We present a detailed calculation of the rare decay $\overrightarrow{Z}\overline{\nu }\nu \gamma \gamma$ via the quartic neutral gauge boson coupling $\mathrm{ZZ}\gamma \gamma$ in the framework of the effective Lagrangian approach. The current experimental bound on this decay mode is then used to constrain the coefficients of this coupling. It is found that the bounds obtained in this way, of the order of ${10}^{-1},$ are weaker than the ones obtained from the analysis of triple-boson production at the CERN $e^{-}{e}^{+}$ collider LEP-2.

It has been shown recently that the problem of rapid proton decay induced by dimension-five operators arising from the exchange of colored Higgsinos can be simply avoided in grand unified models where a fifth spatial dimension is compactified on an orbifold. Here we demonstrate that this idea can be used to solve the Higgsino-mediated proton decay problem in any realistic $\mathrm{SO}\left(10\right)\mathrm{}$ model by lifting that model to five dimensions. A particular $\mathrm{SO}\left(10\right)\mathrm{}$ model that has been proposed to explain the pattern of quark and lepton masses and mixings is used as an example. The idea is to break the $\mathrm{SO}\left(10\right)\mathrm{}$ down to the Pati-Salam symmetry by the orbifold boundary conditions. The entire four-dimensional $\mathrm{SO}\left(10\right)\mathrm{}$ model is placed on the physical $\mathrm{SO}\left(10\right)\mathrm{}$ brane except for the gauge fields, the $45$ and a single $10$ of Higgs fields, which are placed in the five-dimensional bulk. The structure of the Higgs superpotential can be somewhat simplified in doing so, while the Yukawa superpotential and mass matrices derived from it remain essentially unaltered.

Results are presented on a measurement of the $t\overline{t}$ pair production cross section in $p\overline{p}$ collisions at $\sqrt{s}=1.8\mathrm{}\mathrm{TeV}$ from nine independent decay channels. The data were collected by the DØ experiment during the 1992–1996 run of the Fermilab Tevatron Collider. A total of 80 candidate events is observed with an expected background of $38.8\pm 3.3$ events. For a top quark mass of $172.1\mathrm{GeV}{/c}^2,$ the measured cross section is $5.69\pm 1.21\left(\mathrm{stat}\right)\pm 1.04\left(\mathrm{syst}\right)\mathrm{pb}.$

We investigate the dynamics of relativistic spinning test particles in the spacetime of a rotating black hole using the Papapetrou equations. We use the method of Lyapunov exponents to determine whether the orbits exhibit sensitive dependence on initial conditions, a signature of chaos. In the case of maximally spinning equal-mass binaries (a limiting case that violates the test-particle approximation) we find unambiguous positive Lyapunov exponents that come in pairs $\pm \lambda ,$ a characteristic of Hamiltonian dynamical systems. We find no evidence for nonvanishing Lyapunov exponents for physically realistic spin parameters, which suggests that chaos may not manifest itself in the gravitational radiation of extreme mass-ratio binary black-hole inspirals (as detectable, for example, by LISA, the Laser Interferometer Space Antenna).

We solve Einstein’s field equations coupled to relativistic hydrodynamics in full $3+1$ general relativity to evolve astrophysical systems characterized by strong gravitational fields. We model rotating, collapsing and binary stars by idealized polytropic equations of state, with neutron stars as the main application. Our scheme is based on the Baumgarte-Shapiro-Shibata-Nakamura formulation of the field equations. We assume adiabatic flow, but allow for the formation of shocks. We determine the appearance of black holes by means of an apparent horizon finder. We introduce several new techniques for integrating the coupled Einstein-hydrodynamics system. For example, we choose our fluid variables so that they can be evolved without employing an artificial atmosphere. We also demonstrate the utility of working in a rotating coordinate system for some problems. We use rotating stars to experiment with several gauge choices for the lapse function and shift vector, and find some choices to be superior to others. We demonstrate the ability of our code to follow a rotating star that collapses from large radius to a black hole. Finally, we exploit rotating coordinates to evolve a corotating binary neutron star system in a quasiequilibrium circular orbit for more than two orbital periods.

We obtain an understanding of baryons and antibaryons in the strong coupling regime $(\kappa \ll 1,$ where κ is the hopping parameter) of Euclidean lattice QCD. It is shown that they arise as tightly bound, bound states of three (anti)quarks. The appearance of each of these particles is manifested by the occurrence of an isolated dispersion curve (upper gap property) in the energy-momentum spectrum, with an asymptotic mass of order $-3\ln \kappa .$ The upper gap property holds in the full gauge invariant space of states, at least up to $-4\ln \kappa .$ In addition, we establish a spectral representation for the two-point baryon correlation function as well as determine symmetry properties. To capture the essence of the mechanism of baryon formation with the minimum of algebraic complexity we consider the single flavor case in $2+1$ space-time dimensions and two-dimensional spin matrices.

