Quantum Collapse of a Small Dust Shell

The full quantum mechanical collapse of a small relativistic dust shell is studied analytically, asymptotically and numerically starting from the exact finite dimensional classical reduced Hamiltonian recently derived by H\'aj{\'\i}\v{c}ek and Kucha\v{r}. The formulation of the quantum mechanics encounters two problems. The first is the multivalued nature of the Hamiltonian and the second is the construction of an appropriate self adjoint momentum operator in the space of the shell motion which is confined to a half line. The first problem is solved by identifying and neglecting orbits of small action in order to obtain a single valued Hamiltonian. The second problem is solved by introducing an appropriate lapse function. The resulting quantum mechanics is then studied by means of analytical and numerical techniques. We find that the region of total collapse has very small probability. We also find that the solution concentrates around the classical Schwarzschild radius. The present work obtains from first principles a quantum mechanics for the shell and provides numerical solutions, whose behavior is explained by a detailed WKB analysis for a wide class of collapsing shells.Comment: 23 pages, 8 figures, Revtex4 fil

Lattice vortices induced by noncommutativity

We show that the Moyal *-product on the algebra of fields induces an effective lattice structure on vortex dynamics which can be explicitly constructed using recent asymptotic results.Comment: 11 PAGES, 0 FIGURE

From nonassociativity to solutions of the KP hierarchy

A recently observed relation between 'weakly nonassociative' algebras A (for which the associator (A,A^2,A) vanishes) and the KP hierarchy (with dependent variable in the middle nucleus A' of A) is recalled. For any such algebra there is a nonassociative hierarchy of ODEs, the solutions of which determine solutions of the KP hierarchy. In a special case, and with A' a matrix algebra, this becomes a matrix Riccati hierarchy which is easily solved. The matrix solution then leads to solutions of the scalar KP hierarchy. We discuss some classes of solutions obtained in this way.Comment: 7 pages, 4 figures, International Colloquium 'Integrable Systems and Quantum Symmetries', Prague, 15-17 June 200

Measurement of CP observables in B± → D(⁎)K± and B± → D(⁎)π± decays

Measurements of CP observables in B ± →D (⁎) K ± and B ± →D (⁎) π ± decays are presented, where D (⁎) indicates a neutral D or D ⁎ meson that is an admixture of D (⁎)0 and D¯ (⁎)0 states. Decays of the D ⁎ meson to the Dπ 0 and Dγ final states are partially reconstructed without inclusion of the neutral pion or photon, resulting in distinctive shapes in the B candidate invariant mass distribution. Decays of the D meson are fully reconstructed in the K ± π ∓ , K + K − and π + π − final states. The analysis uses a sample of charged B mesons produced in pp collisions collected by the LHCb experiment, corresponding to an integrated luminosity of 2.0, 1.0 and 2.0 fb −1 taken at centre-of-mass energies of s=7, 8 and 13 TeV, respectively. The study of B ± →D ⁎ K ± and B ± →D ⁎ π ± decays using a partial reconstruction method is the first of its kind, while the measurement of B ± →DK ± and B ± →Dπ ± decays is an update of previous LHCb measurements. The B ± →DK ± results are the most precise to date

First observation of forward Z→bbˉZ \rightarrow b \bar{b} production in pppp collisions at s=8\sqrt{s}=8 TeV

The decay Z→bb¯ is reconstructed in pp collision data, corresponding to 2 fb −1 of integrated luminosity, collected by the LHCb experiment at a centre-of-mass energy of s=8 TeV. The product of the Z production cross-section and the Z→bb¯ branching fraction is measured for candidates in the fiducial region defined by two particle-level b -quark jets with pseudorapidities in the range 2.220 GeV and dijet invariant mass in the range 4520$GeV and dijet invariant mass in the range$45 < m_{jj} < 165$GeV. From a signal yield of$5462 \pm 763$$Z \rightarrow b \bar{b}$events, where the uncertainty is statistical, a production cross-section times branching fraction of$332 \pm 46 \pm 59$pb is obtained, where the first uncertainty is statistical and the second systematic. The measured significance of the signal yield is 6.0 standard deviations. This measurement represents the first observation of the$Z \rightarrow b \bar{b}$production in the forward region of$pp$ collisions

Study of the lineshape of the chi(c1) (3872) state

A study of the lineshape of the chi(c1) (3872) state is made using a data sample corresponding to an integrated luminosity of 3 fb(-1) collected in pp collisions at center-of-mass energies of 7 and 8 TeV with the LHCb detector. Candidate chi(c1)(3872) and psi(2S) mesons from b-hadron decays are selected in the J/psi pi(+)pi(-) decay mode. Describing the lineshape with a Breit-Wigner function, the mass splitting between the chi(c1 )(3872) and psi(2S) states, Delta m, and the width of the chi(c1 )(3872) state, Gamma(Bw), are determined to be (Delta m=185.598 +/- 0.067 +/- 0.068 Mev,)(Gamma BW=1.39 +/- 0.24 +/- 0.10 Mev,) where the first uncertainty is statistical and the second systematic. Using a Flatte-inspired model, the mode and full width at half maximum of the lineshape are determined to be (mode=3871.69+0.00+0.05 MeV.)(FWHM=0.22-0.04+0.13+0.07+0.11-0.06-0.13 MeV, ) An investigation of the analytic structure of the Flatte amplitude reveals a pole structure, which is compatible with a quasibound D-0(D) over bar*(0) state but a quasivirtual state is still allowed at the level of 2 standard deviations

Rogue edge waves in the ocean

Theoretically possible rogue edge wave are studied over cylindrical bottom in the framework of nonlinear shallow water equations in a weakly nonlinear limit. The nonlinear mechanisms (nonlinear dispersion enhancement, modulation instability and multimodal interactions) of possible anomalous edge wave appearance are analyzed