We discuss Israel layers collapsing inward from rest at infinity along Schwarzschild-Lemaitre geodesics. The dynamics of the collapsing layer and its equation of state are developed. There is a general equation of state which is approximately polytropic in the limit of very low pressure. The equation of state establishes a new limit on the stress-density ratio.

We revisit the problem of the emission of gravitational waves from a test mass orbiting and thus perturbing a Kerr black hole. The source term of the Teukolsky perturbation equation contains a Dirac delta function which represents a point particle. We present a technique to effectively model the delta function and its derivatives using as few as four points on a numerical grid. The source term is then incorporated into a code that evolves the Teukolsky equation in the time domain as a ($2+1$) dimensional partial differential equation. The waveforms and energy fluxes are extracted far from the black hole. Our comparisons with earlier work show an order of magnitude gain in performance (speed) and numerical errors less than $1\%$ for a large fraction of parameter space. As a first application of this code, we analyze the effect of finite extraction radius on the energy fluxes. This paper is the first in a series whose goal is to develop adiabatic waveforms describing the inspiral of a small compact body into a massive Kerr black hole.

Cartan’s first and second structure equations together with first and second Bianchi identities can be interpreted as equations of motion for the tetrad, the connection and a set of two-form fields $T^I$ and $R_J^I$. From this viewpoint, these equations define by themselves a field theory. Restricting the analysis to four-dimensional spacetimes (keeping gravity in mind), it is possible to give an action principle of the $BF$ type from which these equations of motion are obtained. The action turns out to be equivalent to a linear combination of the Nieh-Yan, Pontrjagin, and Euler classes, and so the field theory defined by the action is topological. Once Einstein’s equations are added, the resulting theory is general relativity. Therefore, the current results show that the relationship between general relativity and topological field theories of the $BF$ type is also present in the first-order formalism for general relativity.

We consider the correspondence between the Jordan frame and the Einstein frame descriptions of scalar-tensor theory of gravitation. We argue that since the redefinition of the scalar field is not differentiable at the limit of general relativity the correspondence between the two frames is lost at this limit. To clarify the situation we analyze the dynamics of the scalar field in different frames for two distinct scalar-tensor cosmologies with specific coupling functions and demonstrate that the corresponding scalar field phase portraits are not equivalent for regions containing the general relativity limit. Therefore the answer to the question of whether general relativity is an attractor for the theory depends on the choice of the frame.

We apply a recently developed perturbative formalism which describes the evolution under their self-gravity of particles displaced from a perfect lattice to quantify precisely, up to shell crossing, the effects of discreteness in dissipationless cosmological $N$-body simulations. We give simple expressions, explicitly dependent on the particle density, for the evolution of power in each mode as a function of redshift. For typical starting redshifts the effect of finite particle number is to slow down slightly the growth of power compared to that in the fluid limit (e.g., by about 10% at half the Nyquist frequency), and to induce also dispersion in the growth as a function of direction at a comparable level. In the limit that the initial redshift tends to infinity, at fixed particle density, the evolution in fact diverges from that in the fluid limit (described by the Zeldovich approximation). Contrary to widely held belief, this means that a simulation started at a redshift much higher than the redshift of shell crossing actually gives a worse, rather than a better, result. We also study how these effects are modified when there is a small-scale regularization of the gravitational force. We show that such a smoothing may reduce the anisotropy of the discreteness effects, but it then increases their average effect. This behavior illustrates the fact that the discreteness effects described here are distinct from those usually considered in this context, due to two-body collisions. Indeed the characteristic time for divergence from the collisionless limit is proportional to $N^{2/3}$, rather than $N/\log N$ in the latter case.

Protecting the inflationary potential from quantum corrections typically requires symmetries that constrain the form of couplings of the inflaton to other sectors. We will explore how these restrictions affect reheating in models with UV completions. In particular, we look at how reheating occurs when inflation is governed by closed strings, using N-flation as an example. We find that coupling the inflaton preferentially to the standard modelis difficult, and hidden sectors are typically reheated. Observational constraints are only met by a fraction of the models. In some working models, relativistic relics in the hidden sector provide dark matter candidates with masses that range from keV to PeV, with lighter masses being preferred.

