We present a detailed study of plane waves in noncommutative abelian gauge theories. The dispersion relation is deformed from its usual form whenever a constant background electromagnetic field is present and is similar to that of an anisotropic medium with no Faraday rotation nor birefringence. When the noncommutativity is induced by the Moyal product we find that for some values of the background magnetic field no plane waves are allowed when time is noncommutative. In the Seiberg-Witten context no restriction is found. We also derive the energy-momentum tensor in the Seiberg-Witten case. We show that the generalized Poynting vector obtained from the energy-momentum tensor, the group velocity and the wave vector all point in different directions. In the absence of a constant electromagnetic background we find that the superposition of plane waves is allowed in the Moyal case if the momenta are parallel or satisfy a sort of quantization condition. We also discuss the relation between the solutions found in the Seiberg-Witten and Moyal cases showing that they are not equivalent.

We study moduli stabilization with $F$-term uplifting. As a source of uplifting $F$-term, we consider spontaneous supersymmetry breaking models, e.g. the Polonyi model and the Intriligator-Seiberg-Shih model. We analyze potential minima by requiring almost vanishing vacuum energy and evaluate the size of modulus $F$-term. We also study soft SUSY-breaking terms. In our scenario, the mirage mediation is dominant in gaugino masses. Scalar masses can be comparable with gaugino masses or much heavier, depending on couplings with spontaneous supersymmetry breaking sector.

Simple models of a classical spacetime foam are considered, which consist of identical static defects embedded in Minkowski spacetime. Plane-wave solutions of the vacuum Maxwell equations with appropriate boundary conditions at the defect surfaces are obtained in the long-wavelength limit. The corresponding dispersion relations ${\omega }^2={\omega }^2(\overrightarrow{k})$ are calculated, in particular, the coefficients of the quadratic and quartic terms in $\overrightarrow{k}$. Astronomical observations of gamma-ray bursts and ultra-high-energy cosmic rays then place bounds on the coefficients of the dispersion relations and, thereby, on particular combinations of the fundamental length scales of the static spacetime foam models considered. Spacetime foam models with a single length scale are excluded, even models with a length scale close to the Planck length (as long as a classical spacetime remains relevant).

We use on-shell recursion relations to compute analytically the one-loop corrections to maximally helicity-violating $n$-gluon amplitudes in QCD. The cut-containing parts have been computed previously; our work supplies the remaining rational parts for these amplitudes, which contain two gluons of negative helicity and the rest positive, in an arbitrary color ordering. We also present formulae specific to the six-gluon cases with helicities ($-+-+++$) and ($-++-++$), as well as numerical results for six, seven, and eight gluons. Our construction of the $n$-gluon amplitudes illustrates the relatively modest growth in complexity of the on-shell-recursive calculation as the number of external legs increases. These amplitudes add to the growing body of one-loop amplitudes known for all $n$, which are useful for studies of general properties of amplitudes, including their twistor-space structure.

Naturalness of electroweak symmetry breaking in weak scale supersymmetric theories may suggest the absence of the conventional supersymmetric desert. We present a simple, realistic framework for supersymmetry in which (most of) the virtues of the supersymmetric desert are naturally reproduced without having a large energy interval above the weak scale. The successful supersymmetric prediction for the low-energy gauge couplings is reproduced due to a gauged $R$ symmetry present in the effective theory at the weak scale. The observable sector superpotential naturally takes the form of the next-to-minimal supersymmetric standard model, but without being subject to the Landau pole constraints up to the conventional unification scale. Supersymmetry breaking masses are generated by the $F$-term and $D$-term vacuum expectation values of singlet and $U(1{)}_R$ gauge fields, as well as by anomaly mediation, at a scale not far above the weak scale. We study the resulting pattern of supersymmetry breaking masses in detail and find that it can be quite distinct. We construct classes of explicit models within this framework, based on higher-dimensional unified theories with TeV-sized extra dimensions. A similar model based on a non-$R$ symmetry is also presented. These models have a rich phenomenology at the TeV scale, and allow for detailed analyses of, e.g., electroweak symmetry breaking.

