The periodic standing wave (PSW) method for the binary inspiral of black holes and neutron stars computes exact numerical solutions for periodic standing-wave spacetimes and then extracts approximate solutions of the physical problem, with outgoing waves. The method requires solution of a boundary-value problem with a mixed (hyperbolic and elliptic) character. We present here a new numerical method for such problems, based on three innovations: (i) a coordinate system adapted to the geometry of the problem, (ii) an expansion in multipole moments of these coordinates and a filtering out of higher moments, and (iii) the replacement of the continuum multipole moments with their analogs for a discrete grid. We illustrate the efficiency and accuracy of this method with nonlinear scalar model problems. Finally, we take advantage of the ability of this method to handle highly nonlinear models to demonstrate that the outgoing approximations extracted from the standing-wave solutions are highly accurate even in the presence of strong nonlinearities.

I discuss the accuracy requirements on numerical relativity calculations of inspiraling compact object binaries whose extracted gravitational waveforms are to be used as templates for matched filtering signal extraction and physical parameter estimation in modern interferometric gravitational wave detectors. Using a post-Newtonian point particle model for the premerger phase of the binary inspiral, I calculate the maximum allowable errors for the mass and relative velocity and positions of the binary during numerical simulations of the binary inspiral. These maximum allowable errors are compared to the errors of state-of-the-art numerical simulations of multiple-orbit binary neutron star calculations in full general relativity, and are found to be smaller by several orders of magnitude. A post-Newtonian model for the error of these numerical simulations suggests that adaptive mesh refinement coupled with second-order accurate finite difference codes will not be able to robustly obtain the accuracy required for reliable gravitational wave extraction on Terabyte-scale computers. I conclude that higher-order methods (higher-order finite difference methods and/or spectral methods) combined with adaptive mesh refinement and/or multipatch technology will be needed for robustly accurate gravitational wave extraction from numerical relativity calculations of binary coalescence scenarios.

Brane inflation in superstring theory ends when branes collide, initiating the hot big bang. Cosmic superstrings are produced during the brane collision. The cosmic superstrings produced in a $D3$-brane-antibrane inflationary scenario have a spectrum: $(p,q)$ bound states of $p$ fundamental ($F$) strings and $q$ $D$-strings, where $p$ and $q$ are coprime. By extending the velocity-dependent one-scale network evolution equations for Abelian Higgs cosmic strings to allow a spectrum of string tensions, we construct a coupled (infinite) set of equations for strings that interact through binding and self-interactions. We apply this model to a network of $(p,q)$ superstrings. Our numerical solutions show that $(p,q)$ networks rapidly approach a stable scaling solution. We also extract the relative densities of each string type from our solutions. Typically, only a small number of the lowest tension states are populated substantially once scaling is reached. The model we study also has an interesting new feature: the energy released in $(p,q)$ string binding is by itself adequate to allow the network to reach scaling. This result suggests that the scaling solution is robust. To demonstrate that this result is not trivial, we show that choosing a different form for string interactions can lead to network frustration.

The direction dependence of the event rate in WIMP direct detection experiments provides a powerful tool for distinguishing WIMP events from potential backgrounds. We use a variety of (nonparametric) statistical tests to examine the number of events required to distinguish a WIMP signal from an isotropic background when the uncertainty in the reconstruction of the nuclear recoil direction is included in the calculation of the expected signal. We consider a range of models for the Milky Way halo, and also study rotational symmetry tests aimed at detecting nonsphericity/isotropy of the Milky Way halo. Finally we examine ways of detecting tidal streams of WIMPs. We find that if the senses of the recoils are known then of order ten events will be sufficient to distinguish a WIMP signal from an isotropic background for all of the halo models considered, with the uncertainties in reconstructing the recoil direction only mildly increasing the required number of events. If the senses of the recoils are not known the number of events required is an order of magnitude larger, with a large variation between halo models, and the recoil resolution is now an important factor. The rotational symmetry tests require of order a thousand events to distinguish between spherical and significantly triaxial halos, however a deviation of the peak recoil direction from the direction of the solar motion due to a tidal stream could be detected with of order a hundred events, regardless of whether the sense of the recoils is known.

Within the minimal supergravity model (mSUGRA) framework, the expectation for the relic density of neutralinos exceeds the WMAP determination, unless neutralinos (a) have a significant Higgsino component, (b) have a mass close to half that of a heavy Higgs boson, or (c) can efficiently coannihilate with a charged or colored particle. Within a one-parameter extension of the mSUGRA model which includes nonuniversal Higgs masses, we show that agreement with the WMAP data can be obtained over a wide range of mSUGRA parameters for scenarios (a) and (b), so that the phenomenological implications may be much more diverse than in mSUGRA. We show that direct and/or indirect detection of neutralino dark matter should be possible at various current and planned facilities.

