We study a class of $N=1\mathrm{}$ supergravity inflationary models in which the evolution of the inflaton dynamics is controlled by a single power in the inflaton field at the point where the observed density fluctuations are produced, in the context of the braneworld scenario, in light of Wilkinson Microwave Anisotropy Probe results. In particular, we find that the bounds on the spectral index and its running constrain the parameter space both for models where the inflationary potential is dominated by a quadratic term and by a cubic term in the inflaton field. We also find that ${\alpha }_s>0\mathrm{}$ is required for the quadratic model whereas ${\alpha }_s<0\mathrm{}$ for the cubic model. Moreover, we have determined an upper bound on the five-dimensional Planck scale, $M_5\lesssim 0.019\mathrm{M},$ for the quadratic model. On the other hand, a running spectral index with $n_s>1\mathrm{}$ on large scales and $n_s<1\mathrm{}$ on small scales is not possible in either case.

We consider scalar field theory in de Sitter space with a general vacuum invariant under the continuously connected symmetries of the de Sitter group. We begin by reviewing approaches to define this as a perturbative quantum field theory. One approach leads to Feynman diagrams with pinch singularities in the general case, which renders the theory perturbatively ill defined. Another approach leads to well-defined perturbative correlation functions on the imaginary time continuation of de Sitter space. When continued to real time, a path integral with a non-local action generates the time-ordered correlators. Curiously, observables built out of local products of the fields show no sign of this nonlocality. However, once one couples to gravity, we show acausal effects are unavoidable and presumably make the theory ill defined. The Bunch-Davies vacuum state is the unique de Sitter invariant state that avoids these problems.

The kaon-antikaon system is studied in both the atomic and the strongly interacting sector. We discuss the influence of the structures of the $f_0\mathrm{}\left(980\right)\mathrm{}$ and the $a_0\mathrm{}\left(980\right)\mathrm{}$ mesons on the lifetime of kaonium. The strong interactions are generated by vector meson exchange within the framework of the standard ${\mathrm{SU}\left(3\right)\mathrm{}}_V\times {\mathrm{SU}\left(3\right)\mathrm{}}_A$ invariant effective Lagrangian. In the atomic sector, the energy levels and decay widths of kaonium are determined by an eigenvalue equation of the Kudryavtsev-Popov type, with the strong interaction effects entering through the complex scattering length for $K\overline{K}$ scattering and annihilation. The presence of two scalar mesons $f_0\mathrm{}\left(980\right)\mathrm{}$ and $a_0\mathrm{}\left(980\right)\mathrm{}$ leads to a ground state energy for the kaonium atom that is shifted above the point Coulomb value by a few hundred eV. The effect on the lifetime for the kaonium decay into two pions is much more dramatic. This lifetime is reduced by two orders of magnitude from $1.2\times {10}^{-16}\sec$ for annihilation in a pure Coulomb field down to $3.2\times {10}^{-18}\sec$ when the strong interactions are included. The analysis of the two photon decay width of the $f_0\mathrm{}\left(980\right)\mathrm{}$ suggests a generalization of the molecular picture which reduces the lifetime of kaonium still further to $1.1\times {10}^{-18}\hspace{0.5em}\sec .$

We show that an exact nonperturbative quantization of continuum gauge theory is provided by the Faddeev-Popov formula in the Landau gauge, $\delta \left(\partial \cdot A\right)\det \left[-\partial \cdot D\right(A\left)\mathrm{}\right]\exp \left[-S_{\mathrm{YM}}\mathrm{}\right(A\left)\mathrm{}\right],$ restricted to the region where the Faddeev-Popov operator is positive $-\partial \cdot D\left(A\right)>0\mathrm{}$ (Gribov region). Although there are Gribov copies inside this region, they have no influence on expectation values. The starting point of the derivation is stochastic quantization which determines the Euclidean probability distribution $P\left(A\right)\mathrm{}$ by a method that is free of the Gribov critique. In the Landau-gauge limit the support of $P\left(A\right)\mathrm{}$ shrinks down to the Gribov region with Faddeev-Popov weight. The cutoff of the resulting functional integral on the boundary of the Gribov region does not change the form of the Dyson-Schwinger (DS) equations because $\det \left[-\partial \cdot D\right(A\left)\mathrm{}\right]$ vanishes on the boundary, so there is no boundary contribution. However this cutoff does provide supplementary conditions that govern the choice of solution of the DS equations. In particular the “horizon condition,” though consistent with the perturbative renormalization group, puts QCD into a nonperturbative phase. The infrared asymptotic limit of the DS equations of QCD is obtained by neglecting the Yang-Mills action $S_{\mathrm{YM}}.$ We sketch the extension to a BRST-invariant formulation. In the infrared asymptotic limit, the BRST-invariant action becomes BRST exact, and defines a topological quantum field theory with an infinite mass gap. Confinement of quarks is discussed briefly.

