We introduce matching functions as a means of summing heavy-quark logarithms to any order. Our analysis is based on Witten’s approach, where heavy quarks are decoupled one at a time in a mass-independent renormalization scheme. The outcome is a generalization of the matching conditions of Bernreuther and Wetzel: we show how to derive closed formulas for summed logarithms to any order, and present explicit expressions for leading order and next-to-leading order contributions. The decoupling of heavy particles in theories lacking asymptotic freedom is also considered.

We review the predictions of the theory of a color glass condensate for a gluon production cross section in $p\left(d\right)A$ collisions. We demonstrate that, at moderate energies, when the gluon production cross section can be calculated in the framework of the McLerran-Venugopalan model, it has only a partonic level Cronin effect in it. At higher energies or rapidities corresponding to smaller values of the Bjorken x, quantum evolution becomes important. The effect of quantum evolution at higher energies or rapidities is to introduce the suppression of high-$p_T$ gluons slightly decreasing the Cronin enhancement. At still higher energies or rapidities quantum evolution leads to the suppression of produced gluons at all values of $p_T.$

We use the recently proposed directed-path algorithm to study the chiral limit of a strongly coupled lattice QCD with staggered quarks at finite temperatures. The new algorithm allows us to compute the chiral susceptibility and the pion decay constant accurately on large lattices for massless quarks. In the low temperature phase we find clear evidence for the singularities predicted by chiral perturbation theory. We also show convincingly that the chiral phase transition is of second order and belongs to the O(2) universality class.

We study intersecting D-branes in a type IIB plane wave background using the Green-Schwarz worldsheet formulation. We consider all possible ${\mathrm{D}}_{\pm }$-branes intersecting at angles in the plane wave background and identify their residual supersymmetries. We find, in particular, that ${\mathrm{D}}_{\mp }-{\mathrm{D}}_{\pm }$ brane intersections preserve no supersymmetry. We also present the explicit worldsheet expressions of conserved supercharges and their supersymmetry algebras.

The tachyon effective field theory describing the dynamics of a non-BPS $\mathrm{D}-p$-brane has electric flux tube solutions where the electric field is at its critical value and the tachyon is at its vacuum. It has been suggested that these solutions have the interpretation of fundamental strings. We show that in order that an electric flux tube can “end” on a kink solution representing a BPS $\mathrm{D}-\left(p-1\right)$-brane, the electric flux must be embedded in a tubular region inside which the tachyon is finite rather than at its vacuum where it is infinite. Energetic considerations then force the transverse “area” of this tube to vanish. We suggest a possible interpretation of the original electric flux tube solutions around the tachyon vacuum as well as of tachyon matter as system of closed strings at a density far above the Hagedorn density.

Recently it was shown that high density QCD supports of number of topological defects. In particular, there are ${U\left(1\right)\mathrm{}}_Y$ strings that arise due to $K^0$ condensation that occurs when the strange quark mass is relatively large. The unique feature of these strings is that they possess a nonzero $K^{+}$ condensate that is trapped on the core. In the following we will show that these strings (with nontrivial core structure) can form closed loops with conserved charge and currents trapped on the string world sheet. The presence of conserved charges allows these topological defects, called vortons, to carry angular momentum, which makes them classically stable objects. We also give arguments demonstrating that vortons carry angular momentum very efficiently (in terms of energy per unit angular momentum) such that they might be the important degrees of freedom in the cores of neutron stars.

The exact fermion propagator in a classical time-dependent gauge field is derived by solving the equation of motion for the Dirac Green’s functions. From the retarded propagator obtained in this way the momentum spectrum for the produced fermion pairs is calculated. Different approximations and the exact solution for the propagator and the momentum spectrum are presented.

A new approach to space-time asymptotics is presented, refining Penrose’s idea of conformal transformations with infinity represented by the conformal boundary of space-time. It is proposed that the Penrose conformal factor be a product of advanced and retarded conformal factors, which asymptotically relate physical and conformal null coordinates and vanish at future and past null infinity respectively. A refined definition of asymptotic flatness at both spatial and null infinity is given, including that the conformal boundary is locally a light cone, with spatial infinity as the vertex. It is shown how to choose the conformal factors so that this asymptotic light cone is locally a metric light cone. The theory is implemented in the spin-coefficient (or null-tetrad) formalism by a joint transformation of the spin-metric and spin-basis (or metric and tetrad). Asymptotic regularity conditions are proposed, based on the conformal boundary locally being a smoothly embedded metric light cone. These conditions ensure that the Bondi-Sachs energy-flux integrals of ingoing and outgoing gravitational radiation decay at spatial infinity such that the total radiated energy is finite, and that the Bondi-Sachs energy-momentum has a unique limit at spatial infinity, coinciding with the uniquely rendered ADM energy-momentum.

