay, which are expected to be measured in B factories, the deviation of in can reach 0.1 from SM, which could be seen in B factories, and the average of the normal polarization can reach several percent for and it is 0.05 or so for , which could be measured in the future super B factories and provide useful information to probe new physics and discriminate different models.Received: 30 October 2004, Published online: 9 March 2005     

Tachyonic cyclotron radiation

We study superluminal cyclotron emission by electrons and muons in semiclassical orbits. The tachyonic line spectra of hydrogenic ions such as , , and , as well as their muonic counterparts , and are calculated, in particular the tachyonic power transversally and longitudinally radiated, the total intensity, and the power radiated in the individual harmonics. We also investigate tachyonic continuum radiation from electrons and protons cycling in the surface and light cylinder fields of -ray and millisecond pulsars, such as the Crab pulsar, PSR B1509-58, and PSR J0218 + 4232. The superluminal spectral densities generated by non-relativistic, mildly relativistic and ultra-relativistic source particles are derived. We study the parameters determining the global shape of the transversal and longitudinal densities and the energy scales of the broadband spectrum. The observed cutoff frequency in the -ray band of the pulsars is used to infer the upper edge of the orbital energy, and we conclude that electrons and nuclei cycling in the surface fields can reach energies beyond the "ankle" of the cosmic ray spectrum. This suggests -ray pulsars as sources of ultra-high energy cosmic rays. Arrival of the final proofs: 17 November 2005 PACS: 41.60.Ap, 11.10.Lm, 36.10.Dr, 98.70.Sa     

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 .     

Measurement of charm fragmentation ratios and fractionsin photoproduction at HERA

The production of , D⁰, D ⁺ , D_s ⁺ and charm hadrons and their antiparticles in e p scattering at HERA was measured with the ZEUS detector using an integrated luminosity of . The measurement has been performed in the photoproduction regime with the exchanged-photon virtuality and for photon-proton centre-of-mass energies in the range . The charm hadrons were reconstructed in the range of transverse momentum and pseudorapidity . The production cross sections were used to determine the ratio of neutral and charged D-meson production rates, , the strangeness-suppression factor, , and the fraction of charged D mesons produced in a vector state, . The measured and values agree with those obtained in deep inelastic scattering and in e ⁺ e^- annihilations. The measured value is smaller than, but consistent with, the previous measurements. The fractions of c quarks hadronising as a particular charm hadron, , were derived in the given kinematic range. The measured open-charm fragmentation fractions are consistent with previous results, although the measured is smaller and is larger than those obtained in e ⁺ e^- annihilations. These results generally support the hypothesis that fragmentation proceeds independently of the hard sub-process. Received: 12 August 2005, Revised: 8 September 2005, Published online: 6 October 2005     

Measurement of inclusive jet cross sections in photoproduction at HERA

Inclusive jet cross sections are measured in photoproduction at HERA using the H1 detector. The data sample of events in the kinematic range of photon virtualities and photon-proton centre-of-mass energies represents an integrated luminosity of . Jets are defined using the inclusive algorithm. Single- and multi-differential cross sections are measured as functions of jet transverse energy E_T ^jet and pseudorapidity in the domain and . The cross sections are found to be in good agreement with next-to-leading order perturbative QCD calculations corrected for fragmentation and underlying event effects. The cross section differential in E_T ^jet, which varies by six orders of magnitude over the measured range, is compared with similar distributions from colliders at equal and higher energies.Received: 24 February 2003, Revised: 26 May 2003, Published online: 11 July 2003     

Production properties of K^\star(892)^\pm vector mesons and their spin alignment as measured in the NOMAD experiment

First measurements of mesons production properties and their spin alignment in charged current (CC) and neutral current (NC) interactions are presented. The analysis of the full data sample of the NOMAD experiment is performed in different kinematic regions. For and mesons produced in CC interactions and decaying into we have found the following yields per event: and respectively, while for the and mesons produced in interactions the corresponding yields per event are: and . The results obtained for the parameter, and for and produced in CC interactions, are compared to theoretical predictions tuned on LEP measurements in annihilation at the pole. For mesons produced in interactions the measured parameter is . PACS 13.15.+g, 13.60.Le, 13.87.Fh, 13.88.+e, 14.40.Ev     

Flavour-independent h<Superscript>0</Superscript>A<Superscript>0</Superscript> search and two Higgs doublet model interpretation of neutral Higgs boson searches at LEP

Upper limits on the cross-section of the pair-production process , assuming 100 branching fraction to hadrons, are derived from a new search for the hadrons final state, independently of the hadronic flavour of the decay products. This study, combined with previously published searches for the neutral Higgs bosons h⁰ and A⁰, is used to constrain the Type II Two Higgs Doublet Model (2HDM(II)) with no CP violation in the Higgs sector and no additional non-Standard Model particles besides the five Higgs bosons. The analysis combines LEP1 and LEP2 data collected with the OPAL detector up to the highest available centre-of-mass energies. The searches are sensitive to the and decay modes of the Higgs bosons. A benchmark scan of the 2HDM(II) parameter space is performed. Large regions of the 2HDM(II) parameter space explored are excluded at the 95% CL in the ( and planes, using both direct neutral Higgs boson searches and indirect limits derived from Standard Model high precision measurements. The region GeV and GeV is excluded at 95 % CL, independently of and for selected values of which are representative of a complete -scan.Received: 28 July 2004, Revised: 4 January 2005, Published online: 3 March 2005     

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.     

