$k$-essence has been proposed as a possible means of explaining the coincidence problem of the Universe beginning to accelerate only at the present epoch. We carry out a comprehensive dynamical systems analysis of the k-essence models given so far in the literature. We numerically study the basin of attraction of the tracker solutions and we highlight the behavior of the field close to sound speed divergences. We find that, when written in terms of parameters with a simple dynamical interpretation, the basins of attraction represent only a small region of the phase space.

We consider CP asymmetries in neutral B meson decays to ${\eta }^{\prime }{K}_S,$ $\phi K_S,$ and $K^{+}{K}^{-}{K}_S.$ We use SU(3) relations to estimate or bound the contributions to these amplitudes proportional to $V_{\mathrm{ub}}^{*}{V}_{\mathrm{us}}.$ Such contributions induce a deviation of the $S_f$ terms measured in these time dependent CP asymmetries from that measured for $\psi K_S.$ For the $K^{+}{K}^{-}{K}_S$ mode, we estimate the deviation to be of order 0.1. For the ${\eta }^{\prime }{K}_S$ mode, we obtain an upper bound on this deviation of order 0.3. For the $\phi K_S$ mode, we have to add a mild dynamical assumption to the SU(3) analysis due to insufficient available data, yielding an upper bound of order 0.25. These bounds may improve significantly with future data. While they are large at present compared to the usually assumed standard model contribution, they are obtained with minimal assumptions and hence provide more rigorous tests for new physics. If measurements yield $|S_f-S_{\psi K}|$ that are much larger than our bounds, it would make a convincing case for new physics.

We calculate the fermion self-energy at $O\left({\alpha }_s\right)$ for the Symanzik improved staggered fermion action used in recent lattice simulations by the MILC Collaboration. We demonstrate that the algebraic approach to lattice perturbation theory, suggested by us recently, is a powerful tool also for improved lattice actions.

We first review how the simple K-matrix unitarized linear SU(2) sigma model can explain the experimental data in the scalar $\pi \pi$ scattering channel of QCD up to about 800 MeV. Since it is just a scaled version of the minimal electroweak Higgs sector, which is often treated with the same unitarization method, we interpret the result as support for this approach in the electroweak model with scaled values of the tree-level Higgs boson mass up to at least about 2 TeV. We further note that the relevant QCD effective Lagrangian which fits the data to still higher energies using the same method involves another scalar resonance. This suggests that the method should also be applicable to corresponding beyond minimal electroweak models. Nevertheless, we note that even with one resonance, the minimal K matrix unitarized model behaves smoothly for a large bare Higgs boson mass by effectively “integrating out” the Higgs boson while preserving unitarity. With added confidence in this simple approach, we make a survey of the Higgs sector for the full range of bare Higgs boson mass. One amusing point which emerges is that the characteristic factor of the $W-W$ fusion mechanism for Higgs boson production peaks at the bare mass of the Higgs boson, while the characteristic factor for the gluon fusion mechanism peaks near the generally lower physical mass.

In the early Universe, or near a supernova core, neutrino flavor evolution may be affected by coherent neutrino-neutrino scattering. We develop a microscopic picture of this phenomenon. We show that coherent scattering does not lead to the formation of entangled states in the neutrino ensemble and therefore the evolution of the system can always be described by a set of one-particle equations. We also show that the previously accepted formalism overcounts the neutrino interaction energy; the correct one-particle evolution equations for both active-active and active-sterile oscillations contain additional terms. These additional terms modify the index of refraction of the neutrino medium, but have no effect on oscillation physics.

We elucidate the effects of solar density fluctuations on neutrino propagation through the Sun. Using data from the recent solar neutrino and KamLAND experiments we provide stringent limits on solar density fluctuations. It is shown that the neutrino data constrain solar density fluctuations to be less than $\beta =0.05\mathrm{}$ at the 70% confidence level, where $\beta$ is the fractional fluctuation around the value given by the standard solar model. We find that the best fit to the combined solar neutrino and KamLAND data is given by $\beta =0.\mathrm{}$

We study the dynamical evolution of a phase interface or bubble in the context of a $\lambda {\phi }^4+g{\phi }^6$ scalar quantum field theory. We use a self-consistent mean-field approximation derived from a 2PI effective action to construct an initial value problem for the expectation value of the quantum field and two-point function. We solve the equations of motion numerically in $1+1$ dimensions and compare the results to the purely classical evolution. We find that the quantum fluctuations dress the classical profile, affecting both the early time expansion of the bubble and the behavior upon collision with a neighboring interface.

The orbit of the Earth about the Sun produces an annual modulation in the weakly interacting massive particles (WIMP) direct detection rate. If the local WIMP velocity distribution is isotropic then the modulation is roughly sinusoidal with maximum in June; however, if the velocity distribution is anisotropic the phase and shape of the signal can change. Motivated by conflicting claims about the effect of uncertainties in the local velocity distribution on the interpretation of the DAMA annual modulation signal (and the possibility that the form of the modulation could be used to probe the structure of the Milky Way halo), we study the dependence of the annual modulation on various astrophysical inputs. We first examine the approximations used for the Earth’s motion about the Sun and the Sun’s velocity with respect to the Galactic rest frame. We find that overly simplistic assumptions lead to errors of up to ten days in the phase and up to tens of percent in the shape of the signal, even if the velocity distribution is isotropic. Crucially, if the components of the Earth’s velocity perpendicular to the motion of the Sun are neglected, then the change in the phase which occurs for anisotropic velocity distributions is missed. We then examine how the annual modulation signal varies for physically and observationally well-motivated velocity distributions. We find that the phase of the signal changes by up to 20 days and the mean value and amplitude change by up to tens of percent.

