We perform an accurate computation of the production rate for primordial black holes (PBHs). The reason is that the underlying mass variance had been overestimated systematically, as was shown recently. For scale-free power law primordial spectra, and for a universe with critical density, the mass variance is less than 34% of its value thought earlier for the spectral index in the range $1<~n<~\mathrm{1.3.}$ We then extend our study to spectra with a characteristic scale and find the accurate shape of the corresponding mass variance. For a pure step in the primordial spectrum, the step in the variance is smoothed around the characteristic scale $k_s.$ For a spectrum with large oscillations near $k_s,$ we find a pronounced bump in the variance. This could yield a significant part of the cold dark matter in the form of PBHs with a mass M in the range $5\times {10}^{15}\mathrm{g}\lesssim M\lesssim {10}^{21}\mathrm{g}.$

It is shown that, contrary to previous claims, a scalar tensor theory of Brans-Dicke type provides a relativistic generalization of Newtonian gravity in 2+1 dimensions. The theory is metric and test particles follow the space-time geodesics. The static isotropic solution is studied in vacuum and in regions filled with an incompressible perfect fluid. It is shown that the solutions can be consistently matched at the matter vacuum interface, and that the Newtonian behavior is recovered in the weak field regime.

We study the correlations between the particles emitted by moving mirrors. To this end, we first analyze $〈T_{\mu \nu }{\mathrm{}\left(x\right)T}_{\alpha \beta }{(x}^{\prime })〉,$ the two-point function of the stress tensor of the radiation field. In this we generalize the work undertaken by Carlitz and Willey. To further analyze how the vacuum correlations on ${\mathcal{J}}^{-}$ are scattered by the mirror and redistributed among the pairs of particles produced, we use a more powerful approach based on the value of $T_{\mu \nu }$ which is conditional on the detection of a given particle on ${\mathcal{J}}^{+}.$ We apply both methods to the fluxes emitted by a uniformly accelerated mirror. This case is particularly interesting because of its strong interferences which lead to a vanishing flux, and because of its divergences which are due to the infinite blueshift effects associated with the horizons. Using the conditional value of $T_{\mu \nu },$ we reveal the existence of correlations between the particles created and their partners in a domain where the mean fluxes and the two-point function vanish. This demonstrates that the scattering by an accelerated mirror leads to a steady conversion of vacuum fluctuations into pairs of quanta. In the last section, we study the scattering by two uniformly accelerated mirrors which follow symmetrical trajectories (i.e., which possess the same horizons). When using the Davies-Fulling model, the Bogoliubov coefficients encoding pair creation vanish because of perfectly destructive interferences. When using regularized amplitudes, these interferences are inevitably lost, thereby giving rise to pair creation.

The Davies-Fulling model describes the scattering of a massless field by a moving mirror in $1+1$ dimensions. When the mirror travels under uniform acceleration, one encounters severe problems which are due to the infinite blueshift effects associated with the horizons. On one hand, the Bogoliubov coefficients are ill defined and the total energy emitted diverges. On the other hand, the instantaneous mean flux vanishes. To obtain well-defined expressions we introduce an alternative model based on an action principle. The usefulness of this model is to allow us to switch on and off the interaction at asymptotically large times. By an appropriate choice of the switching function, we obtain analytical expressions for the scattering amplitudes and the fluxes emitted by the mirror. When the coupling is constant, we recover the vanishing flux. However, it is now followed by transients which inevitably become singular when the switching off is performed at late time. Our analysis reveals that the scattering amplitudes (and the Bogoliubov coefficients) should be seen as distributions and not as mere functions. Moreover, our regularized amplitudes can be put in a one to one correspondence with the transition amplitudes of an accelerated detector, thereby unifying the physics of uniformly accelerated systems. In a forthcoming article, we shall use our scattering amplitudes to analyze the quantum correlations among emitted particles which are also ill defined in the Davies-Fulling model in the presence of horizons.

The radiation reaction in compact spinning binaries on eccentric orbits due to the quadrupole-monopole interaction is studied. This contribution is of second post-Newtonian order. As a result of the precession of spins the magnitude L of the orbital angular momentum is not conserved. Therefore a proper characterization of the perturbed radial motion is provided by the energy E and angular average $\overline{L}.$ As powerful computing tools, the generalized true and eccentric anomaly parametrizations are introduced. Then the secular losses in energy and magnitude of the orbital angular momentum together with the secular evolution of the relative orientations of the orbital angular momentum and spins are found for eccentric orbits by use of the residue theorem. The circular orbit limit of the energy loss agrees with Poisson’s earlier result.

We examine the Hartle-Hawking no-boundary initial state for the Ponzano-Regge formulation of gravity in three dimensions. We consider the behavior of conditional probabilities and expectation values for geometrical quantities in this initial state for a simple minisuperspace model consisting of a two-parameter set of anisotropic geometries on a $2$-sphere boundary. We find dependence on the cutoff used in the construction of Ponzano-Regge amplitudes for expectation values of edge lengths. However, these expectation values are cutoff independent when computed in certain, but not all, conditional probability distributions. Conditions that yield cutoff independent expectation values are those that constrain the boundary geometry to a finite range of edge lengths. We argue that such conditions have a correspondence to fixing a range of local time, as classically associated with the area of a surface for spatially closed cosmologies. Thus these results may hint at how classical spacetime emerges from quantum amplitudes.

