We study the effective monopole action obtained in the maximal Abelian projection of the quenched SU(2) lattice QCD. We determine the quadratic part of the lattice action using analytical blocking from the continuum dual superconductor model to the lattice model. The leading contribution to the quadratic action depends explicitly on the value of the monopole condensate. We show that the analytical monopole action matches the numerically obtained action in quenched SU(2) QCD with a good accuracy. The comparison of numerical and analytical results gives us the value of the monopole condensate in quenched SU(2) QCD, $\eta =243\mathrm{}\left(42\right)\mathrm{}\mathrm{MeV}.$

We discuss all contributions from the Zweig-rule-satisfying SU(3)-breaking final state interactions (FSIs) in the $\overrightarrow{B}\mathrm{PP}$ decays (neglecting charmed intermediate states), where $PP=\pi \pi ,$ $\pi K,$ $K\overline{K},$ $\pi \eta \left({\eta }^{\prime }\right),$ and $K\eta \left({\eta }^{\prime }\right).\mathrm{}$ First, the effects of SU(3) breaking in rescattering through Pomeron exchange are studied. Then, after making a plausible assumption concerning the pattern of SU(3) breaking in non-Pomeron FSIs, we give general formulas for how the latter modify short-distance (SD) amplitudes. In the SU(3) limit, these formulas depend on three effective parameters characterizing the strength of all non-Pomeron rescattering effects. We point out that the experimental bounds on the $\overrightarrow{B}{K}^{+}{K}^{-}$ branching ratio may limit the value of only one of these FSI parameters. Thus, the smallness of the $\overrightarrow{B}{K}^{+}{K}^{-}$ decay rate does not imply negligible rescattering effects in other decays. Assuming a vanishing value of this parameter, we perform various fits to the available $\overrightarrow{B}\mathrm{PP}$ branching ratios. The fits determine the quark-diagram SD amplitudes, the two remaining FSI parameters and the weak angle $\gamma .$ While the set of all $\overrightarrow{B}\mathrm{PP}$ branching ratios is well described with $\gamma$ around its expected standard model (SM) value, the fits permit other values of $\gamma$ as well. For a couple of such good fits, we predict asymmetries for the $\overrightarrow{B}K\pi ,$ ${\pi }^{+}\eta \left({\eta }^{\prime }\right),$ $K^{+}\eta \left({\eta }^{\prime }\right)$ decays as well as the values of the CP-violating parameters $S_{\pi \pi }$ and $C_{\pi \pi }$ for the time-dependent rate of $B^0\mathrm{}\left(t\right)\mathrm{}\to {\pi }^{+}{\pi }^{-}.$ Apart from a problem with the recent $B^{+}\to {\pi }^{+}\eta$ asymmetry measurement, comparison with the data seems to favor the values of $\gamma$ in accordance with SM expectations.

We explore the phenomenology of, and models for, the $Z^{*}$ resonances, the lowest of which is now well established, and called the $\Theta .$ We provide an overview of three models which have been proposed to explain its existence and/or its small width, and point out other relevant predictions and potential problems, for each. The relation to what is known about KN scattering, including possible resonance signals in other channels, is also discussed.

We examine spherical p-branes in ${\mathrm{AdS}}_m\times {\mathrm{S}}^n$ that wrap an $S^p$ in either ${\mathrm{AdS}}_m$ $(p=m-2)$ or ${\mathrm{S}}^n$ $(p=n-2).$ We first construct a two-spin giant solution expanding in ${\mathrm{S}}^n$ and has spins both in ${\mathrm{AdS}}_m$ and ${\mathrm{S}}^n.$ For $\mathrm{}(m,n)=\{\mathrm{}(5,5),(4,7),(7,4)\mathrm{}\},$ it is 1/2 supersymmetric, and it reduces to the single-spin giant graviton when the AdS spin vanishes. We study some of its basic properties such as instantons, noncommutativity, zero modes, and the perturbative spectrum. All vibration modes have real and positive frequencies determined uniquely by the spacetime curvature, and evenly spaced. We next consider the (0+1)-dimensional sigma models obtained by keeping generally time-dependent transverse coordinates, describing a warped product of a breathing mode and a point particle on ${\mathrm{S}}^n$ or ${\mathrm{AdS}}_m\times {\mathrm{S}}^1.$ The Bogomol’nyi-Prasad-Sommerfield bounds show that the only spherical supersymmetric solutions are the single and the two-spin giants. Moreover, we integrate the sigma model and separate the canonical variables. We quantize exactly the point-particle part of the motion, which in local coordinates gives Pöschl-Teller type potentials, and calculate its contribution to the anomalous dimension.