Using CLEO data, we study the production of the antideuteron, $\overline{d}$, in ${\rm Y}(nS)$ resonance decays and the nearby continuum. The branching ratios obtained are ${\mathcal{B}}^{\mathrm{dir}}({\rm Y}(1S)\to \overline{d}X)=(3.36\pm 0.23\pm 0.25)\times {10}^{-5}$, $\mathcal{B}({\rm Y}(1S)\to \overline{d}X)=(2.86\pm 0.19\pm 0.21)\times {10}^{-5}$, and $\mathcal{B}({\rm Y}(2S)\to \overline{d}X)=(3.37\pm 0.50\pm 0.25)\times {10}^{-5}$, where the “dir” superscript indicates that decays produced via reannihilation of the $b\overline{b}$ pair to a ${\gamma }^{*}$ are removed from both the signal and the normalizing number of ${\rm Y}(1S)$ decays in order to isolate direct decays of the ${\rm Y}(1S)$ to $ggg$, $gg\gamma$. Upper limits at 90% C.L. are given for $\mathcal{B}({\rm Y}(4S)\to \overline{d}X)<1.3\times {10}^{-5}$, and continuum production $\sigma (e^{+}{e}^{-}\to \overline{d}X)<0.031\mathrm{pb}$. The ${\rm Y}(2S)$ data is also used to extract a limit on ${\chi }_{bJ}\to \overline{d}X$. The results indicate enhanced deuteron production in $ggg$, $gg\gamma$ hadronization compared to ${\gamma }^{*}\to q\overline{q}$. Baryon number compensation is also investigated with the large ${\rm Y}(1S)\to \overline{d}X$ sample.

Improved staggered-fermion formulations are a popular choice for lattice QCD calculations. Historically, the algorithm used for such calculations has been the inexact $R$ algorithm, which has systematic errors that only vanish as the square of the integration step size. We describe how the exact rational hybrid Monte Carlo (RHMC) algorithm may be used in this context, and show that for parameters corresponding to current state-of-the-art computations it leads to a factor of approximately seven decrease in cost as well as having no step-size errors.

The conformal extensions of three kinds of special relativity with $ISO(1,3)/SO(1,4)/SO(2,3)$ invariance on Mink/dS/AdS space, respectively, are realized on an $SO(2,4)/{\mathbb{Z}}_2$ invariant projective null cone $[\mathcal{N}]$ as the (projective) boundary of the 5-d AdS space. The relations among the conformal Mink/dS/AdS spaces, the motions of light signals and the conformal field theories on them can be given. Thus, there should be a triality for these conformal issues and the conjectured AdS/CFT correspondence.

We derive the properties of hard thermal effective actions in gauge theories from the point of view of Schwinger’s proper time formulation. This analysis is simplified by introducing a set of generalized energy and momenta which are conserved and are nonlocal in general. These constants of motion, which embody energy-momentum exchanges between the fields and the particles along their trajectories, can be related to a class of gauge invariant or covariant potentials in the hard thermal regime. We show that in this regime the generalized energy, which is nonlocal in general, generates the characteristic nonlocal behavior of the hard thermal effective actions.