The Einstein-Maxwell equations in D dimensions admitting $\left(D-3\right)$ commuting Killing vector fields have been investigated. The existence of the electric, magnetic, and twist potentials has been proved. The system is formulated as the harmonic map coupled to gravity on three-dimensional base space generalizing the Ernst system in the four-dimensional stationary Einstein-Maxwell theory. Some classes of the new exact solutions have been provided, which include the electromagnetic generalization of the Myers-Perry solution, which describes the rotating black hole immersed in a magnetic universe, and the static charged black ring solution.

The model of cylindrical gravitational waves is employed to work out and check a recent proposal of how a diffeomorphism-invariant Hamiltonian dynamics is to be constructed. The starting point is the action by Ashtekar and Pierri because it contains the boundary term that makes it differentiable for nontrivial variations at infinity. With the help of parametrization at infinity, the notion of gauge transformation is clearly separated from that of asymptotic symmetry. The symplectic geometry of asymptotic symmetries and asymptotic time is described and the role of the asymptotic structures in defining a zero-motion frame for the Hamiltonian dynamics of Dirac observables is explained. Complete sets of Dirac observables associated with the asymptotic fields are found and the action of the asymptotic symmetries on them is calculated. The construction of the corresponding quantum theory is sketched: the Fock space, operators of asymptotic fields, the Hamiltonian and the scattering matrix are determined.

We study the evolution of domain wall networks appearing after phase transitions in the early Universe. They exhibit interesting dynamical scaling behavior which is not yet well understood, and are also simple models for the more phenomenologically acceptable string networks. We have run numerical simulations in two- and three-dimensional lattices of sizes up to ${4096}^3.$ The theoretically predicted scaling solution for the wall area density $A\propto 1/t$ is supported by the simulation results, while no evidence of a logarithmic correction reported in previous studies could be found. The energy loss mechanism appears to be direct radiation, rather than the formation and collapse of closed loops or spheres. We discuss the implications for the evolution of string networks.

We consider a general brane-world model parametrized by the brane tension scale f and the branon mass M. For a low tension compared to the fundamental gravitational scale, we calculate the relic branon abundance and its contribution to the cosmological dark matter. We compare this result with the current observational limits on the total and hot dark matter energy densities and derive the corresponding bounds on f and M. Using the nucleosynthesis bounds on the number of relativistic species, we also set a limit on the number of light branons in terms of the brane tension. Finally, we estimate the bounds coming from the energy loss rate in supernovae explosions due to massive branon emission.

We report on a comparison between the flux of muons in the atmosphere measured by the CAPRICE98 experiment and simulations performed with the air shower simulation program AIRES. To reduce systematic uncertainties we have used as input the primary fluxes of protons and helium nuclei also measured by the CAPRICE98 experiment. Heavy nuclei are also taken into account in the primary flux, and their contribution to the muon flux is discussed. The results of the simulations show a very good agreement with the experimental data, at all altitudes and for all muon momenta. With the exception of a few isolated points, the relative differences between measured data and simulations are smaller than 20%; and in all cases compatible with zero within two standard deviations. The influence of the input cosmic ray flux on the results of the simulations is also discussed. This report includes also an extensive analysis of the characteristics of the simulated fluxes.

Ultrahigh energy ${(E}_{\nu }>{10}^8$ GeV) neutrino-nucleon total cross sections ${\sigma }^{\nu N}$ are estimated from a soft nonperturbative model complemented by an approximate QCD evolution, explicitly calculated. The resulting asymptotic energy behavior of the neutrino-nucleon charged-current total cross section is derived analytically, and predictions concerning the observation of ultrahigh energy neutrinos in future experiments are presented.

