Directed polymers in high dimensions

We study directed polymers subject to a quenched random potential in d transversal dimensions. This system is closely related to the Kardar-Parisi-Zhang equation of nonlinear stochastic growth. By a careful analysis of the perturbation theory we show that physical quantities develop singular behavior for d to 4. For example, the universal finite size amplitude of the free energy at the roughening transition is proportional to (4-d)^(1/2). This shows that the dimension d=4 plays a special role for this system and points towards d=4 as the upper critical dimension of the Kardar-Parisi-Zhang problem.Comment: 37 pages REVTEX including 4 PostScript figure

The resultant on compact Riemann surfaces

We introduce a notion of resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential theory and give explicit formulas for the algebraic dependence between two meromorphic functions on a compact Riemann surface. As a particular application, the exponential transform of a quadrature domain in the complex plane is expressed in terms of the resultant of two meromorphic functions on the Schottky double of the domain.Comment: 44 page

Gravitational quasinormal modes of AdS black branes in d spacetime dimensions

The AdS/CFT duality has established a mapping between quantities in the bulk AdS black-hole physics and observables in a boundary finite-temperature field theory. Such a relationship appears to be valid for an arbitrary number of spacetime dimensions, extrapolating the original formulations of Maldacena's correspondence. In the same sense properties like the hydrodynamic behavior of AdS black-hole fluctuations have been proved to be universal. We investigate in this work the complete quasinormal spectra of gravitational perturbations of $d$-dimensional plane-symmetric AdS black holes (black branes). Holographically the frequencies of the quasinormal modes correspond to the poles of two-point correlation functions of the field-theory stress-energy tensor. The important issue of the correct boundary condition to be imposed on the gauge-invariant perturbation fields at the AdS boundary is studied and elucidated in a fully $d$-dimensional context. We obtain the dispersion relations of the first few modes in the low-, intermediate- and high-wavenumber regimes. The sound-wave (shear-mode) behavior of scalar (vector)-type low-frequency quasinormal mode is analytically and numerically confirmed. These results are found employing both a power series method and a direct numerical integration scheme.Comment: added references, typos corrected, minor changes, final version for JHE

Determination of the Form Factors for the Decay B0 --> D*-l+nu_l and of the CKM Matrix Element |Vcb|

We present a combined measurement of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$ and of the parameters $\rho^2$, $R_1$, and $R_2$, which fully characterize the form factors of the $B^0 \to D^{*-}\ell^{+}\nu_\ell$ decay in the framework of HQET, based on a sample of about 52,800 $B^0 \to D^{*-}\ell^{+}\nu_\ell$ decays recorded by the BABAR detector. The kinematical information of the fully reconstructed decay is used to extract the following values for the parameters (where the first errors are statistical and the second systematic): $\rho^2 = 1.156 \pm 0.094 \pm 0.028$, $R_1 = 1.329 \pm 0.131 \pm 0.044$, $R_2 = 0.859 \pm 0.077 \pm 0.022$, $\mathcal{F}(1)|V_{cb}| = (35.03 \pm 0.39 \pm 1.15) \times 10^{-3}$. By combining these measurements with the previous BABAR measurements of the form factors which employs a different technique on a partial sample of the data, we improve the statistical accuracy of the measurement, obtaining: $\rho^2 = 1.179 \pm 0.048 \pm 0.028, R_1 = 1.417 \pm 0.061 \pm 0.044, R_2 = 0.836 \pm 0.037 \pm 0.022,$ and $\mathcal{F}(1)|V_{cb}| = (34.68 \pm 0.32 \pm 1.15) \times 10^{-3}.$ Using the lattice calculations for the axial form factor $\mathcal{F}(1)$, we extract $|V_{cb}| =(37.74 \pm 0.35 \pm 1.25 \pm ^{1.23}_{1.44}) \times 10^{-3}$, where the third error is due to the uncertainty in $\mathcal{F}(1)$

Study of the Exclusive Initial-State Radiation Production of the DDˉD \bar D System

A study of exclusive production of the $D \bar D$ system through initial-state r adiation is performed in a search for charmonium states, where $D=D^0$ or $D^+$. The $D^0$ mesons are reconstructed in the $D^0 \to K^- \pi^+$, $D^0 \to K^- \pi^+ \pi^0$, and $D^0 \to K^- \pi^+ \pi^+ \pi^-$ decay modes. The $D^+$ is reconstructed through the $D^+ \to K^- \pi^+ \pi^+$ decay mode. The analysis makes use of an integrated luminosity of 288.5 fb$^{-1}$ collected by the BaBar experiment. The $D \bar D$ mass spectrum shows a clear $\psi(3770)$ signal. Further structures appear in the 3.9 and 4.1 GeV/$c^2$ regions. No evidence is found for Y(4260) decays to $D \bar D$, implying an up per limit \frac{\BR(Y(4260)\to D \bar D)}{\BR(Y(4260)\to J/\psi \pi^+ \pi^-)} < 7.6 (95 % confidence level)

A search for the decay B+→K+ννˉB^+ \to K^+ \nu \bar{\nu}

We search for the rare flavor-changing neutral-current decay $B^+ \to K^+ \nu \bar{\nu}$ in a data sample of 82 fb$^{-1}$ collected with the {\sl BABAR} detector at the PEP-II B-factory. Signal events are selected by examining the properties of the system recoiling against either a reconstructed hadronic or semileptonic charged-B decay. Using these two independent samples we obtain a combined limit of ${\mathcal B}(B^+ \to K^+ \nu \bar{\nu})<5.2 \times 10^{-5}$ at the 90% confidence level. In addition, by selecting for pions rather than kaons, we obtain a limit of ${\mathcal B}(B^+ \to \pi^+ \nu \bar{\nu})<1.0 \times 10^{-4}$ using only the hadronic B reconstruction method.Comment: 7 pages, 8 postscript figures, submitted to Phys. Rev. Let

High-reflectivity broadband distributed Bragg reflector lattice matched to ZnTe

We report on the realization of a high quality distributed Bragg reflector with both high and low refractive index layers lattice matched to ZnTe. Our structure is grown by molecular beam epitaxy and is based on binary compounds only. The high refractive index layer is made of ZnTe, while the low index material is made of a short period triple superlattice containing MgSe, MgTe, and ZnTe. The high refractive index step of Delta_n=0.5 in the structure results in a broad stopband and the reflectivity coefficient exceeding 99% for only 15 Bragg pairs.Comment: 4 pages, 3 figure