The dominance of the direct production of elementary Goldstone waves is demonstrated in tachyonic preheating by numerically determining the evolution of the dispersion relation, the equation of state, and the kinetic power spectra for the angular degree of freedom of the complex matter field. The importance of the domain structure in the order parameter distribution for a quantitative understanding of the excitation mechanism is emphasized. Evidence is presented for the very early decoupling of the low-momentum Goldstone modes.

The methods of dynamical systems have been used to study homogeneous and isotropic cosmological models with a varying speed of light (VSL). We propose two methods for the reduction of the dynamics to the form of planar Hamiltonian dynamical systems for models with a time dependent equation of state. The solutions are analyzed on two-dimensional phase space in the variables $(x,\mathrm{ẋ})$ where x is a function of a scale factor a. Then we show how the horizon problem may be solved on some evolutional paths. It is shown that the models with a negative curvature overcome the horizon and flatness problems. The presented method of reduction can be adapted to the analysis of the dynamics of the Universe with the general form of the equation of state $p=\gamma \mathrm{}\left(a\right)\mathrm{}\epsilon .$ This is demonstrated using as an example the dynamics of VSL models filled with a noninteracting fluid. We demonstrate a new type of evolution near the initial singularity caused by a varying speed of light. Singularity-free oscillating universes are also admitted for a positive cosmological constant. We consider a quantum VSL Friedmann-Robertson-Walker closed model with radiation and show that the highest tunneling rate occurs for a constant velocity of light if $c\left(a\right)\mathrm{}\propto a^n$ and $-1<n<~0.$ It is also proved that the class of models considered is structurally unstable for the case of $n<\mathrm{}0.\mathrm{}$

We present a semianalytic calculation of the tau-lepton flux emerging from the Earth induced by incident high energy neutrinos interacting inside the Earth for ${10}^5<~E_{\nu }/\mathrm{GeV}<~{10}^{10}.$ We obtain results for the energy dependence of the tau-lepton flux coming from the Earth-skimming neutrinos, because of the neutrino-nucleon charged-current scattering as well as the resonant ${\overline{\nu }}_e{e}^{-}$ scattering. We illustrate our results for several anticipated high energy astrophysical neutrino sources such as the active galactic nuclei, the gamma-ray bursts, and the Greisen-Zatsepin-Kuzmin neutrino fluxes. The tau-lepton fluxes resulting from rock-skimming and ocean-skimming neutrinos are compared. Such comparisons can render useful information about the spectral indices of incident neutrino fluxes.

In this paper we study the powerlike confining potentials $r^{\alpha }.$ The region of allowed $\alpha ’\mathrm{s}$ is identified, the mass-gap equation is constructed for an arbitrary $\alpha$ and solved for several values of the latter, and the vacuum energy and the chiral condensate are calculated. The question of replica solutions to the mass-gap equation for such potentials is addressed, and it is demonstrated that the number of replicas is infinite for any $\alpha ,$ as a consequence of the peculiar behavior of the quark self-energy in the infrared domain.

We study the regularization of theories of “brane induced” gravity in codimension $N>\mathrm{}1.\mathrm{}$ The brane can be interpreted as a thin dielectric with a large dielectric constant, embedded in a higher dimensional space. The kinetic term for the higher dimensional graviton is enhanced over the brane. A four dimensional gravitation is found on the brane at distances smaller than a critical distance $r<\mathrm{}{r}_c,$ and is due to the exchange of a massive resonant graviton. The crossover scale $r_c$ is determined by the mass of the resonance. The suppression of the couplings of light Kaluza-Klein modes to brane matter results in a higher dimensional force law at large distances. We show that the resulting theory is free of ghosts or tachyons.

We construct analogues of the flat space Kaluza-Klein (KK) monopoles in locally anti–de Sitter (AdS) spaces for $D>~5+1.$ We show that, unlike the flat space KK monopole, there is no five-dimensional static KK monopole in AdS spacetime that smoothly reduces to the flat space one as the cosmological constant goes to zero. Thus, one needs at least two extra dimensions, one of which is compact, to get a static KK monopole in cosmological backgrounds.

We study solutions of Einstein’s equations corresponding to codimension $n>\mathrm{}2\mathrm{}$ global topological defects with de Sitter slices. We analyze a class of solutions that are cylindrically symmetric and admit a positive, negative, or zero bulk cosmological constant. We derive the relevant graviton equations. For an extended brane, the properties of the solution depend on the appropriate boundary conditions that have to be satisfied by the exterior solutions near the core. As an alternative we consider matching copies of the exterior solution related by symmetry. We show that we can get localization only when the bulk cosmological constant is negative. We obtain a condition on the global defect symmetry breaking scale which ultimately controls the size of the $n-1$ internal dimensions at the position of the brane. The induced metric on the brane, in the case of mirror spacetimes, is a direct product of a de Sitter space and an $\left(n-1\right)$-sphere, while the metric of the embedding spacetime is a warped product and the actual size of the $\left(n-1\right)$-sphere changes as we move along the radial direction. The solutions possess naked singularities, which nevertheless satisfy no-flow conditions.

