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

Algebraic Reduction of Feynman Diagrams to Scalar Integrals: a Mathematica implementation of LERG-I

A Mathematica implementation of the program LERG-I is presented that performs the reduction of tensor integrals, encountered in one-loop Feynman diagram calculations, to scalar integrals. The program was originally coded in REDUCE and in that incarnation was applied to a number of problems of physical interest.Comment: 16 page

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

Noise-induced vortex reversal of self-propelled particles

We report an interesting phenomenon of noise-induced vortex reversal in a two-dimensional system of self-propelled particles (SPP) with soft-core interactions. With the aid of forward flux sampling, we analyze the configurations along the reversal pathway and thus identify the mechanism of vortex reversal. We find that statistically the reversal exhibits a hierarchical process: those particles at the periphery first change their motion directions, and then more inner layers of particles reverse later on. Furthermore, we calculate the dependence of the average reversal rate on noise intensity $D$ and the number $N$ of SPP. We find that the rate decreases exponentially with the reciprocal of $D$. Interestingly, the rate varies nonmonotonically with $N$ and a minimal rate exists for an intermediate value of $N$.Comment: 4 pages, 5 figure

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