General relativity is extended by promoting the three-dimensional gravitational Chern-Simons term to four dimensions. This entails choosing an embedding coordinate $v_{\mu }$—an external quantity, which we fix to be a nonvanishing constant in its time component. The theory is identical to one in which the embedding coordinate is itself a dynamical variable, rather than a fixed, external quantity. Consequently diffeomorphism symmetry breaking is hidden in the modified theory: the Schwarzschild metric is a solution; gravitational waves possess two polarizations, each traveling at the velocity of light; a conserved energy-momentum (pseudo)tensor can be constructed. The modification is visible in the intensity of gravitational radiation: the two polarizations of a gravity wave carry intensities that are suppressed or enhanced by the extension.

By means of an identity that equates the elliptic genus partition function of a supersymmetric sigma model on the N-fold symmetric product $S^{N}X$ of X ${(S}^N{X=X}^N{/S}_N,$ where $S_N$ is the symmetric group of N elements) to the partition function of a second-quantized string theory, we derive the asymptotic expansion of the partition function as well as the asymptotic for the degeneracy of spectrum in string theory. The asymptotic expansion for the state counting reproduces the logarithmic correction to the black hole entropy.

We consider a special class of dimension-6 operators which are assumed to be induced by some new physics with typical scales of order $\Lambda .$ This special class of operators have two quarks which can mediate transitions between quark flavors. We show that under quite general assumptions the effect of these operators can be parametrized in terms of six parameters, leading to a modification of the (at tree-level flavor diagonal) neutral currents and to an “effective Cabibbo-Kobayashi-Maskawa matrix” for the charged currents, which is not necessarily unitary anymore. The effects of these operators on charged and neutral currents are studied.

We investigate the decay mechanisms in the $D_s^{+}\to \omega {\pi }^{+}$ and $D_s^{+}\to {\rho }^0{\pi }^{+}$ transitions. The naive factorization ansatz predicts a vanishing amplitude for the $D_s^{+}\to \omega {\pi }^{+}$ decay, while the $D_s^{+}\to {\rho }^0{\pi }^{+}$ decay amplitude does have an annihilation contribution also in this limit. Both decays can proceed through intermediate states of hidden strangeness, e.g. ${K,K}^{*},$ which we estimate in this paper. These contributions can explain the experimental value for the $D_s^{+}\to \omega {\pi }^{+}$ decay rate, which no longer can be viewed as a clean signature of the annihilation decay of $D_s^{+}.$ The combination of the $\pi \mathrm{}\left(1300\right)\mathrm{}$ pole dominated annihilation contribution and the internal ${K,K}^{*}$ exchange can saturate the present experimental upper bound on the $D_s^{+}\to {\rho }^0{\pi }^{+}$ decay rate, which is therefore expected to be within experimental reach. Finally, the proposed mechanism of hidden strangeness final state interactions constitutes only a small correction to the Cabibbo allowed decay rates $D_s\to {\mathrm{KK}}^{*},\phi \pi ,$ which are well described already in the factorization approximation.

Recent observations of the spectrum of $J/\psi$ produced in $e^{+}{e}^{-}$ collisions at the ${\rm Y}\mathrm{}\left(4S\right)\mathrm{}$ resonance are in conflict with fixed-order calculations using the nonrelativistic QCD effective field theory. One problem is that leading order color-octet mechanisms predict an enhancement of the cross section for $J/\psi$ with a maximal energy that is not observed in the data. However, in this region of phase space large perturbative corrections (Sudakov logarithms) as well as enhanced nonperturbative effects are important. In this paper we use the newly developed soft-collinear effective theory (SCET) to systematically include these effects. We find that these corrections significantly broaden the color-octet contribution to the $J/\psi$ spectrum. Our calculation employs a one-stage renormalization group evolution rather than the two-stage evolution used in previous SCET calculations. We give a simple argument for why the two methods yield identical results to lowest order in the SCET power counting.

We discuss whether bimaximal mixing given at the grand unified theory scale is consistent with solar mixing at the normal side at low energy. We consider radiative corrections due to the $\tau$-Yukawa, neutrino-Yukawa, and the slepton threshold corrections and discuss in what situation the maximal solar angle rotates toward the normal side. In this scheme, $|V_{13}|$ and the Dirac CP phase $\delta$ are induced radiatively, and we estimate these values.