This is the completion of an exploratory study of compact lattice quantum electrodynamics with a weak four-Fermi interaction and four species of massless fermions. In this formulation of quantum electrodynamics massless fermions can be simulated directly and finite size scaling analyses can be performed at the theory’s chiral symmetry breaking critical point. High statistics simulations on lattices ranging from $8^4$ to ${24}^4$ yield the equation of state, critical indices, scaling functions and cumulants. The measurements are well fit with the orthodox hypothesis that the theory is logarithmically trivial and its continuum limit suffers from Landau’s zero charge problem.

We investigate OZI rule violation in $\omega$ and $\varphi$-meson photoproduction off nucleons. Data on the total cross sections indicate a large $\varphi /\omega$ ratio of about 0.8 at the maximal available photon energy that is in good agreement with expectations from QCD. On the other hand, data at large four-momentum transfer exhibit a ratio of about 0.07, showing that the perturbative QCD regime is not approached at $|t|>2{\mathrm{GeV}}^2$ and photon energies $E_{\gamma }<4\mathrm{GeV}$. The anomanously large $\varphi /\omega$ ratio at low energies, that is close to the reaction threshold, remains to be explained within nonperturbative QCD.

We present measurements of the branching fractions $\mathcal{B}(B^0\to D^{*-}{D}_s^{*+})$ and $\mathcal{B}(D_s^{+}\to \varphi {\pi }^{+})$, based on $123\times {10}^6{\rm Y}(4S)\to B\overline{B}$ decays collected by the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}B$ factory. A partial reconstruction technique is used to measure $\mathcal{B}(B^0\to D^{*-}{D}_s^{*+})$ and the decay chain is fully reconstructed to measure the branching fraction product $\mathcal{B}(B^0\to D^{*-}{D}_s^{*+})\times \mathcal{B}(D_s^{+}\to \varphi {\pi }^{+})$. Comparing these two measurements provides a model-independent determination of the $D_s^{+}\to \varphi {\pi }^{+}$ branching fraction. We obtain $\mathcal{B}(B^0\to D^{*-}{D}_s^{*+})=(1.88\pm 0.09\pm 0.17)\%$ and $\mathcal{B}(D_s^{+}\to \varphi {\pi }^{+})=(4.81\pm 0.52\pm 0.38)\%$, where the first uncertainties are statistical and the second systematic.

We report a search for $B\to J/\psi D$ decays, based on a sample of $124\times {10}^6$ $B\overline{B}$ events collected with the BABAR detector at the PEP-II storage ring of the Stanford Linear Accelerator Center. No significant signal is found. We obtain upper limits on the branching fractions of $1.3\times {10}^{-5}$ for $B^0\to J/\psi {\overline{D}}^0$ and $1.2\times {10}^{-4}$ for $B^{+}\to J/\psi D^{+}$ at 90% confidence level.

We study the global structure of the moduli space of BPS walls in the Higgs branch of supersymmetric theories with eight supercharges. We examine the structure in the neighborhood of a special Lagrangian submanifold $M$, and find that the dimension of the moduli space can be larger than that naively suggested by the index theorem, contrary to previous examples of BPS solitons. We investigate BPS wall solutions in an explicit example of $M$ using Abelian gauge theory. Its Higgs branch turns out to contain several special Lagrangian submanifolds including $M$. We show that the total moduli space of BPS walls is the union of these submanifolds. We also find interesting dynamics between BPS walls as a by-product of the analysis. Namely, mutual repulsion and attraction between BPS walls sometimes forbid a movement of a wall and lock it in a certain position; we also find that a pair of walls can transmute to another pair of walls with different tension after they pass through.

Baryons in the large $N$ limit of ($1+1$)-dimensional Gross-Neveu models with either discrete or continuous chiral symmetry have long been known. We generalize their construction to the case where the symmetry is explicitly broken by a bare mass term in the Lagrangian. In the discrete symmetry case, the exact solution is found for arbitrary bare fermion mass, using the Hartree-Fock approach. It is mathematically closely related to polarons and bipolarons in conducting polymers. In the continuous symmetry case, a derivative expansion allows us to rederive a formerly proposed Skyrme-type model and to compute systematically corrections to the leading order description based on an effective sine-Gordon theory.

Killing-Yano tensors are natural generalizations of Killing vectors to arbitrary rank antisymmetric tensor fields. It was recently shown that Killing-Yano tensors lead to conserved gravitational charges, called Yano-Arnowitt-Deser-Misner (Y-ADM) charges. These new charges are interesting because they measure e.g. the mass density of a $p$-brane, rather than the total ADM mass which may be infinite. In this paper, we show that the spinorial techniques used by Witten, in his proof of the positive energy theorem, may be straightforwardly extended to study the positivity properties of the Y-ADM mass density for $p$-brane spacetimes. Although the resulting formalism is quite similar to the ADM case, we show that establishing a positivity bound in the higher rank Y-ADM case requires imposing a condition on the Weyl tensor in addition to an energy condition. We find appropriate energy conditions for spacetimes that are conformally flat or algebraically special, and for spacetimes that have an exact Killing vector along the brane. Finally we discuss our expression for the Y-ADM mass density from the Hamiltonian point of view.