Using a Hamiltonian treatment, charged thin shells, static and dynamic, in spherically symmetric spacetimes, containing black holes or other specific types of solutions, in $d$ dimensional Lovelock-Maxwell theory are studied. The free coefficients that appear in the Lovelock theory are chosen to obtain a sensible theory, with a negative cosmological constant appearing naturally. Using an Arnowitt-Deser-Misner (ADM) description, one then finds the Hamiltonian for the charged shell system. Variation of the Hamiltonian with respect to the canonical coordinates and conjugate momenta, and the relevant Lagrange multipliers, yields the dynamic and constraint equations. The vacuum solutions of these equations yield a division of the theory into two branches, namely $d-2k-1>0$ (which includes general relativity, Born-Infeld type theories, and other generic gravities) and $d-2k-1=0$ (which includes Chern-Simons type theories), where $k$ is the parameter giving the highest power of the curvature in the Lagrangian. There appears an additional parameter $\chi =(-1{)}^{k+1}$, which gives the character of the vacuum solutions. For $\chi =1$ the solutions, being of the type found in general relativity, have a black hole character. For $\chi =-1$ the solutions, being of a new type not found in general relativity, have a totally naked singularity character. Since there is a negative cosmological constant, the spacetimes are asymptotically anti-de Sitter (AdS), and AdS when empty (for zero cosmological constant the spacetimes are asymptotically flat). The integration from the interior to the exterior vacuum regions through the thin shell takes care of a smooth junction, showing the power of the method. The subsequent analysis is divided into two cases: static charged thin shell configurations, and gravitationally collapsing charged dust shells (expanding shells are the time reversal of the collapsing shells). In the collapsing case, into an initially nonsingular spacetime with generic character or an empty interior, it is proved that the cosmic censorship is definitely upheld. Physical implications of the dynamics of such shells in a large extra dimension world scenario are also drawn. One concludes that, if such a large extra dimension scenario is correct, one can extract enough information from the outcome of those collisions as to know, not only the actual dimension of spacetime, but also which particular Lovelock gravity, general relativity or any other, is the correct one at these scales, in brief, to know $d$ and $k$.

The comprehensive formulation for loop quantum cosmology in the spatially flat, isotropic model was recently constructed. In this paper, the methods are extended to the anisotropic Bianchi I cosmology. Both the precursor and the improved strategies are applied and the expected results are established: (i) the scalar field again serves as an internal clock and is treated as emergent time; (ii) the total Hamiltonian constraint is derived by imposing the fundamental discreteness and gives the evolution as a difference equation; and (iii) the physical Hilbert space, Dirac observables, and semiclassical states are constructed rigorously. It is also shown that the state in the kinematical Hilbert space associated with the classical singularity is decoupled in the difference evolution equation, indicating that the big bounce may take place when any of the area scales undergoes the vanishing behavior. The investigation affirms the robustness of the framework used in the isotropic model by enlarging its domain of validity and provides foundations to conduct the detailed numerical analysis.

A characterization of initial data sets for the Schwarzschild spacetime is provided. This characterization is obtained by performing a $3+1$ decomposition of a certain invariant characterization of the Schwarzschild spacetime given in terms of concomitants of the Weyl tensor. This procedure renders a set of necessary conditions—which can be written in terms of the electric and magnetic parts of the Weyl tensor and their concomitants—for an initial data set to be a Schwarzschild initial data set. Our approach also provides a formula for a static Killing initial data set candidate—a KID candidate. Sufficient conditions for an initial data set to be a Schwarzschild initial data set are obtained by supplementing the necessary conditions with the requirement that the initial data set possesses a stationary Killing initial data set of the form given by our KID candidate. Thus, we obtain an algorithmic procedure of checking whether a given initial data set is Schwarzschildean or not.

We discuss the realization of inflation and resulting cosmological perturbations in the low-energy effective string theory. In order to obtain nearly scale-invariant spectra of density perturbations and a suppressed tensor-to-scalar ratio, it is generally necessary that the dilaton field $\varphi$ is effectively decoupled from gravity together with the existence of a slowly varying dilaton potential. We also study the effect of second-order corrections to the tree-level action which are the sum of a Gauss-Bonnet term coupled to $\varphi$ and a kinetic term $(\nabla \varphi {)}^4$. We find that it is possible to realize observationally supported spectra of scalar and tensor perturbations provided that the correction is dominated by the $(\nabla \varphi {)}^4$ term even in the absence of the dilaton potential. When the Gauss-Bonnet term is dominant, tensor perturbations exhibit violent negative instabilities on small scales about a de Sitter background in spite of the fact that scale-invariant scalar perturbations can be achieved.