Using a proper time technique, the quadratic response tensor (3-point vertex) in the electromagnetic vacuum is derived from which the scattering amplitudes for photon splitting are obtained for arbitrary fields. In the low frequency limit of the nondispersive vacuum, compact expressions for the scattering amplitudes are obtained whereupon two specific limits are evaluated: one in which both fields are weak and the other in which the electric field is weak and $B\gg E.\mathrm{}$ In the latter limit, for ${E/E}_{\mathrm{cr}}\sim {0.01B/B}_{\mathrm{cr}}$ and $B\gtrsim {5B}_{\mathrm{cr}},$ a new splitting mode, absent in the pure magnetic case, has a rate exceeding that of the previously dominant pure magnetic $\overrightarrow{\perp }\Vert \Vert$ splitting mode. At these stronger electric fields, the process of spontaneous pair production becomes important enough to require consideration. Although it is unlikely that neutron stars with $B\gg B_{\mathrm{cr}}$ and long periods (magnetars) have parallel electric fields of this strength, their progenitors may have. Other candidates include $\gamma$-ray bursters and strange stars. The low frequency results were verified using the Heisenberg-Euler Lagrangian approach.

Considering the Barrett-Crane spin foam model for quantum gravity with a (positive) cosmological constant, we show that speeds must be quantized, and we investigate the physical implications of this effect such as the emergence of an effective deformed Poincaré symmetry.

A Hamiltonian treatment of the gravitational collapse of thin shells is presented. The direct integration of the canonical constraints reproduces the standard shell dynamics for a number of known cases. The formalism is applied in detail to three-dimensional spacetime and the properties of the $\mathrm{}(2+1)\mathrm{}$-dimensional charged black hole collapse are further elucidated. The procedure is also extended to deal with rotating solutions in three dimensions. The general form of the equations providing the shell dynamics implies the stability of black holes, as they cannot be converted into naked singularities by any shell collapse process.

A new framework for exploiting information about the renormalization group (RG) behavior of gravity in a dynamical context is discussed. The Einstein-Hilbert action is RG improved by replacing Newton’s constant and the cosmological constant by scalar functions in the corresponding Lagrangian density. The position dependence of G and $\Lambda$ is governed by a RG equation together with an appropriate identification of RG scales with points in spacetime. The dynamics of the fields G and $\Lambda$ does not admit a Lagrangian description in general. Within the Lagrangian formalism for the gravitational field they have the status of externally prescribed “background” fields. The metric satisfies an effective Einstein equation similar to that of Brans-Dicke theory. Its consistency imposes severe constraints on allowed backgrounds. In the new RG framework, G and $\Lambda$ carry energy and momentum. It is tested in the setting of homogeneous-isotropic cosmology and is compared to alternative approaches where the fields G and $\Lambda$ do not carry gravitating 4-momentum. The fixed point regime of the underlying RG flow is studied in detail.

We perform a detailed comparison of the Wilkinson Microwave Anisotropy Probe measurements of the cosmic microwave background (CMB) temperature and polarization anisotropy with the predictions of quintessence cosmological models of dark energy. We consider a wide range of quintessence models, including a constant equation of state, a simply parametrized, time-evolving equation of state, a class of models of early quintessence, and scalar fields with an inverse-power law potential. We also provide a joint fit to the Cosmic Background Imager (CBI) and Arcminute Cosmology Bolometer Array Receiver (ACBAR) CMB data, and the type 1a supernovae. Using these select constraints we identify viable, target models which should prove useful for numerical studies of large scale structure formation, and to rapidly estimate the impact to the concordance region when new or improved observations become available.

We extract parameters relevant for distinguishing among single-field inflation models from the Wilkinson Microwave Anisotropy Probe (WMAP) data set, and from a combination of the WMAP data and seven other cosmic microwave background (CMB) experiments. We use only CMB data and perform a likelihood analysis over a grid of models, including the full error covariance matrix. We find that a model with a scale-invariant scalar power spectrum $\mathrm{}(n=1\mathrm{}),$ no tensor contribution, and no running of the spectral index, is within the 1-$\sigma$ contours of both data sets. We then apply the Monte Carlo reconstruction technique to both data sets to generate an ensemble of inflationary potentials consistent with observations. None of the three basic classes of inflation models (small-field, large-field, and hybrid) are completely ruled out, although hybrid models are favored by the best-fit region. The reconstruction process indicates that a wide variety of smooth potentials for the inflaton are consistent with the data, implying that the first-year WMAP result is still too crude to constrain significantly either the height or the shape of the inflaton potential. In particular, the lack of evidence for tensor fluctuations makes it impossible to constrain the energy scale of inflation. Nonetheless, the data rule out a large portion of the available parameter space for inflation. For instance, we find that potentials of the form $V=\lambda {\phi }^4$ are ruled out to $3\sigma$ by the combined data set, but not by the WMAP data taken alone.

