SU(2) gauge theory with nonlinear gauge fixing is investigated. Since this system contains a quartic ghost interaction, there is the possibility of ghost condensation. It is shown that this condensation occurs in Euclidean space, and gauge fields acquire tachyonic masses in the presence of a ghost condensate. We also show that these tachyonic masses are gauge dependent. Contrastingly, there is no condensation in Minkowski space. However, even if we are in Minkowski space, this condensation appears at high temperature, and gauge fields get tachyonic masses.

A model Hamiltonian that exhibits asymptotic freedom and a bound state is used to show an example that the similarity renormalization group procedure can be tuned to improve the convergence of the perturbative derivation of effective Hamiltonians, through the adjustment of the generator of the similarity transformation. The improvement is measured by comparing the eigenvalues of perturbatively calculated renormalized Hamiltonians that couple only a relatively small number of effective basis states with the exact bound state energy in the model. The improved perturbative calculus leads to a few percent accuracy in a systematic expansion.

We study the semiclassical particle creation in the preheating phase after inflation. We work in the long-wavelength limit, in which all fields are considered homogeneous. The particle creation is shown to be intrinsically connected to the existence of chaos in the system.

We prove the $k_T$ factorization theorem in perturbative QCD (PQCD) for exclusive processes by considering $\pi {\gamma }^{*}\to \gamma \left(\pi \right)$ and $\overrightarrow{B}\gamma \left(\pi \right)l\overline{\nu }.$ The relevant form factors are expressed as the convolution of hard amplitudes with two-parton meson wave functions in the impact parameter b space, b being conjugate to the parton transverse momenta $k_T.$ The point is that on-shell valence partons carry longitudinal momenta initially, and acquire $k_T$ through collinear gluon exchanges. The b-dependent two-parton wave functions with an appropriate path for the Wilson links are gauge-invariant. The hard amplitudes, defined as the difference between the parton-level diagrams of on-shell external particles and their collinear approximation, are also gauge-invariant. We compare the predictions for two-body nonleptonic B meson decays derived from $k_T$ factorization (the PQCD approach) and from collinear factorization (the QCD factorization approach).

We construct the string states $|O_p^J{〉}_J,$ $|O_q^{J_1}{〉}_{J_1{J}_2},$ and $|O_0^{J_1{J}_2}{〉}_{J_1{J}_2}$ in the Hilbert space of the quantum mechanical orbifold model so as to calculate the three-point functions and the matrix elements of the light-cone Hamiltonian from the interacting string bit model. With these string states we show that the three-point functions and the matrix elements of the Hamiltonian derived from the interacting string bit model up to $g_2^2$ order precisely match with those computed from the perturbative SYM theory in the BMN limit.

A variational method is used to analyze compact $U\left(1\right)\mathrm{}$ gauge theory in $2+1$ dimensions at finite temperature T, weak coupling g, and where the fundamental magnetic monopoles have magnetic charge $2\pi n/g.\mathrm{}$ The theory undergoes a critical transition from a confining phase at temperatures below $T_c{=2g}^2{/n}^2\pi$ to a deconfined phase at temperatures above $T_c.$ The free energy and all its derivatives are continuous at $T_c,$ indicative of the Berezinski-Kosterlitz-Thouless phase transition. The relevant gauge-invariant correlation functions decay exponentially at large distances. The spatial Wilson loop obeys the area law at all finite temperatures, even for the noncompact theory. The case $n=2\mathrm{}$ corresponds to the compact $U\left(1\right)\mathrm{}$ theory considered as a low energy effective theory for the spontaneously broken Georgi-Glashow model. The results in this case agree with those derived previously for compact $U\left(1\right)\mathrm{}$ in this model using dimensional reduction of the Lagrangian.