The large-volume liquid-scintillator detector LENA (low energy neutrino astronomy) will provide high-grade background discrimination and enable the detection of diffuse supernova neutrinos (DSN) in an almost background-free energy window from $\sim 10$ to 25 MeV. Within ten years of exposure, it will be possible to derive significant constraints on both core-collapse supernova models and the supernova rate in the near universe up to redshifts $z<2$.

We report the results of a detailed numerical analysis of a real resonant spherical gravitational wave antenna operating with six resonant two-mode capacitive transducers read out by superconducting quantum interference devices (SQUID) amplifiers. We derive a set of equations to describe the electromechanical dynamics of the detector. The model takes into account the effect of all the noise sources present in each transducer chain: the thermal noise associated with the mechanical resonators, the thermal noise from the superconducting impedance matching transformer, the backaction noise, and the additive current noise of the SQUID amplifier. Asymmetries in the detector signal-to-noise ratio and bandwidth, coming from considering the transducers not as pointlike objects but as a sensor with physically defined geometry and dimension, are also investigated. We calculate the sensitivity for an ultracryogenic, 30 ton, 2 m in diameter, spherical detector with optimal and nonoptimal impedance matching of the electrical readout scheme to the mechanical modes. The results of the analysis are useful not only to optimize existing smaller mass spherical detector like MiniGrail, in Leiden, but also as a technological guideline for future massive detectors. Furthermore we calculate the antenna patterns when the sphere operates with one, three, and six transducers. The sky coverage for two detectors based in The Netherlands and Brazil and operating in coincidence is also estimated. Finally, we describe and numerically verify a calibration and filtering procedure useful for diagnostic and detection purposes in analogy with existing resonant bar detectors.

The timelike form factor of the charged kaon is evaluated at $|Q^2|=M^2(J/\psi )=9.59{\mathrm{GeV}}^2$ by relating it to $\mathcal{B}(J/\psi \to K^{+}{K}^{-})$, $\mathcal{B}(J/\psi \to K_S{K}_L)$ and $\mathcal{B}(J/\psi \to e^{+}{e}^{-})$. The resulting value, $|Q^2|F_K(9.59{\mathrm{GeV}}^2)=0.81\pm 0.18{\mathrm{GeV}}^2$ is found to be in good agreement with $|Q^2|F_K(13.5{\mathrm{GeV}}^2)=0.85\pm 0.05{\mathrm{GeV}}^2$ obtained recently by the direct measurement of the reaction $e^{+}{e}^{-}\to K^{+}{K}^{-}$.

We present the calculations of the supersymmetric QCD corrections to the total cross sections for single top production at the Fermilab Tevatron and the CERN Large Hadron Collider in the minimal supersymmetric standard model. Our results show that, for the $s$-channel and $t$-channel, the supersymmetric QCD corrections are at most about 1%, but for the associated production process $pp\to tW$, the supersymmetric QCD corrections increase the total cross sections significantly, which can reach about 6% for most values of the parameters. Thus, the supersymmetric QCD corrections should be taken into consideration in future high precision experimental analyses for top physics.

We calculate the branching ratios and $CP$-violating asymmetries for $B^0\to K^0{\overline{K}}^{*0}$, ${\overline{K}}^0{K}^{*0}$, $K^{+}{K}^{*-}$, $K^{-}{K}^{*+}$, and $B^{+}\to K^{+}{\overline{K}}^{*0}$, and ${\overline{K}}^0{K}^{*+}$ decays by employing the low energy effective Hamiltonian and the perturbative QCD (pQCD) factorization approach. The theoretical predictions for the branching ratios are $\mathrm{Br}(B^0/{\overline{B}}^0\to K^{\pm }{K}^{*\mp })\approx 7.4\times {10}^{-8}$, $\mathrm{Br}(B^0/{\overline{B}}^0\to K^0{\overline{K}}^{*0}({\overline{K}}^0{K}^{*0}))\approx 19.6\times {10}^{-7}$, $\mathrm{Br}(B^{+}\to K^{+}{\overline{K}}^{*0})\approx 3\times {10}^{-7}$ and $\mathrm{Br}(B^{+}\to K^{*+}{\overline{K}}^0)\approx 18.3\times {10}^{-7}$, which are consistent with currently available experimental upper limits. We also predict large $CP$-violating asymmetries in these decays: $A_{\mathrm{CP}}^{\mathrm{dir}}(K^{\pm }{\overline{K}}^{*0})\approx -20\%$, $A_{\mathrm{CP}}^{\mathrm{dir}}(K^{*\pm }{\overline{K}}^0)\approx -49\%$, which can be tested by the forthcoming $B$ meson experiments.