We consider an imperfect relativistic fluid in which a shock wave develops and we discuss its structure and thickness, taking into account the effects of viscosity and heat conduction in the form of sound absorption. The junction conditions and the nonlinear equations describing the evolution of the shock are derived with the corresponding Newtonian limit discussed in detail. As in the nonrelativistic regime, the thickness is inversely proportional to the discontinuity in the pressure. However, new terms of purely relativistic origin are also present. In particular, for a viscous polytropic gas, it is found that a purely viscous relativistic shock is thicker than its nonrelativistic counterpart, while for pure heat conduction the contrary is true.

We study spin-dependent sum rules for forward virtual Compton scattering (VVCS) off the nucleon in heavy baryon chiral perturbation theory (HBChPT) at order $\mathcal{O}{(p}^4).\mathrm{}$ We show how these sum rules can be evaluated from low energy expansions (in the virtual photon energy) of the forward VVCS amplitude. We study in particular the Burkhardt-Cottingham sum rule in HBChPT and the higher terms in the low energy expansion, which can be related to the generalized forward spin polarizabilities of the nucleon. The dependence of these observables on the photon virtuality $Q^2$ can be accessed, at small and intermediate $Q^2$ values, from existing and forthcoming data at Jefferson Lab.

The discrepancy between the measured and theoretical production cross section of b quarks at the Fermilab Tevatron can probably be explained by the recently proposed scenario of light gluinos of mass $12–16\mathrm{GeV}$ and light sbottoms of mass $2–5.5\mathrm{GeV}.$ In this scenario, we study a related process at the Z pole, $\overrightarrow{Z}b{b}_1^{*}\tilde{g}+\overline{b}{b}_1\tilde{g}$ followed by $\tilde{g}\to b{b}_1^{*}/\overline{b}{b}_1.$ The hadronic branching ratio for this channel is $(1\mathrm{}–3)\times {10}^{-3},$ which is of the order of the size of the uncertainty in $R_b.$ We find that a typical event consists of an energetic prompt bottom jet back to back with a “fat” bottom jet, which consists of a bottom quark and two bottom squarks. Such events with a ${10}^{-3}$ branching ratio may affect the measurement of $R_b;$ they are even more interesting if the fat bottom jet can be identified.

We study the flavor changing $\overrightarrow{t}{\mathrm{cl}}_1^{-}{l}_2^{+}$ decay in the framework of the general two Higgs doublet model, the so-called model III. We predict the branching ratio for $l_1=\tau ,$ $l_2=\mu$ at the order of magnitude of $\mathrm{BR}\sim {10}^{-8}.$

We report on an investigation of the LANL method for determining the $O\left(a\right)\mathrm{}$ improvement coefficient $c_A$ nonperturbatively. We find we are able to extract reliable estimates for the coefficient using this method. However, our study of systematic errors shows that for very accurate determinations of $c_A,$ the smearing function must be tuned to keep the $O\left(a\right)\mathrm{}$ ambiguity in $c_A$ fixed as $\beta$ varies. Consistency was found with previous results from the LANL group and (within fairly large errors) 1-loop perturbation theory; $c_A$ does not change significantly over the range $\beta =5.93\mathrm{}–\mathrm{6.2.}$ The big difference between our results and those of the ALPHA Collaboration, around $\beta =6.0,$ shows that the $O\left(a\right)\mathrm{}$ differences in $c_A$ between the different methods can be large. We find that the lattice spacing dependence of $f_{\pi }$ and the renormalized quark mass is much smaller using our values of $c_A$ compared to those of the ALPHA Collaboration.

We solve the collisionless transport equations of a quark-gluon plasma interacting through mean chromodynamic fields. The system is assumed to be translation invariant in one or more space-time directions. We present exact solutions that hold if the vector gauge fields in the direction of the translation invariance commute with their covariant derivatives. We also solve the equations perturbatively when the commutation condition is relaxed. Further, we derive the color current and the associated effective action. For the static quasiequilibrium system, our results reproduce the full one-loop effective action of QCD in the presence of constant background fields, where the above mentioned commutation condition is satisfied.

The meson (pion and kaon) form factor is calculated in the perturbative framework with alternative forms for the running coupling constant and the gluon propagator in the infrared kinematic region. These modified forms are employed to test the sensibility of the meson form factor to the nonperturbative contributions. It is a powerful discriminating quantity and the results obtained with a particular choice of modified running coupling constant and gluon propagator have good agreement with the available data for both mesons, indicating the robustness of the method of calculation. Nevertheless, the nonperturbative aspects may be included in the perturbative framework of the calculation of exclusive processes.

