On the water-bag model of dispersionless KP hierarchy

We investigate the bi-Hamiltonian structure of the waterbag model of dKP for two component case. One can establish the third-order and first-order Hamiltonian operator associated with the waterbag model. Also, the dispersive corrections are discussed.Comment: 19 page

On a Camassa-Holm type equation with two dependent variables

We consider a generalization of the Camassa Holm (CH) equation with two dependent variables, called CH2, introduced by Liu and Zhang. We briefly provide an alternative derivation of it based on the theory of Hamiltonian structures on (the dual of) a Lie Algebra. The Lie Algebra here involved is the same algebra underlying the NLS hierarchy. We study the structural properties of the CH2 hierarchy within the bihamiltonian theory of integrable PDEs, and provide its Lax representation. Then we explicitly discuss how to construct classes of solutions, both of peakon and of algebro-geometrical type. We finally sketch the construction of a class of singular solutions, defined by setting to zero one of the two dependent variables.Comment: 22 pages, 2 figures. A few typos correcte

Involutive orbits of non-Noether symmetry groups

We consider set of functions on Poisson manifold related by continues one-parameter group of transformations. Class of vector fields that produce involutive families of functions is investigated and relationship between these vector fields and non-Noether symmetries of Hamiltonian dynamical systems is outlined. Theory is illustrated with sample models: modified Boussinesq system and Broer-Kaup system.Comment: LaTeX 2e, 10 pages, no figure

On negative flows of the AKNS hierarchy and a class of deformations of bihamiltonian structure of hydrodynamic type

A deformation parameter of a bihamiltonian structure of hydrodynamic type is shown to parameterize different extensions of the AKNS hierarchy to include negative flows. This construction establishes a purely algebraic link between, on the one hand, two realizations of the first negative flow of the AKNS model and, on the other, two-component generalizations of Camassa-Holm and Dym type equations. The two-component generalizations of Camassa-Holm and Dym type equations can be obtained from the negative order Hamiltonians constructed from the Lenard relations recursively applied on the Casimir of the first Poisson bracket of hydrodynamic type. The positive order Hamiltonians, which follow from Lenard scheme applied on the Casimir of the second Poisson bracket of hydrodynamic type, are shown to coincide with the Hamiltonians of the AKNS model. The AKNS Hamiltonians give rise to charges conserved with respect to equations of motion of two-component Camassa-Holm and two-component Dym type equations.Comment: 20 pages, Late

Measurement of B(Ds+ -->ell+ nu) and the Decay Constant fDs From 600/pb of e+e- Annihilation Data Near 4170 MeV

We examine e+e- --> Ds^-D_s^{*+} and Ds^{*-}Ds^{+} interactions at 4170 MeV using the CLEO-c detector in order to measure the decay constant fDs with good precision. Previously our measurements were substantially higher than the most precise lattice based QCD calculation of (241 +/- 3) MeV. Here we use the D_s^+ --> ell^+ nu channel, where the ell^+ designates either a mu^+ or a tau^+, when the tau^+ --> pi^+ anti-nu. Analyzing both modes independently, we determine B(D_s^+ --> mu^+ nu)= 0.565 +/- 0.045 +/- 0.017)%, and B(D_s^+ --> mu^+ nu)= (6.42 +/- 0.81 +/- 0.18)%. We also analyze them simultaneously to find an effective value of B^{eff}(D_s^+ --> mu^+ nu)= (0.591 +/- 0.037 +/- 0.018)% and fDs=(263.3 +/- 8.2 +/- 3.9) MeV. Combining with the CLEO-c value determined independently using D_s^+ --> tau^+ nu, tau^+ --> e^+ nu anti-nu decays, we extract fDs=(259.5 +/- 6.6 +/- 3.1) MeV. Combining with our previous determination of B(D^+ --> mu^+ nu), we extract the ratio fDs/fD+=1.26 +/- 0.06 +/- 0.02. No evidence is found for a CP asymmetry between Gamma(D_s^+ --> mu^+\nu) and \Gamma(D_s^- --> mu^- nu); specifically the fractional difference in rates is measured to be (4.8 +/- 6.1)%. Finally, we find B(D_s^+ --> e^+ nu) < 1.2x10^{-4} at 90% confidence level.Comment: 26 pages, 16 figure

Determination of the D0 -> K+pi- Relative Strong Phase Using Quantum-Correlated Measurements in e+e- -> D0 D0bar at CLEO