Quasinormal modes for scalar field perturbations of a Schwarzschild–de Sitter (SdS) black hole are investigated. An analytical approximation is proposed for the problem. The quasinormal modes are evaluated for this approximate model in the limit when the black hole mass is much smaller than the radius of curvature of the spacetime. The model mirrors some striking features observed in numerical studies of time behavior of scalar perturbations of the SdS black hole. In particular, it shows the presence of two sets of modes relevant at two different time scales, proportional to the surface gravities of the black hole and cosmological horizons, respectively. These quasinormal modes are not complete—another feature observed in the numerical studies. Refinements of this model to yield more accurate quantitative agreement with numerical results are discussed. Further investigations of this model are outlined, which would provide valuable insight into time behavior of perturbations in the SdS spacetime.

We consider the possibility of studying novel particles at the TeV scale with enhanced couplings to the top quark via top quark pair production at the CERN Large Hadron Collider (LHC) and VLHC. In particular we discuss the case of neutral scalar and vector resonances associated with a strongly interacting electroweak symmetry breaking sector. We constrain the couplings of these resonances by imposing appropriate partial wave unitarity conditions and known low energy constraints. We evaluate the new physics signals via $W\overrightarrow{W}t\overline{t}$ for various models without making an approximation for the initial state W bosons, and optimize the acceptance cuts for the signal observation. We conclude that QCD backgrounds overwhelm the signals in both the LHC and a 200 TeV VLHC, making it impossible to study this type of physics in the $t\overline{t}$ channel at those machines.

The fermion propagators in the fivebrane background of type II superstring theories are calculated. The propagator can be obtained by explicitly evaluating the transition amplitude between two specific NS-R boundary states by the propagator operator in the nontrivial world-sheet conformal field theory for the fivebrane background. The propagator in the field theory limit can be obtained by using point boundary states. We can explicitly investigate the lowest-lying fermion states propagating in the nontrivial ten-dimensional space-time of the fivebrane background: $M^6\times W_k^{\mathrm{}\left(4\right)\mathrm{}},$ where $W_k^{\mathrm{}\left(4\right)\mathrm{}}$ is the group manifold of $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_k\times \mathrm{U}\mathrm{}\left(1\right).$ Half of the original supersymmetry is spontaneously broken, and the space-time Lorentz symmetry $\mathrm{SO}\mathrm{}(9,1)\mathrm{}$ reduces to $\mathrm{SO}\mathrm{}(5,1)\mathrm{}$ in $\mathrm{SO}\mathrm{}(5,1)\mathrm{}\times \mathrm{SO}\mathrm{}\left(4\right)\mathrm{}\subset \mathrm{SO}\mathrm{}(9,1)\mathrm{}$ by the fivebrane background. We find that there are no propagations of $\mathrm{SO}\mathrm{}\left(4\right)\mathrm{}$ (local Lorentz) spinor fields, which is consistent with the arguments on the fermion zero modes in the fivebrane background of low-energy type II supergravity theories.

Numerical solutions of Einstein’s and scalar-field equations are found for a global defect in a higher-dimensional spacetime. The defect has a $\mathrm{}(3+1)\mathrm{}$-dimensional core and a “hedgehog” scalar-field configuration in $n=3\mathrm{}$ extra dimensions. For sufficiently low symmetry-breaking scales $\eta ,$ the solutions are characterized by a flat worldsheet geometry and a constant solid deficit angle in the extra dimensions, in agreement with previous work. For $\eta$ above the higher-dimensional Planck scale, we find that static-defect solutions are singular. The singularity can be removed if the requirement of staticity is relaxed and defect cores are allowed to inflate. We obtain an analytic solution for the metric of such inflating defects at large distances from the core. The three extra dimensions of the nonsingular solutions have a “cigar” geometry. Although our numerical solutions were obtained for defects of codimension $n=3,$ we argue that the conclusions are likely to apply to all $n>~3.$

Recently, it has been reported that a candidate for a quark star may have been observed. In this article, we consider quark stars with radiation radii in the reported range. We calculate nonradial oscillations of f, w, and $w_{\mathrm{II}}$ modes. We find that the dependence of the f mode quasinormal frequency on the bag constant and stellar radiation radius is very strong and different from that of the lowest $w_{\mathrm{II}}$ mode quasinormal frequency. Furthermore we deduce a new empirical formula between the f mode frequency of gravitational waves and the parameter of the equation of state for quark stars. The observation of gravitational waves both of the f mode and of the lowest $w_{\mathrm{II}}$ mode would provide a powerful probe for the equation of state of quark matter and the properties of quark stars.