Corrections to Einstein’s equations that become important at small curvatures are considered. The field equations are derived using a Palatini variation in which the connection and metric are varied independently. In contrast with the Einstein-Hilbert variation, which yields fourth order equations, the Palatini approach produces second order equations in the metric. The Lagrangian $L\left(R\right)=R-{\alpha }^2/R$ is examined and it is shown that it leads to equations whose solutions approach a de Sitter universe at late times. Thus, the inclusion of $1/R$ curvature terms in the gravitational action offers an alternative explanation for the cosmological acceleration.

A fluid interpretation of Cardassian expansion is developed. Here, the Friedmann equation takes the form $H^2=g\left({\rho }_M\right)$ where ${\rho }_M$ contains only matter and radiation (no vacuum). The function $g\left({\rho }_M\right)$ returns to the usual $8\pi {\rho }_M{/(3m}_{\mathrm{pl}}^2)$ during the early history of the Universe, but takes a different form that drives an accelerated expansion after a redshift $z\sim 1.$ One possible interpretation of this function (and of the right-hand side of Einstein’s equations) is that it describes a fluid with total energy density ${\rho }_{\mathrm{tot}}{=(3m}_{\mathrm{pl}}^2/8\mathrm{}\pi \left)g\right({\rho }_M)={\rho }_M+{\rho }_K$ containing not only matter density (mass times number density) but also interaction terms ${\rho }_K.$ These interaction terms give rise to an effective negative pressure which drives cosmological acceleration. These interactions may be due to interacting dark matter, e.g. with a fifth force between particles $F\sim r^{\alpha -1}.$ Such interactions may be intrinsically four dimensional or may result from higher dimensional physics. A fully relativistic fluid model is developed here, with conservation of energy, momentum, and particle number. A modified Poisson’s equation is derived. A study of fluctuations in the early Universe is presented, although a fully relativistic treatment of the perturbations including gauge choice is as yet incomplete.

The problem of the Majorana neutrino mass generated in the Arkani-Hamed–Dimopoulos–Dvali model with n extra spatial dimensions is discussed. Taking into account constraints on the neutrino masses coming from cosmological observations, it is possible to obtain lower limits on the size of the extra dimensions as large as ${10}^{-6}\mathrm{mm}.$ In the case of $n=4\mathrm{}$ it is easy to lower the fundamental scale of gravity from the Planck energy to the electroweak scale $\sim 1\mathrm{TeV}$ without imposing any additional constraints. A link between the half-life of neutrinoless double beta decay and the size of extra dimensions is discussed.

It is shown that the universality of the initial and final state interactions responsible for the transition between on- and off-mass-shell states leads to energy independence of the ratio of the exclusive $\rho$ electroproduction cross section to the total cross section. It is demonstrated that the above universality and the explicit mass dependence of the exponent in the powerlike energy behavior of the cross section obtained in the approach based on unitarity are in quantitative agreement with the high-energy DESY HERA experimental data. We also discuss the HERA results on the angular distribution of vector-meson production.

The democratic approach to account for fermion masses and mixing is known to be successful not only in the quark sector but also in the lepton sector. Here we extend this ansatz to supersymmetric standard models, in which the Kähler potential obeys the underlying $S_3$ flavor symmetries. The requirement of neutrino bi-large mixing angles constrains the form of the Kähler potential for left-handed lepton multiplets. We find that right-handed sleptons can have nondegenerate masses and flavor mixing, while left-handed sleptons are argued to have universal and hence flavor-blind masses. This mass pattern is testable in future collider experiments when superparticle masses will be measured precisely. Lepton flavor violation arises in this scenario. In particular, $\overrightarrow{\mu }e\gamma$ is expected to be observed in a planned future experiment if supersymmetry breaking scale is close to the weak scale.

We study the predictions for $\mathrm{BR}(\overrightarrow{\mu }e+\gamma )$ and $\mathrm{BR}(\overrightarrow{\tau }e,\mu +\gamma )$ in a class of recently proposed horizontal SU(2) model that leads to a $3\times 2$ seesaw model for neutrino masses. We consider two such models and obtain the correct bilarge mixing pattern for neutrinos. In these models, the effective low-energy theory below the $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_H$ scale is the minimal supersymmetric standard model. Assuming a supersymmetry breaking pattern as in the minimal supergravity models, we find that consistent with present $g-2,$ $\overrightarrow{b}s+\gamma ,$ and Wilkinson Microwave Anisotropy Probe dark matter constraints on the parameters of the model, the $\mathrm{BR}(\overrightarrow{\mu }e+\gamma )$ prediction is accessible to the proposed MEG experiment at PSI making this class of models testable in the near future.