For elastic hadron-hadron diffraction scattering, we examine the relation between the zeros of the scattering amplitude and the zeros of the Fourier-Bessel-transformed eikonal function from the impact-parameter space to the momentum-transfer space. Any zero of the transformed eikonal function produces a zero trajectory which becomes confluent with the one of the black-disk amplitude as the energy goes higher.

We study the exclusive decays of $\overrightarrow{B}{f}_0{\mathrm{}\left(980\right)K}^{\left(*\right)}$ in the framework of perturbative QCD by identifying $f_0\mathrm{}\left(980\right)\mathrm{}$ as the composition of $\overline{s}s$ and $\mathrm{n̄}n=(ūu+\overline{d}d)/\sqrt{2}.$ We find that the influence of the $\mathrm{n̄}n$ content on the predicted branching ratios is crucial. We discuss the possible rescattering and gluonium states which could enhance the branching ratios of the considered decays. We point out that the CP asymmetry in $\overrightarrow{B}{f}_0{\mathrm{}\left(980\right)K}_{S,L}$ could be a new explorer of $\sin 2{\phi }_1.$

We reanalyze hadronic decays of B mesons to a pseudoscalar (P) and a tensor meson $\mathrm{}\left(T\right),$ or a vector meson (V) and a tensor meson, through a $\overrightarrow{b}c$ transition. We discuss the possible large uncertainties to the branching ratios (BR’s) of the relevant modes, mainly arising from the uncertainties to the hadronic form factors for the $\overrightarrow{B}T$ transition. The BR’s and $\mathrm{CP}$ asymmetries for $\overrightarrow{B}\mathrm{PT}$ and $\mathrm{VT}$ decays are then calculated by using the form factors given in the ISGW2 model [the improved version of the original Isgur-Scora-Grinstein-Wise (ISGW) model]. We find that the estimated BR’s of many modes are increased by an order of magnitude, compared to the previous results calculated within the ISGW model.

In QCD the amplitude for $B^0\to D^{\left(*\right)+}{\pi }^{-}$ factorizes in the large $N_c$ limit or in the large energy limit $Q\gg {\Lambda }_{\mathrm{QCD}}$ where $Q=\{m_b{,m}_c{,m}_b-m_c\}.$ Data also suggest factorization in the exclusive processes $\overrightarrow{B}{D}^{*}{\pi }^{+}{\pi }^{-}{\pi }^{-}{\pi }^0$ and $\overrightarrow{B}{D}^{*}\omega {\pi }^{-};$ however, by themselves neither a large $N_c$ nor a large Q can account for this. We give exact large $N_c$ relations among isospin amplitudes for $\overline{B}\to D^{\left(*\right)}X$ and $\overline{B}\to D^{\left(*\right)}{D}^{\left(*\right)}X,$ which can be used to test factorization through exclusive or inclusive measurements. Noting that the condition for large energy release in $B^0\to D^{+}{\pi }^{-}$ is enforced by the small velocity limit, $m_b\gg m_b-m_c\gg \Lambda ,$ we propose that the combined large $N_c$ and SV limits justify factorization in $\overrightarrow{B}{D}^{\left(*\right)}X.\mathrm{}$ This combined limit is tested with the $\overrightarrow{B}{D}^{*}X$ inclusive decay spectrum measured by CLEO.

We propose to measure the $\mathrm{CP}$ phase ${\delta }_{\mathrm{CP}},$ the magnitude of the neutrino mixing matrix element $|U_{e3\mathrm{}}|$ and the sign of the atmospheric scale mass-squared difference $\Delta {\mathrm{m}}_{31}^2$ with a superbeam by the joint analysis of two different long baseline neutrino oscillation experiments. One is a long baseline experiment (LBL) at 300 km and the other is a very long baseline (VLBL) experiment at 2100 km. We take the neutrino source to be the approved high intensity proton synchrotron, HIPA. The neutrino beam for the LBL is the 2-degree off-axis superbeam, and for the VLBL a narrowband superbeam. Taking into account all possible errors, we evaluate the event rates required and the sensitivities that can be attained for the determination of ${\delta }_{\mathrm{CP}}$ and the sign of $\Delta m_{31}^2.$ We arrive at a representative scenario for a reasonably precise probe of this part of neutrino physics.

Quenched lattice QCD simulations and quenched chiral perturbation theory are used together for this study of strangeness in the nucleon. Dependences of the matrix elements on strange quark mass, valence quark mass and momentum transfer are discussed in both the lattice and chiral frameworks. The combined results of this study are in good agreement with existing experimental data and predictions are made for upcoming experiments. Possible future refinements of the theoretical method are suggested.

Recently effective actions have been extensively used to describe tachyon condensation in string theory. While the various effective actions which have appeared in the literature have very similar properties for static configurations, they differ for time-dependent tachyons. In this paper we discuss general properties of nonlinear effective Lagrangians which are first order in derivatives. In particular we show that some observed properties, such as asymptotically vanishing pressure, are rather generic features, although the quantative features differ. On the other hand we argue that certain features of marginal tachyon profiles are beyond the reach of any first order Lagrangian description. We also point out that an effective action, proposed earlier, captures the dynamics of tachyons well.