We study characteristic (quasinormal) modes of a D-dimensional Schwarzschild black hole. It is shown that the real parts of the complex quasinormal modes, representing the real oscillation frequencies, are proportional to the product of the number of dimensions and inverse horizon radius $\sim {\mathrm{Dr}}_0^{-1}.$ The asymptotic formula for large multipole number l and arbitrary D is derived. In addition, the WKB formula for computing QN modes, developed to the third order beyond the eikonal approximation, is extended to the sixth order here. This gives us an accurate and economic way to compute quasinormal frequencies.

This paper presents the results of the observations of the detectors participating in the International Gravitational Event Collaboration (IGEC) from 1997 to 2000 and reviews the data analysis methods. The analysis is designed to search for coincident excitations in multiple detectors. The data set analyzed in this article covers a longer period and is more complete than that given in previous reports. The current analysis is more accurate for determining the false dismissal probability for a time coincidence search and it optimizes the search with respect to a target amplitude and direction of the signal. The statistics of the accidental coincidences agrees with the model used for drawing the results. The observations of this IGEC search are consistent with no detection of gravitational wave burst events. A new conservative upper limit has been set on the rate of gravitational wave bursts with a Fourier component $H>\mathrm{}2\mathrm{}\times {10}^{-21}{\mathrm{Hz}}^{-1},$ both for searches with and without a filter for the galactic center direction. This study confirms that the false alarm rate of the observation can be negligible when at least three detectors are operating simultaneously.

Thermal fluctuations of the gauge field lead to monopole formation at the grand unified phase transition in the early Universe, even if the transition is merely a smooth crossover. The dependence of the produced monopole density on various parameters is qualitatively different from theories with global symmetries, and the monopoles have a positive correlation at short distances. The number density of monopoles may be suppressed if the grand unified symmetry is only restored for a short time by, for instance, nonthermal symmetry restoration after preheating.

In this Brief Report, by using the mixing angles of the one-gluon-exchange (OGE) and one-pion-exchange (OPE) models, and by using the electromagnetic Hamiltonian of Close and Li, we calculate the amplitudes of $L=1\mathrm{}{N}^{*}$ resonances for photoproduction and electroproduction. The results are compared to experimental data. It is found that the data support OGE, not OPE.

We study the Gross-Neveu model in 2+1 dimensions with a baryon chemical potential $\mu$ using both analytical and numerical methods. For $\mu$ greater than a critical value the model is chirally symmetric and has a Fermi surface with $k_F\simeq \mu .$ We have calculated the particle interaction in medium due to scalar meson exchange to leading order in $N_f^{-1},$ where $N_f$ is the number of flavors, in the hard dense loop approach. The result has been used to calculate the relation between $\mu$ and the Fermi momentum and velocity in the resulting Fermi liquid to ${O(N}_f^{-1}).\mathrm{}$ Simulation results from a ${32}^2\times 48$ lattice for fermion and meson dispersion relations and meson wave functions are then presented, showing qualitative and in some cases quantitative agreement with analytic predictions. In particular, the simulations show clear evidence for the in-medium modification of the scalar propagator, oscillatory behavior in the wave function consistent with a sharp Fermi surface, and tentative evidence for a massless pole in the vector meson channel resembling zero sound.

We consider the rare top quark decays in the framework of the top-color-assisted technicolor (TC2) model. We find that the contributions of top-pions and top-Higgs-bosons predicted by the TC2 model can enhance the SM branching ratios by as much as 6–9 orders of magnitude; i.e., in the extreme case, the orders of magnitude of branching ratios are $Br\left(\overrightarrow{t}cg\right)\sim {10}^{-5},$ $Br\left(\overrightarrow{t}cZ\right)\sim {10}^{-5},$ $Br\left(\overrightarrow{t}c\gamma \right)\sim {10}^{-7}.$ With reasonable values of the parameters in the TC2 model, such rare top quark decays may be testable in future experiments. Therefore, rare top quark decays provide a unique way to test the TC2 model.

A variety of strong and electroweak interaction properties of a pion and a light scalar $\sigma$ meson are computed in a relativistic quark model. Under the assumption that the resulting coupling of these mesons to the constituent quarks is identical, the $\sigma$ meson mass is determined as $M_{\sigma }=385.4\mathrm{}\mathrm{MeV}.$ We discuss in detail the gauging of the nonlocal meson-quark interaction and calculate the electromagnetic form factor of the pion and the form factors of the ${\pi }^0\to \gamma \gamma$ and $\overrightarrow{\sigma }\gamma \gamma$ processes. We obtain explicit expressions for the relevant form factors and evaluate the leading and next-to-leading orders for large Euclidean photon virtualities. Turning to the decay properties of $\sigma ,$ we determine the width of the electromagnetic $\overrightarrow{\sigma }\gamma \gamma$ transition and discuss the strong decay $\overrightarrow{\sigma }\pi \pi .$ In a final step we compute the nonleptonic decays $\overrightarrow{D}\sigma \pi$ and $\overrightarrow{B}\sigma \pi$ relevant for the possible observation of the $\sigma$ meson. All our results are compared to available experimental data and to results of other theoretical studies.