We exploit the quantum coherence between pair-produced D0 and D0bar in psi(3770) decays to study charm mixing, which is characterized by the parameters x and y, and to make a first determination of the relative strong phase \delta between doubly Cabibbo-suppressed D0 -> K+pi- and Cabibbo-favored D0bar -> K+pi-. We analyze a sample of 1.0 million D0D0bar pairs from 281 pb^-1 of e+e- collision data collected with the CLEO-c detector at E_cm = 3.77 GeV. By combining CLEO-c measurements with branching fraction input and time-integrated measurements of R_M = (x^2+y^2)/2 and R_{WS} = Gamma(D0 -> K+pi-)/Gamma(D0bar -> K+pi-) from other experiments, we find \cos\delta = 1.03 +0.31-0.17 +- 0.06, where the uncertainties are statistical and systematic, respectively. In addition, by further including external measurements of charm mixing parameters, we obtain an alternate measurement of \cos\delta = 1.10 +- 0.35 +- 0.07, as well as x\sin\delta = (4.4 +2.7-1.8 +- 2.9) x 10^-3 and \delta = 22 +11-12 +9-11 degrees.Comment: 37 pages, also available through http://www.lns.cornell.edu/public/CLNS/2007/. Incorporated referee's comment

Observation of Upsilon(2S) -> eta Upsilon(1S) and search for related transitions

We report the first observation of the transition Upsilon(2S) > eta Upsilon(1S), with branching fraction B=(2.1+0.7-0.6(stat.)+-0.3(syst.)) x 10^{-4} and statistical significance 5.3 sigma. Data were acquired with the CLEO detector at the CESR e+ e- symmetric collider. This is the first process observed involving a b-quark spin flip. Upper limits at 90% confidence level for related processes, in units of 10^{-4}, are B[Upsilon(2S) -> pi0 Upsilon(1S)] eta Upsilon(1S)] pi0 Upsilon(1S)] pi0 Upsilon(2S)] < 5.1.Comment: 9 pages, 2 figures, available through http://www.lns.cornell.edu/public/CLNS/, submitted to PRL. Revised systematic errors. Slightly shortened to conform to PRL line coun

Dalitz plot analysis of the D+ -> K- pi+ pi+ decay

We present a Dalitz plot analysis of the decay D+ -> K- pi+ pi+ based on 281 pb-1 of e+e- collision data produced at the psi(3770) by CESR and observed with the CLEO-c detector. We select 67086 candidate events with a small, ~1.1%, background for this analysis. When using a simple isobar model our results are consistent with the previous measurements done by E791. Since our sample is considerably larger we can explore alternative models. We find better agreement with data when we include an isospin-two pi+pi+ S-wave contribution. We apply a quasi model-independent partial wave analysis and measure the amplitude and phase of the K pi and pi+pi+ S waves in the range of invariant masses from the threshold to the maximum in this decay.Comment: 9 pages postscript,also available through http://www.lepp.cornell.edu/public/CONF/2007, Submitted to EPS/HEP2007: July 19-25, 2007, Manchester, Englan

Measurement of Charm Production Cross Sections in e+e- Annihilation at Energies between 3.97 and 4.26 GeV

Using the CLEO-c detector at the Cornell Electron Storage Ring, we have measured inclusive and exclusive cross sections for the production of D+, D0 and Ds+ mesons in e+e- annihilations at thirteen center-of-mass energies between 3.97 and 4.26 GeV. Exclusive cross sections are presented for final states consisting of two charm mesons (DD, D*D, D*D*, Ds+Ds-, Ds*+Ds-, and Ds*+Ds*-) and for processes in which the charm-meson pair is accompanied by a pion. No enhancement in any final state is observed at the energy of the Y(4260).Comment: 19 pages, postscript also available through http://www.lns.cornell.edu/public/CLNS/2007/, Submitted to PR

Search for Light CP-odd Higgs in Radiative Decays of Upsilon(1S)

We search for a non-SM-like CP-odd Higgs boson (a0_1) with m(a0_1)< 2m(b) in radiative decays of the Upsilon(1S), using 21.5M Upsilon(1S) mesons directly produced in e+e- annihilation. We investigate a0_1 --> tau+tau- and a0_1 --> mu+mu- decay channels. No significant signal is found. We obtain upper limits on the product of B(Upsilon(1S)-->gamma a0_1) and B(a0_1-->tau+tau-) or B(a0_1-->mu+mu-). Our tau+tau- results are almost two orders of magnitude more stringent than previous upper limits. Our data provide no evidence for a Higgs state with a mass of 214 MeV decaying to mu+mu-. Existence of such a state was previously proposed as an explanation for 3 Sigma+ --> p mu+mu- events, having mu+mu- masses just above the kinematic threshold, observed by the HyperCP experiment. Our results constrain NMSSM models.Comment: 12 pages, available through http://www.lns.cornell.edu/public/CLNS/, submitted to PR