We discuss a renormalization scheme for relativistic baryon chiral perturbation theory which provides a simple and consistent power counting for renormalized diagrams. The method involves finite subtractions of dimensionally regularized diagrams beyond the standard $\overline{\mathrm{MS}}$ scheme of chiral perturbation theory to remove contributions violating the power counting. This is achieved by a suitable renormalization of the parameters of the most general effective Lagrangian. In addition to its simplicity our method has the benefit that it can be easily applied to multiloop diagrams. As an application we discuss the mass of the nucleon and compare the result with the expression of the infrared regularization of Becher and Leutwyler.

We present recent results in unquenched lattice QCD with two degenerate light sea quarks using the truncated determinant approximation (TDA). In the TDA the infrared modes contributing to the quark determinant are computed exactly up to some cutoff in quark off-shellness (typically $2{\Lambda }_{\mathrm{QCD}}).\mathrm{}$ This approach allows simulations to be performed at much lighter quark masses than possible with conventional hybrid Monte Carlo techniques. Results for the static energy and topological charge distributions are presented using a large ensemble generated on very coarse ${(6\mathrm{}}^4)$ but physically large lattices. Preliminary results are also reported for the static energy and meson spectrum on ${10}^3\times 20$ lattices (lattice scale $a^{-1}=1.15\mathrm{}\mathrm{GeV})$ at quark masses corresponding to pions of mass $<~200\mathrm{MeV}.$ Using multiboson simulation to compute the ultraviolet part of the quark determinant the TDA approach becomes an exact algorithm with essentially no increase in computational effort. Some preliminary results using this fully unquenched algorithm are presented.

The most general amplitude for the radiative pion decay $\overrightarrow{\pi }e\nu \gamma$ including terms beyond $V-A$ theory is considered. The experimental constraints on the decay amplitude components are discussed. A model independent presentation of the results of high statistics and high resolution experiments is suggested.

We investigate the one-loop supersymmetric QCD (SUSY-QCD) and electroweak (SUSY-EW) corrections to the top quark decay into a b quark and a longitudinal or transverse W boson. The corrections are presented in terms of the longitudinal ratio $\Gamma \left(\overrightarrow{t}{W}_{L}b\right)/\Gamma \left(\overrightarrow{t}Wb\right)$ and the transverse ratio $\Gamma \left(\overrightarrow{t}{W}_{-}b\right)/\Gamma \left(\overrightarrow{t}Wb\right).\mathrm{}$ In most of the parameter space, both SUSY-QCD and SUSY-EW corrections to these ratios are found to be less than 1% in magnitude and they tend to have opposite signs. The corrections to the total width $\Gamma \left(\overrightarrow{t}Wb\right)$ are also presented for comparison with the existing results in the literature. We find that our SUSY-EW corrections to the total width differ significantly from previous studies: the previous studies give a large correction of more than 10% in magnitude for a large part of the parameter space while our results reach only few percent at most.

We propose a method for determining $\gamma$ using $B^{\pm }\to {\mathrm{DK}}^{\pm }$ decays followed by a multibody D decay, such as $\overrightarrow{D}{K}_S{\pi }^{-}{\pi }^{+},$ $\overrightarrow{D}{K}_S{K}^{-}{K}^{+},$ and $\overrightarrow{D}{K}_S{\pi }^{-}{\pi }^{+}{\pi }^0.$ The main advantages of the method are that it uses only Cabibbo allowed D decays, and that large strong phases are expected due to the presence of resonances. Since no knowledge about the resonance structure is needed, $\gamma$ can be extracted without any hadronic uncertainty.

We study the status of the $\mathrm{CPT}$ violating neutrino mass spectrum which has been proposed to simultaneously accommodate the oscillation data from LSND, KamLAND, atmospheric and solar neutrino experiments, as well as the nonobservation of the antineutrino disappearance in short-baseline reactor experiments. We perform a three-generation analysis of the global data with the aim of elucidating the viability of this solution. We find no compatibility between the results of the oscillation analysis of the Liquid Scintillator Neutrino Detector (LSND) and all-but-LSND data sets below 3σ confidence level. Furthermore, the global data without LSND show no evidence for $\mathrm{CPT}$ violation: the best fit point of the all-but-LSND analysis occurs very close to a $\mathrm{CPT}$ conserving scenario.