It is intriguing to consider the possibility that the big bang of the standard (3+1)-dimensional cosmology originated from the collision of two branes within a higher dimensional spacetime, leading to the production of a large amount of entropy. In this paper we study, subject to certain well-defined assumptions, under what conditions such a collision leads to an expanding universe. We assume the absence of novel physics, so that ordinary (4+1)-dimensional Einstein gravity remains a valid approximation. It is necessary that the fifth dimension not become degenerate at the moment of collision. First the case of a symmetric collision of infinitely thin branes having a hyperbolic or flat spatial geometry is considered. We find that a symmetric collision results in a collapsing universe on the final brane unless the preexisting expansion rate in the bulk just prior to the collision is sufficiently large in comparison to the momentum transfer in the fifth dimension. Such prior expansion may either result from negative spatial curvature or from a positive five-dimensional cosmological constant. The relevance of these findings to the colliding bubble braneworld universe scenario is discussed. Finally, results from a numerical study of colliding thick-wall branes is presented, which confirm the results of the thin-wall approximation.

This paper describes the computation of cosmic microwave background (CMB) anisotropies in a universe with multiconnected spatial sections and focuses on the implementation of the topology in standard CMB computer codes. The key ingredient is the computation of the eigenmodes of the Laplacian with boundary conditions compatible with multiconnected space topology. The correlators of the coefficients of the decomposition of the temperature fluctuation in spherical harmonics are computed and examples are given for spatially flat spaces and one family of spherical spaces, namely, the lens spaces. Under the hypothesis of Gaussian initial conditions, these correlators encode all the topological information of the CMB and suffice to simulate CMB maps.

We show that, under general assumptions, in six-dimensional brane-world models with compactified large extra dimensions, the energy density of brane oscillations scales as that of cold dark matter and its present value is compatible with observations. This value is obtained from the only dimensional scale in the theory, namely, the fundamental scale of gravity in six dimensions $M_6\sim 1\mathrm{TeV},$ without any fine-tuning or the introduction of additional mass scales apart from the large size of the extra dimensions. It has been suggested that the same kind of model could provide also the correct magnitude of the cosmological constant. This observation might be relevant for the resolution of the cosmic coincidence problem in the brane-world scenario.

In the CP-invariant supersymmetric theories, the steep S-wave (slow P-wave) rise of the cross section for any nondiagonal neutralino pair production in $e^{+}{e}^{-}$ annihilation, $e^{+}{e}^{-}\to {\tilde{\chi }}_i^0{\tilde{\chi }}_j^0\left(i\ne j\right),$ near threshold is accompanied by the slow P-wave (steep S-wave) decrease of the fermion invariant mass distribution of the three-body neutralino decay, ${\tilde{\chi }}_i^0\to {\tilde{\chi }}_j^{0}f\overline{f}$ $(f=l$ or $q),$ near the end point. These selection rules, unique to the neutralino system due to its Majorana nature, guarantee that the observation of simultaneous sharp S-wave excitations of the production cross section near threshold and the lepton or quark invariant mass distribution near the end point is qualitative, unambiguous evidence for CP violation in the neutralino system.

We explore the influence of open-charm channels on charmonium properties and profile the $1^3{D}_2,$ $1^3{D}_3,$ and $2^1{P}_1$ charmonium candidates for $X\left(3872\right).$ The favored candidates, the $1^3{D}_2$ and $1^3{D}_3$ levels, both have prominent radiative decays. The $1^3{D}_2$ might be visible in the $D^0{D}^{*0}$ channel, while the dominant decay of the $1^3{D}_3$ state should be into $D\overline{D}.$ We propose that additional discrete charmonium levels can be discovered as narrow resonances of charmed and anticharmed mesons.

