The Zeta Function Method and the Harmonic Oscillator Propagator

We show how the pre-exponential factor of the Feynman propagator for the harmonic oscillator can be computed by the generalized $\zeta$-function method. Besides, we establish a direct equivalence between this method and Schwinger's propertime method.Comment: 12 latex pages, no figure

The One Dimensional Damped Forced Harmonic Oscillator Revisited

In this paper we give a general solution to the problem of the damped harmonic oscillator under the influence of an arbitrary time-dependent external force. We employ simple methods accessible for beginners and useful for undergraduate students and professors in an introductory course of mechanics.Comment: 4 Latex page

Study of sequential semileptonic decays of b hadrons produced at the Tevatron

We present a study of rates and kinematical properties of lepton pairs contained in central jets with transverse energy E_T > 15 GeV that are produced at the Fermilab Tevatron collider. We compare the data to a QCD prediction based on the HERWIG and QQ Monte Carlo generator programs.We find that the data are poorly described by the simulation, in which sequential semileptonic decays of single b quarks (b --> l c X with c --> l s X) are the major source of such lepton pairs.Comment: 25 pages, 8 figures. Some typos were fixed in the text and bibliography. Submitted to Phys. Rev.

Current-Phase Relation of a Bose-Einstein Condensate Flowing Through a Weak Link

We study the current-phase relation of a Bose-Einstein condensate flowing through a repulsive square barrier by solving analytically the one dimensional Gross-Pitaevskii equation. The barrier height and width fix the current-phase relation $j(\delta\phi)$, which tends to $j\sim\cos(\delta\phi/2)$ for weak barriers and to the Josephson sinusoidal relation $j\sim\sin(\delta\phi)$ for strong barriers. Between these two limits, the current-phase relation depends on the barrier width. In particular, for wide enough barriers, we observe two families of multivalued current-phase relations. Diagrams belonging to the first family, already known in the literature, can have two different positive values of the current at the same phase difference. The second family, new to our knowledge, can instead allow for three different positive currents still corresponding to the same phase difference. Finally, we show that the multivalued behavior arises from the competition between hydrodynamic and nonlinear-dispersive components of the flow, the latter due to the presence of a soliton inside the barrier region.Comment: 6 pages, 5 figure

Phenomenological study of the atypical heavy flavor production observed at the Fermilab Tevatron

We address known discrepancies between the heavy flavor properties of jets produced at the Tevatron collider and the prediction of conventional-QCD simulations. In this study, we entertain the possibility that these effects are real and due to new physics. We show that all anomalies can be simultaneously fitted by postulating the additional pair production of light bottom squarks with a 100% semileptonic branching fraction.Comment: 30 pages, 13 figures, 3 tables. Submitted to Phys. Rev.

Vacuum energies due to delta-like currents: simulating classical objects along branes with arbitrary codimensions

In this paper we investigate the vacuum energies of several models of quantum fields interacting with static external currents (linear couplings) concentrated along parallel branes with an arbitrary number of codimensions. We show that we can simulate the presence of static charges distributions as well as the presence of classical static dipoles in any dimension for massive and massless fields. We also show that we can produce confining potentials with massless self interacting scalar fields as well as long range anisotropic potentials.Comment: 18 latex page

Diffractive photoproduction of opposite-charge pseudoscalar meson pairs at high energies

We calculate the cross section for diffractive photoproduction of opposite-charge pseudoscalar meson pairs $M^+M^- = \pi^+ \pi^-$, $K^+ K^-$, $D^+ D^-$ and $B^+ B^-$ in a broad range of center-of-mass energies relevant for GlueX/Hall D, FOCUS, COMPASS and HERA experiments. In the case of $\pi^+\pi^-$ production we find that the interference of the $\rho^0$ resonance and the two-pion continuum leads to a considerable deformation of the shape of $\rho^0$ in agreement with the data from the ZEUS collaboration. We also discuss the spectral shape of the $\rho^0$ as a function of the momentum transfer and the contribution of higher partial waves to the $\pi^+\pi^-$ mass spectrum. We predict a sizeable energy-dependent forward-backward asymmetry in the Gottfried-Jackson frame. For the heavy meson production we find that the cross section for diffractive production increases much slower than the one for open charm or bottom production. We discuss lower and upper limits for the cross sections for diffractive production of $D^+ D^-$ and $B^+ B^-$ pairs, which we find can be as large as 10% of the open flavor production.Comment: 14 pages, 19 figure