We study $N=1\mathrm{}$ supergravity inflation in the context of the braneworld scenario. Particular attention is paid to the problem of the onset of inflation at sub-Planckian field values and the ensuing inflationary observables. We find that the so-called $\eta$ problem encountered in supergravity inspired inflationary models can be solved in the context of the braneworld scenario, for some range of the parameters involved. Furthermore, we obtain an upper bound on the scale of the fifth dimension, $M_5\lesssim {10}^{-3}{M}_P,$ in case the inflationary potential is quadratic in the inflaton field $\phi .$ If the inflationary potential is cubic in $\phi ,$ consistency with observational data requires that $M_5\simeq 9.2\times {10}^{-4}{M}_P.$

We analyze the primordial density perturbation when it is generated by a “curvaton” field different from the inflaton. In some cases this perturbation may have large isocurvature components, fully correlated or anticorrelated with the adiabatic component. It may also have a significant non-Gaussian component. All of these effects are calculated in a form which will enable direct comparison with current and forthcoming observational data.

We investigate the potential of a future kilometer-scale neutrino telescope, such as the proposed IceCube detector in the South Pole, to measure and disentangle the yet unknown components of the cosmic neutrino flux, the prompt atmospheric neutrinos coming from the decay of charmed particles and the extra-galactic neutrinos in the 10 TeV to 1 EeV energy range. Assuming a power law type spectra, $d{\phi }_{\nu }{/dE}_{\nu }\sim \alpha E_{\nu }^{\beta },$ we quantify the discriminating power of the IceCube detector and discuss how well we can determine magnitude $\left(\alpha \right)$ as well as slope $\left(\beta \right)$ of these two components of the high energy neutrino spectrum, taking into account the background coming from the conventional atmospheric neutrinos.

We report on a search for electromagnetic and/or hadronic showers (cascades) induced by a diffuse flux of neutrinos with energies between 5 TeV and 300 TeV from extraterrestrial sources. Cascades may be produced by matter interactions of all flavors of neutrinos, and contained cascades have better energy resolution and afford better background rejection than throughgoing ${\nu }_{\mu }$-induced muons. Data taken in 1997 with the AMANDA detector were searched for events with a high-energy cascadelike signature. The observed events are consistent with expected backgrounds from atmospheric neutrinos and catastrophic energy losses from atmospheric muons. Effective volumes for all flavors of neutrinos, which allow the calculation of limits for any neutrino flux model, are presented. The limit on cascades from a diffuse flux of ${\nu }_e+{\nu }_{\mu }+{\nu }_{\tau }+{\overline{\nu }}_e+{\overline{\nu }}_{\mu }+{\overline{\nu }}_{\tau }$ is $E^2(d\Phi /dE)<\mathrm{}9.8\mathrm{}\times {10}^{-6}{\mathrm{GeV}\mathrm{}\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}{\mathrm{sr}}^{-1},$ assuming a neutrino flavor flux ratio of 1:1:1 at the detector. The limit on cascades from a diffuse flux of ${\nu }_e+{\overline{\nu }}_e$ is $E^2(d\Phi /dE)<\mathrm{}6.5\mathrm{}\times {10}^{-6}{\mathrm{GeV}\mathrm{}\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}{\mathrm{sr}}^{-1},$ independent of the assumed neutrino flavor flux ratio.

One way to incorporate systematic uncertainties into the calculation of confidence intervals is by integrating over probability density functions parametrizing the uncertainties. In this paper we present a development of this method which takes into account uncertainties in the prediction of background processes and uncertainties in the signal detection efficiency and background efficiency, and allows for a correlation between the signal and background detection efficiencies. We implement this method with the likelihood ratio (usually denoted as the Feldman-Cousins) approach with and without conditioning. We present studies of coverage for the likelihood ratio and Neyman ordering schemes. In particular, we present two different types of coverage tests for the case where systematic uncertainties are included. To illustrate the method we show the relative effect of including systematic uncertainties in the case of the dark matter search as performed by modern neutrino telescopes.

We consider the question of which potentials in the action of a (1+1) dimensional scalar field theory allowing for spontaneous symmetry breaking have quantum fluctuations corresponding to reflectionless scattering data. The general problem of restoration from known scattering data is formulated and a number of explicit examples are given. Only certain sets of reflectionless scattering data correspond to symmetry breaking and all restored potentials are similar either to the ${\Phi }^4$ model or to the sine-Gordon model.

We study the generation of magnetic fields during the stage of particle production resulting from spinodal instabilities during phase transitions out of equilibrium. The main premise is that long-wavelength instabilities that drive the phase transition lead to strong nonequilibrium charge and current fluctuations which generate electromagnetic fields. We present a formulation based on the nonequilibrium Schwinger-Dyson equations that leads to an exact expression for the spectrum of electromagnetic fields valid for general theories and cosmological backgrounds and whose main ingredient is the transverse photon polarization out of equilibrium. This formulation includes the dissipative effects of the conductivity in the medium. As a prelude to cosmology, we study magnetogenesis in Minkowski spacetime in a theory of N charged scalar fields to lowest order in the gauge coupling and to leading order in the large N within two scenarios of cosmological relevance. The long-wavelength power spectrum for electric and magnetic fields at the end of the phase transition is obtained explicitly. It follows that equipartition between electric and magnetic fields does not hold out of equilibrium. In the case of a transition from a high-temperature phase, the conductivity of the medium severely hinders the generation of magnetic fields; however, the magnetic fields generated are correlated on scales of the order of the domain size, which is much larger than the magnetic diffusion length. The implications of the results to cosmological phase transitions driven by spinodal instabilities are discussed.