We consider high density quark matter in the large $N_c$ and $N_f$ limit with $N_f/N_c$ fixed. In this limit, the color superconductivity disappears. We discuss that the chiral density wave state is also absent in the limit, if we assume the existence of the nonperturbative magnetic screening effect as indicated by recent lattice study. We argue that ferromagnetism can become a candidate for the ground state if quarks are massive.

The profile functions of the SU(3) Skyrme soliton are investigated for the octet, decuplet, and antidecuplet baryons by the mean field approach. In this approach, the profile functions are affected by the spatial rotation, the flavor rotation, and the flavor symmetry breaking. The solitons are stable only in the restricted areas of the parameter space for each multiplet. When the flavor symmetry breaking is large, the area for the antidecuplet is narrow compared to those for the octet and decuplet. The parameters are determined by the baryon mass spectrum, and the deformation of the soliton has sizable effects on the masses.

The renormalizable Abelian quantum field theory model of Kroll, Lee, and Zumino is used to compute the one-loop vertex corrections to the tree-level, vector meson dominance pion form factor. These corrections, together with the known one-loop vacuum polarization contribution, lead to a substantial improvement over vector meson dominance. The resulting pion form factor in the spacelike region is in excellent agreement with data in the whole range of accessible momentum transfers. The timelike form factor, known to reproduce the Gounaris-Sakurai formula at and near the rho-meson peak, is unaffected by the vertex correction at order $\mathcal{O}(g_{\rho \pi \pi }^2)$.

We confront the two-Higgs-doublet model with a variety of experimental constraints as well as theoretical consistency conditions. The most constraining data are the $\overline{B}\to X_s\gamma$ decay rate (at low values of $M_{H^{\pm }}$), and $\Delta \rho$ (at both low and high $M_{H^{\pm }}$). We also take into account the $B\overline{B}$ oscillation rate and $R_b$, or the width $\Gamma (Z\to b\overline{b})$ (both of which restrict the model at low values of $\tan \beta$), and the $B^{-}\to \tau {\nu }_{\tau }$ decay rate, which restricts the model at high $\tan \beta$ and low $M_{H^{\pm }}$. Furthermore, the LEP2 nondiscovery of a light, neutral-Higgs boson is considered, as well as the muon anomalous magnetic moment. Since perturbative unitarity excludes high values of $\tan \beta$, the model turns out to be very constrained. We outline the remaining allowed regions in the $\tan \beta$-$M_{H^{\pm }}$ plane for different values of the masses of the two lightest neutral-Higgs bosons, and describe some of their properties.

Improved actions in SU(2) and SU(3) lattice gauge theories are investigated with an emphasis on asymptotic scaling. A new scheme for tadpole improvement is proposed. The standard but heuristic tadpole improvement emerges from a mean field approximation from the new approach. Scaling is investigated by means of the large distance static quark potential. Both the generic and the new tadpole scheme yield significant improvements on asymptotic scaling when compared with loop improved actions. A study of the rotational symmetry breaking terms, however, reveals that only the new improvement scheme efficiently eliminates the leading irrelevant term from the action.

We study the properties of the chromohydrodynamical instabilities induced by a relativistic jet that crosses the quark-gluon plasma. Assuming that the jet of particles and the plasma can be described using a hydrodynamical approach, we derive and discuss the dispersion laws for the unstable collective modes. In our analysis, the chromohydrodynamical equations for the collective modes are tackled in the linear response approximation. Such an approximation, valid for short time scales, allows one to study in a straightforward way the dependence of the dispersion laws of the collective modes on the velocity of the jet, on the magnitude of the momentum of the collective mode and on the angle between these two quantities. In the conformal limit, we find that unstable modes arise for velocity of the jet larger than the speed of the sound of the plasma and only modes with momenta smaller than a certain value are unstable. Moreover, for ultrarelativistic velocities of the jet, the longitudinal mode becomes stable and the most unstable modes correspond to relative angles between the velocity of the jet and momentum of the collective mode larger than $\sim \pi /8$. Our results suggest an alternative mechanism for the description of the jet quenching phenomenon, where the jet crossing the plasma loses energy exciting colored unstable modes.

