CP Violation in Fourth Generation Quark Decays

We show that, if a fourth generation is discovered at the Tevatron or LHC, one could study CP violation in b' \to s decays. Asymmetries could reach 30% for b'\to sZ for m_{b'} \lesssim 350 GeV, while it could be greater than 50% for b'\to s\gamma and extend to higher m_{b'}. Branching ratios are 10^{-3}--10^{-5}, and CPV measurement requires tagging. Once measured, however, the CPV phase can be extracted with little theoretical uncertainty.Comment: 4 pages, 7 eps figure

Pathways to Rare Baryonic B Decays

We point out new ways to search for charmless baryonic B decays: baryon pair production in association with $\eta^\prime$ is very likely as large as or even a bit larger than two body $K\pi/\pi\pi$ modes. We extend our argument, in weaker form, to $B\to \gamma + X_s$ and $\ell\nu +X$. Although calculations are not reliable, estimates give branching ratios of order $10^{-5}$--$10^{-6}$, where confidence is gained from recent experimental finding that $B \to D^{*} p \bar n$, $D^{*} p \bar p \pi$ are not far below $D^*\pi$ and $D^*\rho$ rates. Observation of charmless baryon modes would help clarify the dynamics of weak decays to baryonic final states, while the self-analyzing prowess of the $\Lambda$-baryon can be helpful in CP- and T-violation studies.Comment: 12 pages, REVTEX, 3 eps figures include

A Quasi-Exactly Solvable N-Body Problem with the sl(N+1) Algebraic Structure

Starting from a one-particle quasi-exactly solvable system, which is characterized by an intrinsic sl(2) algebraic structure and the energy-reflection symmetry, we construct a daughter N-body Hamiltonian presenting a deformation of the Calogero model. The features of this Hamiltonian are (i) it reduces to a quadratic combination of the generators of sl(N+1); (ii) the interaction potential contains two-body terms and interaction with the force center at the origin; (iii) for quantized values of a certain cohomology parameter n it is quasi-exactly solvable, the multiplicity of states in the algebraic sector is (N+n)!/(N!n!); (iv) the energy-reflection symmetry of the parent system is preserved.Comment: Latex, 12 page

Flavor-Changing Top Quark Rare Decays in the Littlest Higgs Model with T-Parity

We analyze the rare and flavor changing decay of the top quark into a charm quark and a gauge boson in the littlest Higgs model with T-parity (LHT). We calculate the one-loop level contributions from the T-parity odd mirror quarks and gauge bosons. We find that the decay $t\to c V, (V=g,\gamma,Z)$ in the LHT model can be significantly enhanced relative to those in the Standard Model. Our numerical results show that the top quark FCNC decay can be as large as $Br(t\to cg)\sim 10^{-2}$, $Br(t\to cZ)\sim 10^{-5}$ and $Br(t\to c\gamma)\sim 10^{-7}$ in the favorite parameter space in the LHT model.Comment: 12 pages, 3 figure

Measuring the Fourth Generation b --> s Quadrangle at the LHC

We show that simultaneous precision measurement of the CP-violating phase in time-dependent Bs --> J/psi phi study and the Bs --> mu+ mu- rate, together with measuring m_t' by direct search at the LHC, would determine V_{t's}^*V_{t'b} and therefore the b --> s quadrangle in the four-generation standard model. The forward-backward asymmetry in B --> K* l+ l- provides further discrimination.Comment: 6 pages, 7 figures, revised based on LHC results released in this summer, to appear in PR

Automatic Detection of Outliers in Multibeam Echo Sounding Data

The data volumes produced by new generation multibeam systems are very large, especially for shallow water systems. Results from recent multibeam surveys indicate that the ratio of the field survey time, to the time used in interactive editing through graphical editing tools, is about 1:1. An important reason for the large amount of processing time is that users subjectively decide which soundings are outliers. There is an apparent need for an automated approach for detecting outliers that would reduce the extensive labor and obtain consistent results from the multibeam data cleaning process, independent of the individual that has processed the data. The proposed automated algorithm for cleaning multibeam soundings was tested using the SAX-99 (Destin FL) multibeam survey data [2]. Eight days of survey data (6.9 Gigabyte) were cleaned in 2.5 hours on an SGI platform. A comparison of the automatically cleaned data with the subjective, interactively cleaned data indicates that the proposed method is, if not better, at least equivalent to interactive editing as used on the SAX-99 multibeam data. Furthermore, the ratio of acquisition to processing time is considerably improved since the time required for cleaning the data was decreased from 192 hours to 2.5 hours (an improvement by a factor of 77)

Tunable Fano-Kondo resonance in side-coupled double quantum dot system

We study the interference between the Fano and Kondo effects in a side-coupled double-quantum- dot system where one of the quantum dots couples to conduction electron bath while the other dot only side-couples to the first dot via antiferromagnetic (AF) spin exchange coupling. We apply both the perturbative renormalization group (RG) and numerical renormalization group (NRG) approaches to study the effect of AF coupling on the Fano lineshape in the conduction leads. With particle-hole symmetry, the AF exchange coupling competes with the Kondo effect and leads to a local spin-singlet ground state for arbitrary small coupling, so called "two-stage Kondo effect". As a result, via NRG we find the spectral properties of the Fano lineshape in the tunneling density of states (TDOS) of conduction electron leads shows double dip-peak features at the energy scale around the Kondo temperature and the one much below it, corresponding to the two-stage Kondo effect; it also shows an universal scaling behavior at very low energies. We find the qualitative agreement between the NRG and the perturbative RG approach. Relevance of our work to the experiments is discussed.Comment: 7 pages, 7 figure

On Singularity Formation of a Nonlinear Nonlocal System

We investigate the singularity formation of a nonlinear nonlocal system. This nonlocal system is a simplified one-dimensional system of the 3D model that was recently proposed by Hou and Lei in [13] for axisymmetric 3D incompressible Navier-Stokes equations with swirl. The main difference between the 3D model of Hou and Lei and the reformulated 3D Navier-Stokes equations is that the convection term is neglected in the 3D model. In the nonlocal system we consider in this paper, we replace the Riesz operator in the 3D model by the Hilbert transform. One of the main results of this paper is that we prove rigorously the finite time singularity formation of the nonlocal system for a large class of smooth initial data with finite energy. We also prove the global regularity for a class of smooth initial data. Numerical results will be presented to demonstrate the asymptotically self-similar blow-up of the solution. The blowup rate of the self-similar singularity of the nonlocal system is similar to that of the 3D model.Comment: 28 pages, 9 figure