Separation of the E and B components of a microwave background polarization map or a weak lensing map is an essential step in extracting science from it, but when the map covers only part of the sky and/or is pixelized, this decomposition cannot be done perfectly. We present a method for decomposing an arbitrary sky map into a sum of three orthogonal components that we term “pure E,” “pure B,” and “ambiguous.” The fluctuations in the pure E and B maps are due only to the E and B power spectra, respectively, whereas the source of those in the ambiguous map is completely indeterminate. This method is useful both for providing intuition for experimental design and for analyzing data sets in practice. We show how to find orthonormal bases for all three components in terms of bi-Laplacian eigenfunctions, thus providing a type of polarized signal-to-noise eigenmodes that simultaneously separate both angular scale and polarization type. The number of pure and ambiguous modes probing a characteristic angular scale θ scales as the map area over ${\theta }^2$ and as the map boundary length over θ, respectively. This implies that fairly round maps (with short perimeters for a given area) will yield the most efficient $E/B$ decomposition and also that the fraction of the information lost to ambiguous modes grows towards larger angular scales. For real-world data analysis, we present a simple matrix eigenvalue method for calculating nearly pure E and B modes in pixelized maps. We find that the dominant source of leakage between E and B is aliasing of small-scale power caused by the pixelization, essentially since derivatives are involved. This problem can be eliminated by heavily oversampling the map, but is exacerbated by the fact that the E power spectrum is expected to be much larger than the B power spectrum and by the extremely blue power spectrum that cosmic microwave background polarization is expected to have. We found that a factor of 2 to 3 more pixels are needed in a polarization map to achieve the same level of contamination by aliased power than in a temperature map. Oversampling is therefore much more important for the polarized case than for the unpolarized case, which should be reflected in experimental design.

A measurement of the deflection of a laser beam in a modulated magnetic field with a prototype apparatus has produced an upper limit on the charge of the photon of $8.5\times {10}^{-17}e.\mathrm{}$ It is shown that an improved apparatus could attain a sensitivity of ${10}^{-21}e.\mathrm{}$

We study top quark Kaluza-Klein (KK) mode mixing in the Randall-Sundrum scenario with all the SM fermions and gauge bosons in the bulk. Even though the simple assumption of a universal bulk fermion mass $m_{\psi }$ leads to the same KK mass spectrum for all SM fermions and thus suppresses new contributions to the flavor changing neutral current and the $\rho$ parameter, the large Yukawa coupling of the top quark generates mixing among its KK modes and breaks the degeneracy: An unacceptably large contribution to $\Delta \rho$ occurs. In order to satisfy the $\Delta \rho$ constraint, we relax the model by assigning a different bulk fermion mass to the SU(2) singlet bottom quark and demonstrate that there exists some limited parameter space where the $\Delta \rho$ constraint is satisfied. It is also shown that the current measurement of $\mathrm{Br}(\overrightarrow{B}{X}_s+\gamma )$ can be accommodated in this modified model, and the one sigma level precision constrains the effective weak scale $k_{\mathrm{EW}}$ such as $k_{\mathrm{EW}}\gtrsim 3\mathrm{TeV}$ for $m_{\psi }/k=-0.4,$ where $k_{\mathrm{EW}}$ is the warp-suppressed ${\mathrm{AdS}}_5$ curvature.

Recently it has been shown that the gross structure of the bottomonium spectrum is reproduced reasonably well within the nonrelativistic bound state theory based on perturbative QCD. In that calculation, however, the fine splittings and the $S–P$ level splittings are predicted to be considerably narrower than the corresponding experimental values. We investigate the bottomonium spectrum within a specific framework based on perturbative QCD, which incorporates all the corrections up to $\mathcal{O}\left({\alpha }_S^5{m}_b\right)$ and $\mathcal{O}\left({\alpha }_S^4{m}_b\right),$ respectively, in the computations of the fine splittings and the $S–P$ splittings. We find that the agreement with the experimental data for the fine splittings improves drastically due to an enhancement of the wave functions close to the origin as compared to the Coulomb wave functions. The agreement of the $S–P$ splittings with the experimental data also becomes better. We find that natural scales of the fine splittings and the $S–P$ splittings are larger than those of the bound states themselves. On the other hand, the predictions of the level spacings between consecutive principal quantum numbers depend rather strongly on the scale $\mu$ of the operator $\propto C_A{/(m}_b{r}^2).\mathrm{}$ The agreement of the whole spectrum with the experimental data is much better than the previous predictions when $\mu \simeq 3–4\mathrm{GeV}$ for ${\alpha }_S{(M}_Z)=\mathrm{0.1181.}\mathrm{}$ There seems to be a phenomenological preference for some suppression mechanism for the above operator.