The Newman-Penrose formalism may be used in numerical relativity to extract coordinate-invariant information about gravitational radiation emitted in strong-field dynamical scenarios. The main challenge in doing so is to identify a null tetrad appropriately adapted to the simulated geometry such that Newman-Penrose quantities computed relative to it have an invariant physical meaning. In black hole perturbation theory, the Teukolsky formalism uses such adapted tetrads, those which differ only perturbatively from the background Kinnersley tetrad. At late times, numerical simulations of astrophysical processes producing isolated black holes ought to admit descriptions in the Teukolsky formalism. However, adapted tetrads in this context must be identified using only the numerically computed metric, since no background Kerr geometry is known a priori. To do this, this paper introduces the notion of a quasi-Kinnersley frame. This frame, when space-time is perturbatively close to Kerr, approximates the background Kinnersley frame. However, it remains calculable much more generally, in space-times nonperturbatively different from Kerr. We give an explicit solution for the tetrad transformation which is required in order to find this frame in a general space-time.

The Teukolsky formalism of black hole perturbation theory describes weak gravitational radiation generated by a mildly dynamical hole near equilibrium. A particular null tetrad of the background Kerr geometry, due to Kinnersley, plays a singularly important role within this formalism. In order to apply the rich physical intuition of Teukolsky’s approach to the results of fully nonlinear numerical simulations, one must approximate this Kinnersley tetrad using raw numerical data, with no a priori knowledge of a background. This paper addresses this issue by identifying the directions of the tetrad fields in a quasi-Kinnersley frame. This frame provides a unique, analytic extension of Kinnersley’s definition for the Kerr geometry to a much broader class of space-times including not only arbitrary perturbations, but also many examples which differ nonperturbatively from Kerr. This paper establishes concrete limits delineating this class and outlines a scheme to calculate the quasi-Kinnersley frame in numerical codes based on the initial-value formulation of geometrodynamics.

The production and decay of the $X(3872)$ are analyzed under the assumption that the $X$ is a weakly bound molecule of the charm mesons $D^0{\overline{D}}^{*0}$ and $D^{*0}{\overline{D}}^0$. The decays imply that the large $D^0{\overline{D}}^{*0}$ scattering length has an imaginary part. An effective field theory for particles with a large complex scattering length is used to derive factorization formulas for production rates and decay rates of $X$. If a partial width is calculated in a model with a particular value of the binding energy, the factorization formula can be used to extrapolate to other values of the binding energy and to take into account the width of the $X$. The factorization formulas relate the rates for production of $X$ to those for production of $D^0{\overline{D}}^{*0}$ and $D^{*0}{\overline{D}}^0$ near threshold. They also imply that the line shape of $X$ differs significantly from that of a Breit-Wigner resonance.

We propose to use the rescaled range analysis to examine the records of rapidity-dependence of multiplicities in high-energy collision processes. We probe event by event the existence of global statistical dependence in the system of produced hadrons, and demonstrate the effectiveness of the above-mentioned statistical method by applying it to the cosmic-ray data of the JACEE collaboration, and by comparing the obtained results with other experimental results for similar reactions at accelerator and collider energies. We present experimental evidence for the validity of Hurst’s empirical law, and the evidence for the existence of global statistical dependence, fractal dimension, and scaling behavior in such systems of hadronic matter. None of these features is directly related to the basis of the conventional physical picture. Hence, it is not clear whether (and if yes, how and why) these striking empirical regularities can be understood in terms of the conventional theory.

We find supergravity solutions corresponding to all $U(1)\times U(1)$ invariant chiral primaries of the D1-D5-KK system. These solutions are 1/8 BPS, carry angular momentum, and are asymptotically flat in the $3+1$ dimensional sense. They can be thought of as representing the ground states of the four-dimensional black hole constructed from the D1-D5-KK-P system. Demanding the absence of unphysical singularities in our solutions determines all free parameters, and gives precise agreement with the quantum numbers expected from the CFT point of view. The physical mechanism behind the smoothness of the solutions is that the D1 branes and D5 branes expand into a KK-monopole supertube in the transverse space of the original KK monopole.

Light deflection in the postlinear gravitational field of two bounded pointlike masses is treated. Both the light source and the observer are assumed to be located at infinity in an asymptotically flat space. The equations of light propagation are explicitly integrated to the second order in $G/c^2$. Some of the integrals are evaluated by making use of an expansion in powers of the ratio of the relative separation distance to the impact parameter $(r_{12}/\xi )$. A discussion of which orders must be retained to be consistent with the expansion in terms of $G/c^2$ is given. It is shown that the expression obtained in this paper for the angle of light deflection is fully equivalent to the expression obtained by Kopeikin and Schäfer up to the order given there. The deflection angle takes a particularly simple form for a light ray originally propagating orthogonal to the orbital plane of a binary with equal masses. Application of the formulas for the deflection angle to the double pulsar PSR J0737-3039 for an impact parameter 5 times greater than the relative separation distance of the binary’s components shows that the corrections to the Epstein-Shapiro light deflection angle of about ${10}^{-6}\mathrm{arcsec}$ lie between ${10}^{-7}$ and ${10}^{-8}\mathrm{arcsec}$.