We study $\mathrm{SU}\left(3\right)\mathrm{}$ gluon electric and magnetic masses at finite temperatures using quenched lattice QCD on a ${20}^2\times 32\times 6$ lattice. We focus on temperature regions between ${T=T}_c$ and ${6T}_c,$ which are realized in BNL Relativistic Heavy Ion Collider and CERN Large Hadron Collider experiments. Stochastic quantization with a gauge-fixing term is employed to calculate gluon propagators. The temperature dependence of the electric mass is found to be consistent with the hard-thermal-loop perturbation, and the magnetic mass has finite values in the temperature region of interest. Both screening masses have little gauge parameter dependence. The behavior of the gluon propagators is very different in confinement or deconfinement physics. The short distance magnetic part behaves like a confined propagator even in the deconfinement phase. A simulation with a larger lattice, ${32}^2\times 48\times 6,$ shows that the magnetic mass has a stronger finite size effect than the electric mass.

We study the application of the joint resummation formalism to Higgs boson production via gluon-gluon fusion at the CERN LHC, defining inverse transforms by analytic continuation. We work at next-to-leading logarithmic accuracy. We find that at low $Q_T$ the resummed Higgs $Q_T$ distributions are comparable in the joint and $\mathrm{pure}{-Q}_T$ formalisms, with a relatively small influence from threshold enhancement in this range. We find a modest (about ten percent) decrease in the inclusive cross section, relative to pure threshold resummation.

We study the very recently discovered ${\Theta }^{+}\mathrm{}\left(1540\right)\mathrm{}$ at SPring-8, at ITEP and at CLAS-Thomas Jefferson Lab. We apply the same RGM techniques that already explained with success the repulsive hard core of nucleon-nucleon, kaon-nucleon exotic scattering, and the attractive hard core present in pion-nucleon and pion-pion nonexotic scattering. We find that the $K-N$ repulsion excludes the ${\Theta }^{+}$ as a $K-N$ s-wave pentaquark. We explore the ${\Theta }^{+}$ as a heptaquark, equivalent to a $N+\pi +K$ Borromean bound state, with positive parity and total isospin $I=0.\mathrm{}$ We find that the kaon-nucleon repulsion is canceled by the attraction existing both in the pion-nucleon and pion-kaon channels. Although we are not yet able to bind the total three body system, we find that the ${\Theta }^{+}$ may still be a heptaquark state. We conclude with predictions that can be tested experimentally.

We present measurements of branching fractions in the $\overrightarrow{b}s\overline{s}s$ penguin-dominated decays $B^{+}\to \phi K^{+}$ and $B^0\to \phi K^0$ in a sample of approximately 89 million $B\overline{B}$ pairs collected by the BABAR detector at the PEP-II asymmetric-energy B-meson factory at SLAC. We determine $\mathcal{B}{(B}^{+}\to \phi K^{+}{)=(10.0\mathrm{}}_{-0.8}^{+0.9\mathrm{}}\pm 0.5)\times {10}^{-6}$ and $\mathcal{B}{(B}^0\to \phi K^0{)=(8.4\mathrm{}}_{-1.3}^{+1.5\mathrm{}}\pm 0.5)\times {10}^{-6}.$ Additionally, we measure the CP-violating charge asymmetry ${\mathcal{A}}_{\mathrm{CP}}{(B}^{\pm }\to \phi K^{\pm })=0.04\mathrm{}\pm 0.09\pm 0.01,$ with a 90% confidence-level interval of [-0.10, 0.18], and set an upper limit on the CKM- and color-suppressed decay $B^{+}\to \phi {\pi }^{+},$ $\mathcal{B}{(B}^{+}\to \phi {\pi }^{+})<\mathrm{}0.41\mathrm{}\times {10}^{-6}$ (at the 90% confidence level).

The topological defects of $\lambda {\phi }^4$ theory, the kink and antikink, are studied in the Hartree approximation. This allows us to discuss quantum effects on defects in both stationary and dynamical systems. The kink mass is calculated for a number of parameters, and compared to classical, one loop and Monte Carlo results known from the literature. We discuss the thermalization of the system after a kink-antikink collision. A classical result, the existence of a critical speed, is rederived and shown for the first time in quantum theory. We also use kink-antikink collisions as a very simple toy model for heavy ion collisions and discuss the differences and similarities, for example, in pressure. Finally, using the Hartree ensemble approximation allows us to study kink-antikink nucleation starting from a thermal (Bose–Einstein) distribution. On a qualitative level, our results show only few dissimilarities with the classical results, but on a quantitative level there are some important differences.

