Geometry of contours and Peierls estimates in d=1 Ising models

Following Fr\"ohlich and Spencer, we study one dimensional Ising spin systems with ferromagnetic, long range interactions which decay as $|x-y|^{-2+\alpha}$, $0\leq \alpha\leq 1/2$. We introduce a geometric description of the spin configurations in terms of triangles which play the role of contours and for which we establish Peierls bounds. This in particular yields a direct proof of the well known result by Dyson about phase transitions at low temperatures.Comment: 28 pages, 3 figure

Cyclic cycle systems of the complete multipartite graph

In this paper, we study the existence problem for cyclic $\ell$-cycle decompositions of the graph $K_m[n]$, the complete multipartite graph with $m$ parts of size $n$, and give necessary and sufficient conditions for their existence in the case that $2\ell \mid (m-1)n$

Integrable semi-discretization of the coupled nonlinear Schr\"{o}dinger equations

A system of semi-discrete coupled nonlinear Schr\"{o}dinger equations is studied. To show the complete integrability of the model with multiple components, we extend the discrete version of the inverse scattering method for the single-component discrete nonlinear Schr\"{o}dinger equation proposed by Ablowitz and Ladik. By means of the extension, the initial-value problem of the model is solved. Further, the integrals of motion and the soliton solutions are constructed within the framework of the extension of the inverse scattering method.Comment: 27 pages, LaTeX2e (IOP style

Study of the Decay phi --> eta pi0 gamma with the KLOE detector

In a sample of 5.3x10^7 phi-decays observed with the KLOE detector at the Frascati phi-factory Dafne we find 605 eta pi0 gamma events with eta --> gamma\gamma and 197 eta pi0 gamma events with eta --> pi+ pi- pi0. The decay phi --> eta pi0 gamma is dominated by the process phi --> a0 gamma. From a fit to the eta pi0 mass spectrum we find BR(phi --> ao(980) gamma)= (7.4 +- 0.7)x10^-5.Comment: 12 pages, 6 figures, submitted to Phys.Lett.

Measurement of the branching fraction for the decay KS --> pi e nu

We present a measurement of the branching ratio BR(KS --> pi e nu) performed using the KLOE detector. KS mesons are produced in the reaction e+ e- --> phi --> KS KL at the DAFNE collider. In a sample of about 5 million KS-tagged events we find 624 +- 30 semileptonic KS decays. Normalizing to the KS --> pi+ pi- count in the same data sample, we obtain BR(KS --> pi e nu) = (6.91 +- 0.37) 10^-4, in agreement with the Standard Model expectation.Comment: 9 pages, 5 Encapsulated Postscript figures. Submitted to Phys. Lett.

Measuring the hadronic cross section via radiative return

Recently it has been demonstrated that particle factories, such as DAPHNE and PEP-II, operating at fixed center-of-mass energies, are able to measure hadronic cross sections as a function of the hadronic system energy using the raditive return. This paper is an experimental overview of the progress in this aera. Preliminary results from KLOE for the process e+e- -> \rho \gamma -> \pi+\pi-\gamma and a fit to the pion form factor are presented. Some first results from the BABAR collaboration are also shown.Comment: Invited talk presented at RADCOR/Loops and Legs 2002, Kloster Banz/Germany, September 8-13 2002, 6 pages, 2 Figures; v1: references added, typos correcte

Measurement of hadronic cross section and preliminary results on the pion form factor using the radiative return at DAPHNE

In the fixed energy environment of the $e^{+}e^{-}$ collider DA$\Phi$NE, KLOE can measure the cross section of the process $e^{+}e^{-} \to$ hadrons as a function of the hadronic system energy using the radiative return. At energies below 1 GeV, $e^{+}e^{-} \to \rho \to \pi^{+}\pi^{-}$ is the dominating hadronic process. We report here on the status of the analysis for the e^{+}e^{-} \to \ppg channel, which allows to obtain a preliminary measurement of the pion form factor using an integrated luminosity of $\sim73 pb^{-1}$.Comment: Invited talk at the Seventh International Workshop on Tau Lepton Physics (TAU02-WE07), Santa Cruz, Ca, USA, Sept 2002, 9 pages, LaTeX, 9 eps figure

Measurement of the Branching Fraction of the Decay B+→π+π−ℓ+νℓ\boldsymbol{B^{+}\to\pi^{+}\pi^{-}\ell^{+}\nu_\ell} in Fully Reconstructed Events at Belle

We present an analysis of the exclusive $B^{+}\to\pi^{+}\pi^{-}\ell^{+}\nu_{\ell}$ decay, where $\ell$ represents an electron or a muon, with the assumption of charge-conjugation symmetry and lepton universality. The analysis uses the full $\Upsilon(4S)$ data sample collected by the Belle detector, corresponding to 711 fb$^{-1}$ of integrated luminosity. We select the events by fully reconstructing one $B$ meson in hadronic decay modes, subsequently determining the properties of the other $B$ meson. We extract the signal yields using a binned maximum-likelihood fit to the missing-mass squared distribution in bins of the invariant mass of the two pions or the momentum transfer squared. We measure a total branching fraction of ${{\cal B}(B^{+}\to \pi^{+}\pi^{-}\ell^{+}\nu_{\ell})= [22.7 ^{+1.9}_{-1.6} (\mathrm{stat}) \pm 3.5(\mathrm{syst}) ]\times 10^{-5}}$, where the uncertainties are statistical and systematic, respectively. This result is the first reported measurement of this decay.Comment: 23 pages, 19 figure

Integrable discretizations of derivative nonlinear Schroedinger equations

We propose integrable discretizations of derivative nonlinear Schroedinger (DNLS) equations such as the Kaup-Newell equation, the Chen-Lee-Liu equation and the Gerdjikov-Ivanov equation by constructing Lax pairs. The discrete DNLS systems admit the reduction of complex conjugation between two dependent variables and possess bi-Hamiltonian structure. Through transformations of variables and reductions, we obtain novel integrable discretizations of the nonlinear Schroedinger (NLS), modified KdV (mKdV), mixed NLS, matrix NLS, matrix KdV, matrix mKdV, coupled NLS, coupled Hirota, coupled Sasa-Satsuma and Burgers equations. We also discuss integrable discretizations of the sine-Gordon equation, the massive Thirring model and their generalizations.Comment: 24 pages, LaTeX2e (IOP style), final versio