Two theories of special relativity with an additional invariant scale, “doubly special relativity,” are tested with calculations of particle process kinematics. Using the Judes-Visser modified conservation laws, thresholds are studied in both theories. In contrast with some linear approximations, which allow for particle processes forbidden in special relativity, both the Amelino-Camelia and Magueijo-Smolin frameworks allow no additional processes. To first order, the Amelino-Camelia framework thresholds are lowered and the Magueijo-Smolin framework thresholds may be raised or lowered.

Using equations of motion accurate to the third post-Newtonian (3PN) order $[{O(v/c)\mathrm{}}^6$ beyond Newtonian gravity], we derive expressions for the total energy E and angular momentum J of the orbits of compact binary systems (black holes or neutron stars) for arbitrary orbital eccentricity. We also incorporate finite-size contributions such as spin-orbit and spin-spin coupling, and rotational and tidal distortions, calculated to the lowest order of approximation, but we exclude the effects of gravitational radiation damping. We describe how these formulas may be used as an accurate diagnostic of the physical content of quasiequilibrium configurations of compact binary systems of black holes and neutron stars generated using numerical relativity. As an example, we show that quasiequilibrium configurations of corotating neutron stars recently reported by Miller et al. can be fit by our diagnostic to better than one percent with a circular orbit and with physically reasonable tidal coefficients.

We consider primordial non-Gaussianity due to quadratic corrections in the gravitational potential parametrized by a nonlinear coupling parameter $f_{\mathrm{NL}}.$ We study constraints on $f_{\mathrm{NL}}$ from measurements of the galaxy bispectrum in redshift surveys. Using estimates for idealized survey geometries of the 2dF and SDSS surveys and realistic ones from SDSS mock catalogs, we show that it is possible to probe $|f_{\mathrm{NL}}|\simeq 100,$ after marginalization over bias parameters. We apply our methods to the galaxy bispectrum measured from the PSCz survey, and obtain a $2\sigma$ constraint $|f_{\mathrm{NL}}|\lesssim 1800.$ We estimate that an all sky redshift survey up to $z\simeq 1$ can probe $|f_{\mathrm{NL}}|\simeq 1.$ We also consider the use of cluster abundance to constrain $f_{\mathrm{NL}}$ and find that in order to be sensitive to $|f_{\mathrm{NL}}|\simeq 100,$ cluster masses need to be determined with an accuracy of a few percent, assuming perfect knowledge of the mass function and cosmological parameters.

It has recently been suggested that an isotropic singularity may be a generic feature of brane cosmologies, even in the inhomogeneous case. Using the covariant and gauge-invariant approach we present a detailed analysis of linear perturbations of the isotropic model ${\mathcal{F}}_b,$ which is a past attractor in the phase space of homogeneous Bianchi models on the brane. We find that for matter with an equation of state parameter $\gamma >1,$ the dimensionless variables representing generic anisotropic and inhomogeneous perturbations decay as $\overrightarrow{t}0,$ showing that the model ${\mathcal{F}}_b$ is asymptotically stable in the past. We conclude that brane universes are born with isotropy naturally built-in, contrary to standard cosmology. The observed large-scale homogeneity and isotropy of the Universe can therefore be explained as a consequence of the initial conditions if the braneworld paradigm represents a description of the very early Universe.

While the naive factorization assumption works well for many two-body nonleptonic B meson decay modes, the recent measurement of $\overline{B}\to D^{\left(*\right)0\mathrm{}}{M}^0$ with $M=\pi ,$ $\rho ,$ and $\omega$ shows a large deviation from this assumption. We analyze the $\overrightarrow{B}{D}^{\left(*\right)}M$ decays in the perturbative QCD approach based on the $k_T$ factorization theorem, in which both factorizable and nonfactorizable contributions can be calculated in the same framework. Our predictions for the Bauer-Stech-Wirbel parameters, $|a_2{/a}_1|=0.43\mathrm{}\pm 0.04$ and $\mathrm{Arg}{(a}_2{/a}_1)\sim -42°$ and $|a_2{/a}_1|=0.47\mathrm{}\pm 0.05$ and $\mathrm{Arg}{(a}_2{/a}_1)\sim -41°,$ are consistent with the observed $\overrightarrow{B}D\pi$ and $\overrightarrow{B}{D}^{*}\pi$ branching ratios, respectively. It is found that the large magnitude $|a_2|$ and the large relative phase between $a_2$ and $a_1$ come from color-suppressed nonfactorizable amplitudes. Our predictions for the $B^0\to D^{*0}{\rho }^0{,D}^{*0}\omega$ branching ratios can be confronted with future experimental data.