We study the condition of black hole formation in five-dimensional space-time. We analytically solve the constraint equations of five-dimensional Einstein equations for momentarily static and conformally flat initial data of a spheroidal mass. We numerically search for an apparent horizon in various initial hypersurfaces and find both necessary and sufficient conditions for the horizon formation in terms of inequalities relating a geometric quantity and a mass defined in an appropriate manner. In the case of infinitely thin spheroid, our results suggest a possibility of naked singularity formation by the spindle gravitational collapse in five-dimensional space-time.

We consider an electric charge, minimally coupled to the Maxwell field, rotating around a Schwarzschild black hole. We investigate how much of the radiation emitted from the swirling charge is absorbed by the black hole and show that most of the photons escape to infinity. For this purpose we use the Gupta-Bleuler quantization of the electromagnetic field in the modified Feynman gauge developed in the context of quantum field theory in Schwarzschild spacetime. We obtain that the two photon polarizations contribute quite differently to the emitted power. In addition, we discuss the accurateness of the results obtained in a full general relativistic approach in comparison with the ones obtained when the electric charge is assumed to be orbiting a massive object due to a Newtonian force.

In this paper we construct the Hamiltonian constraint operator of loop quantum cosmology using holonomies defined for arbitrary irreducible SU(2) representations labeled by spin $J$. We show that modifications to the effective semiclassical equations of motion arise both in the gravitational part of the constraint as well as matter terms. The modifications are important for phenomenological investigations of the cosmological imprints of loop quantum cosmology. We discuss the implications for the early universe evolution.

We find that sudden future singularities of pressure may also appear in spatially inhomogeneous Stephani models of the universe. They are temporal pressure singularities and may appear independently of the spatial finite density singularities already known to exist in these models. It is shown that the main advantage of the homogeneous sudden future singularities which is the fulfillment of the strong and weak energy conditions may not be the case in the inhomogeneous case.

The quantum discrete kinetic equations are solved to study the propagation of plane waves in a system of composite particles under the magnetic field which is subjected to the Beltrami field condition and particles being also under uniform external gravitational field. We compare the dispersion relations thus obtained by the relevant Pauli-blocking factor $\theta$ which describes the different-statistics particles for the quantum analog of the discrete Boltzmann system when $\theta$ is positive (say, $\theta =1$ for Bose gases), zero (Boltzmann gases), and negative ($\theta =-1$ for Fermi Gases). We found, as the effect of magnetic field being zero (using the Beltrami field condition), the gravitational field effect will induce anomalous dispersion relations (e.g., negative sound speed).

We compare updated predictions for the elastic scattering of supersymmetric neutralino dark matter with the improved experimental upper limit recently published by Cryogenic Dark Matter Search (CDMS) II. We take into account the possibility that the $\pi$-nucleon $\Sigma$ term may be somewhat larger than was previously considered plausible, as may be supported by the masses of exotic baryons reported recently. We also incorporate the new central value of $m_t$, which affects indirectly constraints on the supersymmetric parameter space, for example, via calculations of the relic density. Even if a large value of $\Sigma$ is assumed, the CDMS II data currently exclude only small parts of the parameter space in the constrained minimal standard model (CMSSM) with universal soft supersymmetry-breaking Higgs, squark, and slepton masses. None of the previously proposed CMSSM benchmark scenarios is excluded for any value of $\Sigma$, and the CDMS II data do not impinge on the domains of the CMSSM parameter space favored at the 90% confidence level in a recent likelihood analysis. However, some models with nonuniversal Higgs, squark, and slepton masses and neutralino masses $\lesssim 700\mathrm{GeV}$ are excluded by the CDMS II data.

We discuss the symmetries of quenched QCD with Wilson fermions, starting from its Lagrangian formulation, taking into account the constraints needed for convergence of the ghost-quark functional integral. We construct the corresponding chiral effective Lagrangian, including terms linear and quadratic in the lattice spacing. This allows us to study the phase structure of the quenched theory, and compare it to that in the unquenched theory. In particular we study whether there may be an Aoki phase (with parity and flavor spontaneously broken) or a first-order transition line (with no symmetry breaking but meson masses proportional to the lattice spacing), which are the two possibilities in the unquenched theory. The presence of such phase structure, and the concomitant long-range correlations, has important implications for numerical studies using both quenched and dynamical overlap and domain-wall fermions. We argue that the phase structure is qualitatively the same as in the unquenched theory, with the choice between the two possibilities depending on the sign of a parameter in the low-energy effective theory.

We study the transverse momentum spectra of fermions and bosons produced in a strong, time-dependent Abelian field. The transverse size of the Abelian field is finite, similarly to color strings and ropes. Different time-dependent field strengths are investigated in a kinetic model, and transverse momentum spectra are calculated for fermions and bosons. These spectra display exponential or polynomial behavior at high $p_T$, depending on the given time dependence. We compare our spectra to the lattice result for a classical gluon field and obtain surprisingly good agreement in certain cases.