Fluctuations in the mass and decay rate of a heavy particle which for some period dominates the energy density of the Universe are known to lead to adiabatic density perturbations. We show that generically the annihilation cross section of the same particle also receives fluctuations, which leads to entropy perturbations at freeze-out. If the particle comes to dominate the energy density of the Universe and subsequently decays, this leads to an additional source of adiabatic density perturbations. On the other hand, nonadiabatic density perturbations result when the particle does not decay but contributes to the observed dark matter.

We show that the isocurvature perturbations imply that the gravitationally produced superheavy dark matter must have masses larger than a few times the Hubble expansion rate at the end of inflation. This together with the bound on tensor to scalar contribution to the CMB induces a lower bound on the reheating temperature for superheavy dark matter to be about ${10}^7\mathrm{GeV}$. Hence, if the superheavy dark-matter scenario is embedded in supergravity models with gravity mediated supersymmetry breaking, the gravitino bound will squeeze this scenario. Furthermore, the CMB constraint strengthens the statement that a gravitationally produced superheavy dark-matter scenario prefers a relatively large tensor mode amplitude if the reheating temperature must be less than ${10}^9\mathrm{GeV}$.

Claims concerning the possible discovery of the ${\Theta }^{+}$ pentaquark, with minimal quark content $uudd\overline{s}$, have motivated our comprehensive study into possible pentaquark states using lattice QCD. We review various spin-$\frac{1}{2}$ pentaquark interpolating fields in the literature and create a new candidate ideal for lattice QCD simulations. Using these interpolating fields we attempt to isolate a signal for a five-quark resonance. Calculations are performed using improved actions on a large ${20}^3\times 40$ lattice in the quenched approximation. The standard lattice resonance signal of binding at quark masses near the physical regime, observed for established baryon resonances, is not observed for spin-$\frac{1}{2}$ pentaquark states. Thus we find no evidence supporting the existence of a spin-$\frac{1}{2}$ pentaquark resonance in quenched QCD.

We consider the effects of a light quark mass in the soft-collinear effective theory (SCET) and we apply them to $\overline{B}\to X_s\gamma$ in the end point region. We find that the reparameterization invariance can be extended by including the collinear quark mass in the SCET Lagrangian. This symmetry constrains the theory with the quark mass terms, and we present explicit results at one loop. It also relates the Wilson coefficients of some mass operators to those of the leading operators, which are useful in organizing the subleading effects due to the quark mass in $\overline{B}\to X_s\gamma$. We present strange quark mass corrections to $\overline{B}\to X_s\gamma$ in the end point region as an application. The forward scattering amplitude from the mass corrections is factorized, and it can be expressed as a convolution of the $m_s^2/p_X^2$-suppressed jet function and the leading-order shape function of the $B$ meson. This contribution should be added to the existing subleading contributions from the $B$ meson shape functions to obtain complete subleading corrections.

Electromagnetic energy loss of tau leptons is an important ingredient for eventual tau neutrino detection from high energy astrophysical sources. Proposals have been made to use mountains as neutrino converters, in which the emerging tau decays in an air shower. We use a stochastic evaluation of both tau neutrino conversion to taus and of tau electromagnetic energy loss. We examine the effects of the propagation for monoenergetic incident tau neutrinos as well as for several neutrino power-law spectra. Our main result is a parameterization of the tau electromagnetic energy loss parameter $\beta$. We compare the results from the analytic expression for the tau flux using this $\beta$ with other parameterizations of $\beta$.

We examine the light-front zero-mode contribution to the good ($+$) current matrix elements between pseudoscalar and vector mesons. In particular, we discuss the transition form factor $f(q^2)$ which has been suspected to have the light-front zero-mode contribution. While the zero-mode contribution in principle depends on the form of the vector meson vertex ${\Gamma }^{\mu }={\gamma }^{\mu }-(P_V-2k{)}^{\mu }/D$, the form factor $f(q^2)$ is found to be free from the zero-mode contribution if the denominator $D$ contains the term proportional to the light-front energy $(k^{-}{)}^n$ with the power $n>0$. The lack of zero-mode contribution benefits the light-front quark model phenomenology. We present our numerical calculations for the $B\to \rho$ transition.