Within the closed time path formalism a general nonperturbative expression is derived which resums through the Bethe-Salpter equation all leading order contributions to the shear viscosity in hot scalar field theory. Using a previously derived generalized fluctuation-dissipation theorem for nonlinear response functions in the real-time formalism, it is shown that the Bethe-Salpeter equation decouples in the so-called $\mathrm{}(r,a)\mathrm{}$ basis. The general result is applied to scalar field theory with pure $\lambda {\phi }^4$ and mixed $g{\phi }^3+\lambda {\phi }^4$ interactions. In both cases our calculation confirms the leading order expression for the shear viscosity previously obtained in the imaginary time formalism.

The unexpected discovery of hairy black hole solutions in theories with scalar fields simply by considering asymptotically anti–de Sitter (AdS) space, rather than asymptotically flat boundary conditions is analyzed in a way that exhibits in a clear manner the differences between the two situations. It is shown that the trivial Schwarzschild–anti–de Sitter space becomes unstable in some of these situations, and the possible relevance of this fact for the AdS conformal field theory conjecture is pointed out.

We derive two classes of brane-world solutions arising in the presence of a bulk scalar field. For static field configurations, we adopt a time-dependent, factorizable metric ansatz that allows for radion stabilization. The solutions are characterized by a nontrivial warping along the extra dimension, even in the case of a vanishing bulk cosmological constant, and lead to a variety of inflationary, time-dependent solutions of the 3D scale factor on the brane. We also derive the constraints necessary for the stability of these solutions under time-dependent perturbations of the radion field, and we demonstrate the existence of phenomenologically interesting, stable solutions with a positive cosmological constant on the brane.

Results from a phenomenological analysis of dijet and W hard diffractive hadroproduction at Fermilab Tevatron energies are reported. The theoretical framework employed here is a modified version of the Ingelman-Schlein approach which includes Dokhshitzer-Gribov-Lipatov-Altarelli-Parisi–evolved structure functions. Different from what has been achieved by the DESY $\mathrm{ep}$ HERA reactions, a reasonable overall description of such diffractive hadron processes is obtained only when a complex, quark-rich Pomeron structure function is employed in the calculation.

I study the weak basis $\mathrm{CP}$-violating invariants in supersymmetric models, in particular those which cannot be expressed in terms of the Jarlskog-type invariants, and find basis-independent conditions for $\mathrm{CP}$ conservation. With an example of the $K-\overline{K}$ mixing, I clarify the combinations of supersymmetric parameters which are constrained by experiment.

The quark number susceptibility near the QCD critical end point (CEP), the tricritical point (TCP) and the $O\left(4\right)\mathrm{}$ critical line at finite temperature and quark chemical potential are investigated. Based on the universality argument and numerical model calculations we propose the possibility that the hidden tricritical point strongly affects the critical phenomena around the critical end-point. We make a semiquantitative study of the quark number susceptibility near CEP or TCP for several quark masses on the basis of the Cornwall-Jackiw-Tomboulis potential for QCD in the improved-ladder approximation. The results show that the susceptibility is enhanced in a wide region around the CEP, inside which the critical exponent gradually changes from that of the CEP to that of the TCP, indicating a crossover of different universality classes.

The mass spectra and electromagnetic decay rates of charmonium, bottomonium, and $B_c$ mesons are comprehensively investigated in the relativistic quark model. The presence of only heavy quarks allows the expansion in powers of their velocities. All relativistic corrections of order $v^2{/c}^2,$ including retardation effects and one-loop radiative corrections, are systematically taken into account in the computations of the mass spectra. The obtained wave functions are used for the calculation of radiative magnetic dipole $\mathrm{}\left(M1\mathrm{}\right)\mathrm{}$ and electric dipole $\mathrm{}\left(E1\mathrm{}\right)\mathrm{}$ transitions. It is found that relativistic effects play a substantial role. Their account and the proper choice of the Lorentz structure of the quark-antiquark interaction in a meson is crucial for bringing theoretical predictions in accord with experimental data. A detailed comparison of the calculated decay rates and branching fractions with available experimental data for radiative decays of charmonium and bottomonium is presented. The possibilities to observe the currently missing spin-singlet S and P states as well as D states in bottomonium are discussed. The results for $B_c$ masses and decays are compared with other quark model predictions.