An exploratory study of charmless 3-body decays of $B$ mesons is presented using a simple model based on the framework of the factorization approach. The nonresonant contributions arising from $B\to P_1{P}_2$ transitions are evaluated using heavy meson chiral perturbation theory (HMChPT). The momentum dependence of nonresonant amplitudes is assumed to be in the exponential form $e^{-{\alpha }_{\mathrm{NR}}{p}_B·(p_i+p_j)}$ so that the HMChPT results are recovered in the soft meson limit $p_i,p_j\to 0$. In addition, we have identified another large source of the nonresonant signal in the matrix elements of scalar densities, e.g. $⟨K\overline{K}|\overline{s}s|0⟩$, which can be constrained from the decay ${\overline{B}}^0\to K_S{K}_S{K}_S$ or $B^{-}\to K^{-}{K}_S{K}_S$. The intermediate vector-meson contributions to 3-body decays are identified through the vector current, while the scalar meson resonances are mainly associated with the scalar density. Their effects are described in terms of the Breit-Wigner formalism. Our main results are: (i) All $KKK$ modes are dominated by the nonresonant background. The predicted branching ratios of $K^{+}{K}^{-}{K}_{S(L)}$, $K^{+}{K}^{-}{K}^{-}$ and $K^{-}{K}_S{K}_S$ modes are consistent with the data within errors. (ii) Although the penguin-dominated $B^0\to K^{+}{K}^{-}{K}_S$ decay is subject to a potentially significant tree pollution, its effective $\sin 2\beta$ is very similar to that of the $K_S{K}_S{K}_S$ mode. However, direct $CP$ asymmetry of the former, being of order $-4\%$, is more prominent than the latter. (iii) For $B\to K\pi \pi$ decays, we found sizable nonresonant contributions in $K^{-}{\pi }^{+}{\pi }^{-}$ and ${\overline{K}}^0{\pi }^{+}{\pi }^{-}$ modes, in agreement with the Belle measurements but larger than the BABAR result. (iv) Time-dependent $CP$ asymmetries in $K_S{\pi }^0{\pi }^0$, a purely $CP$-even state, and $K_S{\pi }^{+}{\pi }^{-}$, an admixture of $CP$-even and $CP$-odd components, are studied. (v) The ${\pi }^{+}{\pi }^{-}{\pi }^0$ mode is found to have a rate larger than ${\pi }^{+}{\pi }^{-}{\pi }^{-}$ even though the former involves a ${\pi }^0$ in the final state. They are both dominated by resonant $\rho$ contributions. (vi) We have computed the resonant contributions to 3-body decays and determined the rates for the quasi-two-body decays $B\to VP$ and $B\to SP$. The predicted $\rho \pi$, $f_0(980)K$ and $f_0(980)\pi$ rates are in agreement with the data, while the calculated $\varphi K$, $K^{*}\pi$, $\rho K$ and $K_0^{*}(1430)\pi$ are in general too small compared to experiment. (vii) Sizable direct $CP$ asymmetry is found in $K^{+}{K}^{-}{K}^{-}$ and $K^{+}{K}^{-}{\pi }^{-}$ modes.

The pattern of a large approximate degeneracy of the excited hadron spectra (larger than the chiral restoration degeneracy) is present in the recent experimental report of Bugg. Here we try to model this degeneracy with state of the art quark models. We review how the Coulomb Gauge chiral invariant and confining Bethe-Salpeter equation simplifies in the case of very excited quark-antiquark mesons, including angular or radial excitations, to a Salpeter equation with an ultrarelativistic kinetic energy with the spin-independent part of the potential. The resulting meson spectrum is solved, and the excited chiral restoration is recovered, for all mesons with $J>0$. Applying the ultrarelativistic simplification to a linear equal-time potential, linear Regge trajectories are obtained, for both angular and radial excitations. The spectrum is also compared with the semiclassical Bohr-Sommerfeld quantization relation. However, the excited angular and radial spectra do not coincide exactly. We then search, with the classical Bertrand theorem, for central potentials producing always classical closed orbits with the ultrarelativistic kinetic energy. We find that no such potential exists, and this implies that no exact larger degeneracy can be obtained in our equal-time framework, with a single principal quantum number comparable to the nonrelativistic Coulomb or harmonic oscillator potentials. Nevertheless we find it plausible that the large experimental approximate degeneracy will be modeled in the future by quark models beyond the present state of the art.