We calculate the $CP$-averaged branching ratios and $CP$-violating asymmetries for $B^0\to \eta \eta$, $\eta {\eta }^{\prime }$ and ${\eta }^{\prime }{\eta }^{\prime }$ decays by employing the perturbative QCD (pQCD) factorization approach. The pQCD predictions for the $CP$-averaged branching ratios are $\mathrm{Br}(B^0\to \eta \eta )\approx 0.67\times {10}^{-7}$, $\mathrm{Br}(B^0\to \eta {\eta }^{\prime })\approx 0.18\times {10}^{-7}$, and $\mathrm{Br}(B^0\to {\eta }^{\prime }{\eta }^{\prime })\approx 0.11\times {10}^{-7}$, which are consistent with currently available experimental upper limits. We also predict large $CP$-violating asymmetries for the considered three decay modes, which can be tested by the future $B$ meson experiments.

We present measurements of the branching fractions for the charmless two-body decays $B^0\to {\pi }^{+}{\pi }^{-}$ and $B^0\to K^{+}{\pi }^{-}$, and a search for the decay $B^0\to K^{+}{K}^{-}$. We include the effects of final-state radiation from the daughter mesons for the first time, and quote branching fractions for the inclusive processes $B^0\to h^{+}{h}^{\prime -}n\gamma$, where $h$ and $h^{\prime }$ are pions or kaons. The maximum value of the sum of the energies of the $n$ undetected photons, $E_{\gamma }^{\max }$, is mode-dependent. Using a data sample of approximately $227\times {10}^6$ $\mathit{{\rm Y}}(4S)\to B\overline{B}$ decays collected with the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider at SLAC, we measure: $\mathcal{B}(B^0\to {\pi }^{+}{\pi }^{-}n\gamma ;E_{\gamma }^{\max }=150\mathrm{MeV})=(5.1\pm 0.4\pm 0.2)\times {10}^{-6}$, $\mathcal{B}(B^0\to K^{+}{\pi }^{-}n\gamma ;E_{\gamma }^{\max }=105\mathrm{MeV})=(18.1\pm 0.6\pm 0.6)\times {10}^{-6}$, $\mathcal{B}(B^0\to K^{+}{K}^{-}n\gamma ;E_{\gamma }^{\max }=59\mathrm{MeV})<0.5\times {10}^{-6}(90\%\mathrm{\text{confidence level}})$, where the first uncertainty is statistical and the second is systematic. Theoretical calculations can be used to extrapolate from the above measurements the nonradiative branching fractions, ${\mathcal{B}}^0$. Using one such calculation, we find: ${\mathcal{B}}^0(B^0\to {\pi }^{+}{\pi }^{-})=(5.5\pm 0.4\pm 0.3)\times {10}^{-6}$, ${\mathcal{B}}^0(B^0\to K^{+}{\pi }^{-})=(19.1\pm 0.6\pm 0.6)\times {10}^{-6}$, ${\mathcal{B}}^0(B^0\to K^{+}{K}^{-})<0.5\times {10}^{-6}(90\%\mathrm{\text{confidence level}})$. Meaningful comparison between theory and experiment, as well as combination of measurements from different experiments, can be performed only in terms of these nonradiative quantities.