Singularities of improper affine spheres and surfaces of constant Gaussian curvature

We study the equation for improper (parabolic) affine spheres from the view point of contact geometry and provide the generic classification of singularities appearing in geometric solutions to the equation as well as their duals. We also show the results for surfaces of constant Gaussian curvatureand for developable surfaces. In particular we confirm that generic singularities appearing in such a surface are just cuspidal edges and swallowtails.Comment: 20 pages, 1 figure

Classification of phase singularities for complex scalar waves

Motivated by the importance and universal character of phase singularities which are clarified recently, we study the local structure of equi-phase loci near the dislocation locus of complex valued planar and spatial waves, from the viewpoint of singularity theory of differentiable mappings, initiated by H. Whitney and R. Thom. The classification of phase-singularities are reduced to the classification of planar curves by radial transformations due to the theory of A. du Plessis, T. Gaffney, and L. Wilson. Then fold singularities are classified into hyperbolic and elliptic singularities. We show that the elliptic singularities are never realized by any Helmholtz waves, while the hyperbolic singularities are realized in fact. Moreover, the classification and realizability of Whitney's cusp, as well as its bifurcation problem are considered in order to explain the three points bifurcation of phase singularities. In this paper, we treat the dislocation of linear waves mainly, developing the basic and universal method, the method of jets and transversality, which is applicable also to non-linear waves.Comment: 17 pages, 5 figure

Infinitesimal deformations and stabilities of singular Lugendre submanifolds

We give the characterization of Arnol'd-Mather type for stable singular Legendre immersions. The most building block of the theory is providing a module structure on the space of infinitesimal integral deformations by means of the notion of natural liftings of differential systems and of contact Hamiltonian vector fields

Observation of Two Resonant Structures in e+e- to pi+ pi- psi(2S) via Initial State Radiation at Belle

The cross section for e+e- to pi+ pi- psi(2S) between threshold and \sqrt{s}=5.5 GeV is measured using 673 fb^{-1} of data on and off the \Upsilon(4S) resonance collected with the Belle detector at KEKB. Two resonant structures are observed in the pi+ pi- psi(2S) invariant mass distribution, one at 4361\pm 9\pm 9 MeV/c2 with a width of 74\pm 15\pm 10 MeV/c2, and another at 4664\pm 11\pm 5 MeV/c2 with a width of 48\pm 15\pm 3 MeV/c2, if the mass spectrum is parameterized with the coherent sum of two Breit-Wigner functions. These values do not match those of any of the known charmonium states.Comment: 10 pages, 5 figures, 2 tables, version to appear in Phys. Rev. Let

Search for Resonant B±→K±h→K±γγB^{\pm}\to K^{\pm} h \to K^{\pm} \gamma \gamma Decays at Belle

We report measurements and searches for resonant $B^{\pm} \to K^{\pm} h \to K^{\pm} \gamma \gamma$ decays where $h$ is a $\eta,\eta^{\prime},\eta_{c},\eta_{c}(2S),\chi_{c0},\chi_{c2},J/\psi$ meson or the X(3872) particle.Comment: accepted by Physics Letters

Time-Dependent CP Asymmetries in B0 -> Ks pi0 gamma transitions

We report measurements of CP violation parameters in B0->Ks pi0 gamma transitions based on a data sample of 535x10^6 BB pairs collected with the Belle detector at the KEKB asymmetric-energy e+ e- collider. One neutral B meson is fully reconstructed in the B0->Ks pi0 gamma mode. The flavor of the accompanying B meson is identified from its decay products. For a Ks pi0 invariant mass up to 1.8 GeV/c^2, we obtain S = -0.10 +- 0.31 +- 0.07 and A = -0.20 +- 0.20 +- 0.06. For a Ks pi0 invariant mass near the K*0(892) resonance, we obtain S = -0.32 +0.36-0.33 +-0.05 and A=-0.20 +-0.24 +-0.05.Comment: 6 pages, 3 figures, accepted by PR