We find exact tachyon kink solutions of Dirac-Born-Infeld–type effective action describing an unstable D5-brane with a world volume gauge field turned on in a curved background. The background of interest is the ten-dimensional lift of the Salam-Sezgin vacuum and, in the asymptotic limit, it approaches ${\mathrm{R}}^{1,4}\times {\mathrm{T}}^2\times {\mathrm{S}}^3$. The solutions are identified as composites of lower-dimensional D-branes and fundamental strings, and, in the BPS limit, they become a D4D2F1 composite wrapped on ${\mathrm{R}}^{1,2}\times {\mathrm{T}}^2$ where ${\mathrm{T}}^2$ is inside ${\mathrm{S}}^3$. In one class of solutions we find an infinite degeneracy with respect to a constant magnetic field along the direction of the Neveu-Schwarz–Neveu-Schwarz field on ${\mathrm{S}}^3$.

Motivated by recent discussions of the string-theory landscape, we propose field-theoretic realizations of models with large numbers of vacua. These models contain multiple $U(1)$ gauge groups, and can be interpreted as deconstructed versions of higher-dimensional gauge theory models with fluxes in the compact space. We find that the vacuum structure of these models is very rich, defined by parameter-space regions with different classes of stable vacua separated by boundaries. This allows us to explicitly calculate physical quantities such as the supersymmetry-breaking scale, the presence or absence of $R$ symmetries, and probabilities of stable versus unstable vacua. Furthermore, we find that this landscape picture evolves with energy, allowing vacua to undergo phase transitions as they cross the boundaries between different regions in the landscape. We also demonstrate that supergravity effects are crucial in order to stabilize most of these vacua, and in order to allow the possibility of canceling the cosmological constant.

We present an extension of the twistor-motivated MHV vertices and accompanying rules presented by Cachazo, Svrček and Witten to the construction of vector-boson currents coupling to an arbitrary source. In particular, we give rules for constructing off-shell vector-boson currents with one fermion pair and $n$ gluons of arbitrary helicity. These currents may be employed directly in the computation of electroweak amplitudes. The rules yield expressions in agreement with previously-obtained results for $Z,W,{\gamma }^{*}\to \overline{q}q+n$ gluons (analytically up to $n=3$, beyond via the Berends-Giele recursion relations). We also confirm that the contribution to a seven-point amplitude containing the nonabelian triple vector-boson coupling obtained using the next-to-MHV currents matches the previous result in the literature.

We study cosmology in the five-dimensional Randall-Sundrum brane world with a stabilizing effective potential for the radion and matter localized on the branes. The analysis is performed by employing a perturbative expansion in the ratio $\rho /V$ between the matter energy density on the branes and the brane tensions around the static Randall-Sundrum solution (which has $\rho =0$ and brane tensions $\pm V$). This approach ensures that the matter evolves adiabatically and allows us to find approximate solutions to second order in $\rho /V$. Some particular cases are then analyzed in detail.

A general framework is presented for supersymmetric theories that do not suffer from fine-tuning in electroweak symmetry breaking. Supersymmetry is dynamically broken at a scale $\Lambda \approx (10–100)\mathrm{TeV}$, which is transmitted to the supersymmetric standard model sector through standard model gauge interactions. The dynamical supersymmetry-breaking sector possesses an approximate global $SU(5)$ symmetry, whose $SU(3)\times SU(2)\times U(1)$ subgroup is explicitly gauged and identified as the standard model gauge group. This $SU(5)$ symmetry is dynamically broken at the scale $\Lambda$, leading to pseudo-Goldstone boson states, which we call xyons. We perform a detailed estimate for the xyon mass and find that it is naturally in the multi-TeV region. We study general properties of xyons, including their lifetime, and study their collider signatures. A generic signature is highly ionizing tracks caused by stable charged bound states of xyons, which may be observed at the CERN LHC. We also consider cosmology in our scenario and find that a consistent picture can be obtained. Our framework is general and does not depend on the detailed structure of the Higgs sector, nor on the mechanism of gaugino-mass generation.

We compute spin-dependent decay matrix elements for $S$-wave charmonium and bottomonium in lattice nonrelativistic quantum chromodynamics (NRQCD). Particular emphasis is placed upon the color-octet matrix elements, since the corresponding production matrix elements are expected to appear in the dominant contributions to the production cross sections at large transverse momenta. We use three slightly different versions of the heavy-quark lattice Green’s functions in order to minimize the contributions that scale as powers of the ultraviolet cutoff. The lattice matrix elements that we calculate obey the hierarchy that is suggested by the velocity-scaling rules of NRQCD.