Three Classes of Orthomodular Lattices

Let denote the class of all orthomodular lattices and denote the class of those that are commutator-finite. Also, let denote the class of orthomodular lattices that satisfy the block extension property, those that satisfy the weak block extension property, and those that are locally finite. We show that the following strict containments hold: Dedicated to the memory of Günter Bruns.     

ATLAS sensitivity to top quark and W boson polarizationin $t\bar{t}$ events

The inelastic production of mesons in ep collisions has been studied with the ZEUS detector at HERA using an integrated luminosity of . The mesons were identified using the decay channel . The measurements were performed in the kinematic range , , 0.2 < z < 0.9 and , where Q² is the virtuality of the exchanged photon, W is the photon-proton centre-of-mass energy, z is the fraction of the photon energy carried by the meson in the proton rest frame and is the rapidity of the in the laboratory frame. The measured cross sections are compared to theoretical predictions within the non-relativistic QCD framework including colour-singlet and colour-octet contributions, as well as to predictions based on the k_T-factorisation approach. Calculations of the colour-singlet process generally agree with the data, whereas inclusion of colour-octet terms spoils this agreement.Received: 18 May 2005, Revised: 24 June 2005, Published online: 27 July 2005     

Search for lepton-flavor violation at HERA

A search for lepton-flavor-violating interactions and has been performed with the ZEUS detector using the entire HERA I data sample, corresponding to an integrated luminosity of . The data were taken at center-of-mass energies, , of 300 and . No evidence of lepton-flavor violation was found, and constraints were derived on leptoquarks (LQs) that could mediate such interactions. For LQ masses below , limits were set on , where is the coupling of the LQ to an electron and a first-generation quark q₁, and is the branching ratio of the LQ to the final-state lepton (μ or ) and a quark q. For LQ masses much larger than , limits were set on the four-fermion interaction term for LQs that couple to an electron and a quark and to a lepton and a quark , where and are quark generation indices. Some of the limits are also applicable to lepton-flavor-violating processes mediated by squarks in R-Parity-violating supersymmetric models. In some cases, especially when a higher-generation quark is involved and for the process , the ZEUS limits are the most stringent to date. Received: 1 April 2005, Revised: 13 July 2005, Published online: 18 October 2005     

Preferred Invariant Symplectic Connections on Compact Coadjoint Orbits

Let be the Haag--Kastler net generated by the (2) chiral current algebra at level 1. We classify the SL(2, )-covariant subsystems by showing that they are all fixed points nets ^H for some subgroup H of the gauge automorphisms group SO(3) of . Then, using the fact that the net ₁ generated by the (1) chiral current can be regarded as a subsystem of , we classify the subsystems of ₁. In this case, there are two distinct proper subsystems: the one generated by the energy-momentum tensor and the gauge invariant subsystem .     

Probing the light neutral Higgs boson scenario of the <Emphasis Type="Italic">CP</Emphasis>-violating MSSM Higgs sector at the LHC

In the CP-violating minimal supersymmetric standard model (MSSM), for certain values of the CP-violating phases associated to the universal trilinear couplings (A_t, A_b) and the gluino mass , e.g., or , for GeV and -5, the lightest Higgs boson mass ( ) is GeV. This mass interval is still allowed by results of standard LEP Higgs searches because of a strongly suppressed H₁ZZ coupling. However, in the same region of parameter space in which these two conditions occur, the coupling is enhanced because the two mentioned sets of couplings satisfy a sum rule. In this paper we probe such a light Higgs scenario at the Large Hadron Collider (LHC) by studying associate production, leading to a signal. We show that the latter is readily accessible at the CERN hadron collider, upon the application of suitable selection cuts against the standard model (SM) backgrounds. Our parton level Monte Carlo (MC) analysis yields -45 signal events, completely free of SM background, for - 30 fb^-1 of accumulated luminosity, after taking into account the overall efficiency for tagging four b-jets.Received: 21 February 2005, Published online: 6 July 2005     

Remarks on the Balance Relations for the Two-Dimensional Navier–Stokes Equation with Random Forcing

We use the balance relations for the stationary in time solutions of the randomly forced 2D Navier-Stokes equations, found in [10], to study these solutions further. We show that the vorticity ξ(t,x) of a stationary solution has a finite exponential moment, and that for any the expectation of the integral of over the level-set , up to a constant factor equals the expectation of the integral of over the same set.