Flavor and CP Violation with Fourth Generations Revisited

The Standard Model predicts a very small CP violation phase $\sin2\Phi^{\rm SM}_{B_s} \simeq -0.04$%= \arg M_{12} \simeq \arg\,(V^*_{ts}V_{tb})^2$in$B_s$--$\bar B_s$mixing.$\lambda^2\eta$. Any finite value of$\Phi_{B_s}$measured at the Tevatron would imply New Physics. With recent hints for finite$\sin2\Phi_{B_s}$, experiments at the Tevatron, we reconsider the possibility of a 4th generation. As recent direct search bounds have become considerably heavier than 300 GeV, we take the$t'$mass to be near the unitarity bound of 500 GeV. Combining the measured values of$\Delta m_{B_s}$with${\cal B}(B \to X_s\ell^+\ell^-)$, together with typical$f_{B_s}$values, we find a sizable$\sin2\Phi^{\rm SM4}_{B_s} \sim -0.33$. Using$m_{b'} = 480$GeV, we extract the range$0.06 < |V_{t'b}| < 0.13$from the constraints of$\Gamma(Z\to b\bar b)$,$\Delta m_{D}$and${\cal B}(K^+\to\pi^+\nu\bar\nu)$. A future measurement of${\cal B}(K_L\to\pi^0\nu\bar\nu)$will determine$V_{t'd}$.Comment: 8 pages, 11 figure

The observed spiral structure of the Milky Way

The spiral structure of the Milky Way is not yet well determined. The keys to understanding this structure are to increase the number of reliable spiral tracers and to determine their distances as accurately as possible. HII regions, giant molecular clouds (GMCs), and 6.7-GHz methanol masers are closely related to high mass star formation, and hence they are excellent spiral tracers. We update the catalogs of Galactic HII regions, GMCs, and 6.7-GHz methanol masers, and then outline the spiral structure of the Milky Way. We collected data for more than 2500 known HII regions, 1300 GMCs, and 900 6.7-GHz methanol masers. If the photometric or trigonometric distance was not yet available, we determined the kinematic distance using a Galaxy rotation curve with the current IAU standard, $R_0$ = 8.5 kpc and $\Theta_0$ = 220 km s$^{-1}$, and the most recent updated values of $R_0$ = 8.3 kpc and $\Theta_0$ = 239 km s$^{-1}$, after we modified the velocities of tracers with the adopted solar motions. With the weight factors based on the excitation parameters of HII regions or the masses of GMCs, we get the distributions of these spiral tracers. The distribution of tracers shows at least four segments of arms in the first Galactic quadrant, and three segments in the fourth quadrant. The Perseus Arm and the Local Arm are also delineated by many bright HII regions. The arm segments traced by massive star forming regions and GMCs are able to match the HI arms in the outer Galaxy. We found that the models of three-arm and four-arm logarithmic spirals are able to connect most spiral tracers. A model of polynomial-logarithmic spirals is also proposed, which not only delineates the tracer distribution, but also matches the observed tangential directions.Comment: 22 Pages, 16 Figures, 7 Tables, updated to match the published versio

Infinite Hopf family of elliptic algebras and bosonization

Elliptic current algebras E_{q,p}(\hat{g}) for arbitrary simply laced finite dimensional Lie algebra g are defined and their co-algebraic structures are studied. It is shown that under the Drinfeld like comultiplications, the algebra E_{q,p}(\hat{g}) is not co-closed for any g. However putting the algebras E_{q,p}(\hat{g}) with different deformation parameters together, we can establish a structure of infinite Hopf family of algebras. The level 1 bosonic realization for the algebra E_{q,p}(\hat{g}) is also established.Comment: LaTeX, 11 pages. This is the new and final versio

Robust pricing and hedging under trading restrictions and the emergence of local martingale models

We consider the pricing of derivatives in a setting with trading restrictions, but without any probabilistic assumptions on the underlying model, in discrete and continuous time. In particular, we assume that European put or call options are traded at certain maturities, and the forward price implied by these option prices may be strictly decreasing in time. In discrete time, when call options are traded, the short-selling restrictions ensure no arbitrage, and we show that classical duality holds between the smallest super-replication price and the supremum over expectations of the payoff over all supermartingale measures. More surprisingly in the case where the only vanilla options are put options, we show that there is a duality gap. Embedding the discrete time model into a continuous time setup, we make a connection with (strict) local-martingale models, and derive framework and results often seen in the literature on financial bubbles. This connection suggests a certain natural interpretation of many existing results in the literature on financial bubbles

A 3D Numerical Method for Studying Vortex Formation Behind a Moving Plate

In this paper, we introduce a three-dimensional numerical method for computing the wake behind a flat plate advancing perpendicular to the flow. Our numerical method is inspired by the panel method of J. Katz and A. Plotkin [J. Katz and A. Plotkin, Low-speed Aerodynamics, 2001] and the 2D vortex blob method of Krasny [R. Krasny, Lectures in Appl. Math., 28 (1991), pp. 385--402]. The accuracy of the method will be demonstrated by comparing the 3D computation at the center section of a very high aspect ratio plate with the corresponding two-dimensional computation. Furthermore, we compare the numerical results obtained by our 3D numerical method with the corresponding experimental results obtained recently by Ringuette [M. J. Ringuette, Ph.D. Thesis, 2004] in the towing tank. Our numerical results are shown to be in excellent agreement with the experimental results up to the so-called formation time

On the algebra A_{\hbar,\eta}(osp(2|2)^{(2)}) and free boson representations

A two-parameter quantum deformation of the affine Lie super algebra $osp(2|2)^{(2)}$ is introduced and studied in some detail. This algebra is the first example associated with nonsimply-laced and twisted root systems of a quantum current algebra with the structure of a so-called infinite Hopf family of (super)algebras. A representation of this algebra at $c=1$ is realized in the product Fock space of two commuting sets of Heisenberg algebras.Comment: 14 pages, LaTe