We point out some properties of the amplitude of the dipion transition ${\rm Y}(3S)\to {\rm Y}(1S)\pi \pi$ in relation to the recently reported results of a CLEO analysis of form factors in this amplitude. We find that the reported significant complex phase between two of the form factors, under the assumption that the third form factor is zero, is not consistent with the picture where the phase shifts arise due to the final state interaction in the $\pi \pi$ channel. It is also shown that in an analysis that uses no information on the polarization of both the initial and the final ${\rm Y}$ resonances it is impossible in principle to determine all the relevant terms. We suggest that a study of a simple correlation between the direction of the total momentum of the two pions and the axis of the initial beams is sufficient to resolve the ambiguity in the fit for the form factors.

We present an implementation of a parton shower algorithm for hadron colliders and electron-positron colliders based on the dipole factorization formulas. The algorithm treats initial-state partons on equal footing with final-state partons. We implemented the algorithm for massless and massive partons.

We present the studies of the decays $B\to a_1(1260)\pi$ and $a_1(1260)K$ within the framework of QCD factorization. Because of the G-parity, unlike the vector meson, the chiral-odd two-parton light-cone distribution amplitudes of the $a_1$ are antisymmetric under the exchange of quark and antiquark momentum fractions in the SU(2) limit. The branching ratios for $a_1\pi$ modes are sensitive to tree-penguin interference. The resultant $\mathcal{B}(B^0\to a_1^{\pm }{\pi }^{\mp })$ are in good agreement with the data. However, using the current Cabibbo-Kobayashi-Maskawa angles, $\beta =22.0°$ and $\gamma =59.0°$, our results for the mixing-induced parameter $S$ and ${\alpha }_{\mathrm{eff}}$ differ from the measurements of the time-dependent $CP$ asymmetries in the decay $B^0\to a_1^{\pm }{\pi }^{\mp }$ at about the $3.7\sigma$ level. This puzzle may be resolved by using a larger $\gamma \gtrsim 80°$. For $a_{1}K$ modes, the annihilation topologies give sizable contributions and are sensitive to the first Gegenbauer moment of the leading-twist tensor (chiral-odd) distribution amplitude of the $a_1$ meson. The $B\to a_{1}K$ amplitudes resemble the corresponding $B\to \pi K$ ones very much. Taking the ratios of corresponding $CP$-averaged $a_{1}K$ and $\pi K$ branching ratios, we can extract information relevant to the electroweak penguins and annihilations. The existence of new physics in the electroweak penguin sector and final-state interactions during decays can thus be explored.

The leading-order vacuum polarization contribution of very light millicharged fermions and scalar (spin-0) particles with charge $\epsilon e$ and mass $\mu$ to the Lamb shift of the hydrogen atom is shown to imply universal, i.e. $\mu$-independent, upper bounds on $\epsilon$: $\epsilon \lesssim {10}^{-4}$ for $\mu \lesssim 1\mathrm{keV}$ in the case of fermions, and for scalars this bound is increased by a factor of 2. This is in contrast to expectations based on the commonly used approximation to the Uehling potential relevant only for conventionally large fermion (and scalar) masses.

We study the confinement/deconfinement phase transition of holographic AdS/QCD models by using Ricci flat ${\mathrm{AdS}}_5$ black holes up to $\mathcal{O}({\alpha }^{\prime 3})$, which corresponds to the $\lambda$ expansion correction in the dual field theory to ${\lambda }^{-3/2}$, where $\lambda$ is the ’t Hooft coupling constant. We consider two cases: one is the hard-wall AdS/QCD model where a small radius region of the ${\mathrm{AdS}}_5$ is removed; the other is the case where one of the spatial coordinates for the ${\mathrm{AdS}}_5$ space is compactified, resulting in Witten’s QCD model in $2+1$ dimensions. We find that in the hard-wall AdS/QCD model, the deconfinement temperature decreases when the $\lambda$ expansion corrections are taken into account, while in Witten’s QCD model, the deconfinement transition always happens when the ratio of inverse temperature $\beta$ to the period ${\beta }_s$ of the compactified coordinate decreases to one, $\beta /{\beta }_s=1$, the same as the case without the $\mathcal{O}({\alpha }^{\prime 3})$ correction.