We apply methods of dynamical systems to study the behavior of a universe dominated by the generalized Chaplygin gas. We reduce the dynamics to a two-dimensional Hamiltonian system and study its behavior for various ranges of parameters. The dynamics is studied on the phase plane by using methods of a qualitative analysis of differential equations. The behavior of trajectories at infinity is studied in some convenient coordinates introduced on the phase plane. Hence we show that the Friedmann-Robertson-Walker model with the generalized Chaplygin gas is structurally stable. We clearly find the domains of cosmic acceleration as well as conditions for which the horizon problem is solved. We also define some general class of fluids which generalize the Chaplygin gas. The dynamics of such models in terms of energy conditions is also discussed.

An approximation to Einstein’s field equations in the Arnowitt-Deser-Misner canonical formalism is presented, which corresponds to the magnetohydrodynamics approximation in electrodynamics. It results in coupled elliptic equations which represent the maximum of elliptic-type structure of Einstein’s theory and naturally generalizes previous conformal-flat truncations of the theory. The Hamiltonian, in this approximation, is identical with the nondissipative part of the Einsteinian one through the third post-Newtonian order. The proposed scheme, where stationary spacetimes are exactly reproduced, should be useful to construct realistic initial data for general relativistic simulations as well as to model astrophysical scenarios, where the gravitational radiation reaction can be neglected.

We investigate inflation in a closed Friedmann-Robertson-Walker universe filled with the scalar field with a power-law potential. For a wide range of powers and parameters of the potential we numerically calculate the slow-roll parameters and scalar spectral index at the epoch when the present Hubble scale leaves the horizon and at the end of inflation. Also we compare the results of our numerical calculations with recent observational data. This allows us to set a constraint on the power of the potential: $\alpha \lesssim (3.5\mathrm{}–4.5).$

We report the results of a search for $B^{-}\to J/\psi \Lambda \overline{p}$ based on a data set of $78{\mathrm{fb}}^{-1}$ data collected at the ${\rm Y}\mathrm{}\left(4S\right)\mathrm{}$ resonance with the Belle detector at the KEKB asymmetric $e^{+}{e}^{-}$ collider. No substantial signal is found, and we set the branching fraction upper limit $\mathcal{B}{(B}^{-}\to J/\psi \Lambda \overline{p})<\mathrm{}4.1\mathrm{}\times {10}^{-5}$ at 90% confidence level.

A simple inspection of the one loop quark self-energy suggests a prescription of the CKM matrix renormalization in the standard model. It leads to a CKM matrix counterterm which is gauge parameter independent and satisfies the unitarity constraint, and renormalized physical amplitudes which are gauge parameter independent and smooth in quark mass difference. We make a point that caution should be practiced when interpreting the CKM martix counterterm in terms of those of parameters in a given representation due to rephasing effects from renormalization. We show how this can be done using the degrees of freedom in the on-shell renormalization scheme.

The supersymmetric CP problem is studied within superstring-motivated extensions of the minimal supersymmetric standard model (MSSM) with an additional ${U\left(1\right)\mathrm{}}^{\prime }$ gauge symmetry broken at the TeV scale. This class of models offers an attractive solution to the $\mu$ problem of the MSSM, in which ${U\left(1\right)\mathrm{}}^{\prime }$ gauge invariance forbids the bare $\mu$ term, but an effective $\mu$ parameter is generated by the vacuum expectation value of a standard model singlet S which has a superpotential coupling of the form ${\mathrm{SH}}_u{H}_d$ to the electroweak Higgs doublets. The effective $\mu$ parameter is thus dynamically determined as a function of the soft supersymmetry breaking parameters, and can be complex if the soft parameters have nontrivial CP-violating phases. We examine the phenomenological constraints on the reparametrization invariant phase combinations within this framework, and find that the supersymmetric CP problem can be greatly alleviated in models in which the phase of the $\mathrm{SU}\left(2\right)\mathrm{}$ gaugino mass parameter is aligned with the soft trilinear scalar mass parameter associated with the ${\mathrm{SH}}_u{H}_d$ coupling. We also study how the phases filter into the Higgs sector, including only the dominant top quark and top squark loops. We find that while the Higgs sector conserves CP at the renormalizable level to all orders of perturbation theory, CP violation can enter at the nonrenormalizable level at one-loop order. In the majority of the parameter space, the lightest Higgs boson remains essentially CP even but the heavier Higgs bosons can exhibit large CP-violating mixings, similar to the CP-violating MSSM with large $\mu$ parameter.