Study of J/psi to p pbar, Lambda Lambdabar and observation of eta_c to Lambda Lambdabar at Belle

We study the baryonic charmonium decays of B mesons, B+ to etac K+ and B+ to J/psi K+, where the etac and J/psi subsequently decay into a p pbar or Lambda Lambdabar pair. We measure the J/psi to p pbar, Lambda Lambdabar anisotropy parameters, alpha_B = -0.60 +- 0.13 +-0.14 (p pbar), -0.44 +- 0.51 +- 0.31 (Lambda Lambdabar) and compare to results from e+e- to J/psi formation experiments. We also report the first observation of etac to Lambda Lambdabar. The measured branching fraction is B(etac to Lambda Lambdabar) = (0.87 +0.24 -0.21(stat) +0.09 -0.14(syst) +- 0.27 (PDG)) x 10^-3. This study is based on a 357 fb^-1 data sample recorded on the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider.Comment: 8 pages, two figures (4 figure files), an update of hep-ex/0509020 for journal submissio

Spectra of prompt electrons from decays of B+ and B0 mesons and ratio of inclusive semielectronic branching fractions

We present spectra of prompt electrons from decays of neutral and charged B mesons. The results are based on 140 /fb of data collected by the Belle detector on the Upsilon(4S) resonance at the KEKB e+e- asymmetric collider. We tag Upsilon(4S) -> B \bar{B} events by reconstructing a B meson in one of several hadronic decay modes; the semileptonic decay of the other B meson is inferred from the presence of an identified electron. We obtain for charged and neutral B mesons the partial rates of semileptonic decay, to electrons with momentum greater than 0.6 GeV/c in the B rest frame, and their ratio b_+/b_0 = 1.08 +- 0.05 +- 0.02, where the first and second errors are statistical and systematic, respectively.Comment: 16 pages, 2 figure files, submitted to Phys. Lett.

Observation of B0ˉ\bar{B^0} -> DsJ*(2317)+ K- decay

The decays $\bar{B^0} \to D_{sJ}^+ K^-$ and $\bar{B^0} \to D_{sJ}^- \pi^+$ are studied for the first time. A significant signal is observed in the $\bar{B^0} \to D_{sJ}^*(2317)^+ K^-$ decay channel with ${\cal B}(\bar{B^0} \to D_{sJ}^*(2317)^+ K^-) \times {\cal B} (D_{sJ}^*(2317)^+ \to D_s^+ \pi^0) = (5.3^{+1.5}_{-1.3} \pm 0.7 \pm 1.4) \times 10^{-5}$. No signals are observed in the $\bar{B^0} \to D_{sJ}^*(2317)^- \pi^+$, $\bar{B^0} \to D_{sJ}(2460)^+ K^-$ and $\bar{B^0} \to D_{sJ}(2460)^- \pi^+$ decay modes, and upper limits are obtained. The analysis is based on a dataset of 140 fb$^{-1}$ collected by the Belle experiment at the asymmetric $e^+ e^-$ collider KEKB.Comment: 9 pages, 2 figures, submitted to PR

Study of time-dependent CP violation in B0 -> J/Psi pi0 decays

We report a measurement of CP asymmetry parameters in the decay B0(B0bar) -> J/Psi pi0, which is governed by the b->c cbar d transition. The analysis is based on a 140/fb data sample accumulated at the Upsilon(4S) resonance by the belle detector at the KEKB asymmetric-energy e+e- collider. We fully reconstruct one neutral B meson in the J/Psi pi0 final state. The accompanying B meson flavor is identified by its decay products. From the distribution of proper time intervals between the two B decays, we obtain the following CP-violating parameters: S_{J/Psi pi0}=-0.72+-0.42+-0.09 and A_{J/Psi pi0}=-0.01 +-0.29+-0.03.Comment: 5 pages, 2 figures, submitted to PR