B-physics: new states, rare decays and branching ratios in CDF

We present results and prospects for searches for rare B and D meson decays with final state dimuons, including B_s\to\mu\mu, B_d\to\mu\mu, and D\to\mu\mu. Upper limits on the branching fractions are compared to previous CDF measurements, recent results from the B factories and theoretical expectations. We also report on new measurements of production and decay properties of the X(3872) particle, discovered in 2003 by the Belle Collaboration. New results on the measurement of the relative branching fraction for the Cabibbo suppressed decay B^+\to J/\psi\pi^+ Br(B^+\to J/\psi\pi^+)/Br(B^+\to J/\psi K^+) are presented too. The presented results are based on the analyses of 70 to 220 pb^-1 of data collected by the CDF II detector in p\bar p collisions at \sqrt{s} = 1.96 GeV at Fermilab Tevatron.Comment: Presented at the 6th International Conference on Hyperons, Charm & Beauty Hadrons (BEACH04), Chicago, IL, June 27 - July 03 2004. 5 page

Chaotic Electron Motion in Superlattices. Quantum-Classical Correspondence of the Structure of Eigenstates and LDOS

We investigate the classical-quantum correspondence for particle motion in a superlattice in the form of a 2D channel with periodic modulated boundaries. Its classical dynamics undergoes the generic transition to chaos of Hamiltonian systems as the amplitude of the modulation is increased. We show that for strong chaotic motion, the classical counterpart of the structure of eigenstates (SES) in energy space reveals an excellent agreement with the quantum one. This correspondence allows us to understand important features of the SES in terms of classical trajectories. We also show that for typical 2D modulated waveguides there exist, at any energy range, extremely localized eigenstates (in energy) which are practically unperturbed by the modulation. These states contribute to the strong fluctuations around the classical SES. The approach to the classical limit is discussed.Comment: 4 pages, 4 figure

Track Extrapolation and Distribution for the CDF-II Trigger System

The CDF-II experiment is a multipurpose detector designed to study a wide range of processes observed in the high energy proton-antiproton collisions produced by the Fermilab Tevatron. With event rates greater than 1MHz, the CDF-II trigger system is crucial for selecting interesting events for subsequent analysis. This document provides an overview of the Track Extrapolation System (XTRP), a component of the CDF-II trigger system. The XTRP is a fully digital system that is utilized in the track-based selection of high momentum lepton and heavy flavor signatures. The design of the XTRP system includes five different custom boards utilizing discrete and FPGA technology residing in a single VME crate. We describe the design, construction, commissioning and operation of this system.Comment: 34 pages, 9 figures, submitted to Nucl.Inst.Meth.

Spherical CR Dehn Surgery

Consider a three dimensional cusped spherical $\mathrm{CR}$ manifold $M$ and suppose that the holonomy representation of $\pi_1(M)$ can be deformed in such a way that the peripheral holonomy is generated by a non-parabolic element. We prove that, in this case, there is a spherical $\mathrm{CR}$ structure on some Dehn surgeries of $M$. The result is very similar to R. Schwartz's spherical $\mathrm{CR}$ Dehn surgery theorem, but has weaker hypotheses and does not give the unifomizability of the structure. We apply our theorem in the case of the Deraux-Falbel structure on the Figure Eight knot complement and obtain spherical $\mathrm{CR}$ structures on all Dehn surgeries of slope $-3 + r$ for $r \in \mathbb{Q}^{+}$ small enough.Comment: 27 page

On-surface radiation condition for multiple scattering of waves

The formulation of the on-surface radiation condition (OSRC) is extended to handle wave scattering problems in the presence of multiple obstacles. The new multiple-OSRC simultaneously accounts for the outgoing behavior of the wave fields, as well as, the multiple wave reflections between the obstacles. Like boundary integral equations (BIE), this method leads to a reduction in dimensionality (from volume to surface) of the discretization region. However, as opposed to BIE, the proposed technique leads to boundary integral equations with smooth kernels. Hence, these Fredholm integral equations can be handled accurately and robustly with standard numerical approaches without the need to remove singularities. Moreover, under weak scattering conditions, this approach renders a convergent iterative method which bypasses the need to solve single scattering problems at each iteration. Inherited from the original OSRC, the proposed multiple-OSRC is generally a crude approximate method. If accuracy is not satisfactory, this approach may serve as a good initial guess or as an inexpensive pre-conditioner for Krylov iterative solutions of BIE

Recovery of the absorption coefficient in radiative transport from a single measurement

In this paper, we investigate the recovery of the absorption coefficient from boundary data assuming that the region of interest is illuminated at an initial time. We consider a sufficiently strong and isotropic, but otherwise unknown initial state of radiation. This work is part of an effort to reconstruct optical properties using unknown illumination embedded in the unknown medium. We break the problem into two steps. First, in a linear framework, we seek the simultaneous recovery of a forcing term of the form $\sigma(t,x,\theta) f(x)$ (with $\sigma$ known) and an isotropic initial condition $u_{0}(x)$ using the single measurement induced by these data. Based on exact boundary controllability, we derive a system of equations for the unknown terms $f$ and $u_{0}$. The system is shown to be Fredholm if $\sigma$ satisfies a certain positivity condition. We show that for generic term $\sigma$ and weakly absorbing media, this linear inverse problem is uniquely solvable with a stability estimate. In the second step, we use the stability results from the linear problem to address the nonlinearity in the recovery of a weak absorbing coefficient. We obtain a locally Lipschitz stability estimate

Asymptotic Expansion and the LG/(Fano, General Type) Correspondence

The celebrated LG/CY correspondence asserts that the Gromov-Witten theory of a Calabi-Yau (CY) hypersurface in weighted projective space is equivalent to its corresponding FJRW-theory (LG) via analytic continuation. It is well known that this correspondence fails in non-Calabi-Yau cases. The main obstruction is a collapsing or dimensional reduction of the state space of the Landau-Ginzburg model in the Fano case, and a similar collapsing of the state space of Gromov-Witten theory in the general type case. We state and prove a modified version of the cohomological correspondence that describes this collapsing phenomenon at the level of state spaces. This result confirms a physical conjecture of Witten-Hori-Vafa. The main purpose of this article is to provide a quantum explanation for the collapsing phenomenon. A key observation is that the corresponding Picard-Fuchs equation develops irregular singularities precisely at the points where the collapsing occurs. Our main idea is to replace analytic continuation with asymptotic expansion in this non-Calabi-Yau setting. The main result of this article is that the reduction in rank of the Gromov-Witten I-function due to power series asymptotic expansions matches precisely the dimensional reduction of the corresponding state space. Furthermore, asymptotic expansion under a different asymptotic sequence yields a different I-function which can be considered as the mathematical counterpart to the additional "massive vacua" of physics.Comment: 47 pages, 3 figure