We study the phenomenon of parton-hadron duality in both polarized and unpolarized electron proton scattering using the HERMES and the Jefferson Lab data, respectively. In both cases we extend a systematic perturbative QCD based analysis to the integrals of the structure functions in the resonance region. After subtracting target mass corrections and large x resummation effects, we extract the remaining power corrections up to order ${1/Q}^2.$ We find a sizable suppression of these terms with respect to analyses using deep inelastic scattering data. The suppression appears consistently in both polarized and unpolarized data, except for the low $Q^2$ polarized data, where a large negative higher twist contribution remains. A similar trend is found by using phenomenological parametrizations of the data, which include nonperturbative type corrections. Possible scenarios generating this behavior are discussed.

I calculate the kaon B parameter $B_K,$ defined via ${8(m}_K{f}_K{)}^2{B}_K/3=〈\overline{K}|\overline{s}{\gamma }_{\mu }\left(1\mathrm{}-{\gamma }_5\right)d\overline{s}{\gamma }_{\mu }\left(1\mathrm{}-{\gamma }_5\right)d|K〉,$ with a lattice simulation in the quenched approximation. The lattice simulation uses an action possessing exact lattice chiral symmetry, an overlap action. Computations are performed at two lattice spacings, about 0.13 and 0.09 fm (parametrized by Wilson gauge action couplings $\beta =5.9\mathrm{}$ and 6.1) with nearly the same physical volumes and quark masses. I describe particular potential difficulties which arise due to the use of such a lattice action in finite volume. The continuum-extrapolated result for quenched $B_K^{\mathrm{NDR}}(\mu =2\mathrm{}\mathrm{GeV})=0.55\mathrm{}\left(7\right)\mathrm{}$ where the uncertainty includes statistics, extrapolation, and an estimate of uncertainty from the choice of matching factor and strange quark mass.

We derive the semiclassical (instanton-induced) contribution to the inelastic cross section of two color dipoles at large $\sqrt{s}.$ We study its dependence on the dipole sizes, orientations, and most importantly the impact parameter. The inelastic cross section is approximately quadratic in the dipole sizes and Gaussian like in the impact parameter with a width of the order of the instanton size. These results are directly relevant to double DIS ${\gamma }^{*}{\gamma }^{*},$ as well as ${\gamma }^{*}\gamma$ and standard DIS ${\gamma }^{*}h$ at small x when a real photon and a hadron can be approximated by a dipole. For such cases, with one small dipole scattering on a large dipole, the impact parameter profile exhibits a width of about 1/2 fm, which is in good agreement with the impact parameter profile recently extracted from DIS DESY HERA data, including diffractive ${\gamma }^{*}\to J/\psi .$

By comparing SU(3)-breaking scales of linear mass formulas, it is shown that the lowest vector and scalar mesons all have a $\overline{q}q$ configuration, while the ground-state octet and decuplet baryons are qqq. Also, the quark-level linear $\sigma$ model is employed to predict similar $\overline{q}q$ and qqq states. Furthermore, the approximate mass degeneracy of the scalar $a_0\mathrm{}\left(985\right)\mathrm{}$ and $f_0\mathrm{}\left(980\right)\mathrm{}$ mesons is demonstrated to be accidental. Finally, it is shown that various strong, electromagnetic, and weak mesonic decay rates are successfully explained within the framework of the quark-level linear $\sigma$ model.

We investigate the photoproduction of the ${\Theta }^{+}\mathrm{}\left(1540\right)\mathrm{}$ on a nucleon $(\gamma \overrightarrow{n}{K}^{-}{\Theta }^{+},$ $\gamma \overrightarrow{p}{K}^0{\Theta }^{+})$ and the pion-induced ${\Theta }^{+}$ production reaction on the proton $\left({\pi }^{-}\overrightarrow{p}{K}^{-}{\Theta }^{+}\right).\mathrm{}$ The total cross sections near threshold are estimated by using hadronic models with effective interaction Lagrangians and form factors that preserve the gauge invariance of the electromagnetic current. The photoproduction cross sections are found to be a few hundred nb, with the cross section on the proton being larger than that on the neutron. The pion-induced production cross section is found to be around a few hundred $\mu \mathrm{b}$ but sensitive to the $K^{*}N\Theta$ coupling whose value is not yet known. We also study the production cross section assuming that ${\Theta }^{+}$ has negative parity. The cross sections are then found to be very suppressed compared to the case where ${\Theta }^{+}$ has positive parity. Hence, the interpretation of the ${\Theta }^{+}$ as an odd-parity pentaquark state seems to be disfavored from the estimates of the cross section for the photon-proton reaction from the SAPHIR experiment.