We introduce a new color decomposition for multiparton amplitudes in QCD, free of fundamental-representation matrices and structure constants. This decomposition has a physical interpretation in terms of the flow of color, which makes it ideal for merging with shower Monte Carlo programs. The color-flow decomposition allows for very efficient evaluation of amplitudes with many quarks and gluons, many times faster than the standard color decomposition based on fundamental-representation matrices. This will increase the speed of event generators for multijet processes, which are the principal backgrounds to signals of new physics at colliders.

We present the results of a complete analysis of the one-loop electroweak corrections to $e^{-}{e}^{+}\to \gamma \gamma ,Z\gamma ,\mathrm{ZZ}$ in the standard model (SM) and the minimal supersymmetric standard model (MSSM). A special emphasis is put on the high energy behavior of the various helicity amplitudes and the way the logarithmic structure is generated. The large magnitude of these effects, which induce striking differences between the SM and MSSM cases at high energies, offers the possibility of making global tests which could check the consistency of these models, and even decide whether any additional new physics is required.

Next-to-leading-order QCD analyses of the ZEUS data on deep inelastic scattering together with fixed-target data have been performed, from which the gluon and quark densities of the proton and the value of the strong coupling constant ${\alpha }_s{(M}_Z)$ were extracted. The study includes a full treatment of the experimental systematic uncertainties including point-to-point correlations. The resulting uncertainties in the parton density functions are presented. A combined fit for ${\alpha }_s{(M}_Z)$ and the gluon and quark densities yields a value for ${\alpha }_s{(M}_Z)$ in agreement with the world average. The parton density functions derived from ZEUS data alone indicate the importance of HERA data in determining the sea quark and gluon distributions at low x. The limits of applicability of the theoretical formalism have been explored by comparing the fit predictions to ZEUS data at very low $Q^2.$

Using an approach developed in the context of zero-temperature QCD to systematically sum higher order effects whose form is fixed by the renormalization group equation, we sum to all orders the leading log (LL) and next-to-leading log (NLL) contributions to the thermodynamic free energy in hot QCD. While the result varies considerably less with changes in the renormalization scale than does the purely perturbative result, a novel ambiguity arises which reflects the strong scheme dependence of thermal perturbation theory.

Recently Giedt discussed a mechanism, entitled optical unification, whereby string scale unification is facilitated via exotic matter with intermediate scale mass. This mechanism guarantees that a virtual minimal supersymmetric standard model unification below the string scale is extrapolated from the running of gauge couplings upward from $M_{Z^o}$ when an intermediate scale desert is assumed. In this paper we explore the possibility of optical unification within the context of weakly coupled heterotic strings. In particular, we investigate this for models of free fermionic construction containing the Nanopoulos-Antoniadis-Hagelin-Ellis (NAHE) set of basis vectors. This class is of particular interest for optical unification, because it provides a standard hypercharge embedding within $\mathrm{SO}\left(10\right),$ giving the standard $k_Y=\frac{5}{3}$ hypercharge level, which was shown necessary for optical unification. We present a NAHE model for which the set of exotic ${\mathrm{SU}\left(3\right)\mathrm{}}_C$ triplet-antitriplet pairs, ${\mathrm{SU}\left(2\right)\mathrm{}}_L$ doublets, and non-Abelian singlets with hypercharge offers the possibility of optical unification. Whether this model can realize optical unification is conditional upon these exotics not receiving Fayet-Iliopoulos (FI) scale masses when a flat direction of scalar vacuum expectation values is nonperturbatively chosen to cancel the FI D term $\xi$ generated by the anomalous $U\left(1\right)\mathrm{}$-breaking Green-Schwarz-Dine-Seiberg-Witten mechanism. A study of perturbative flat directions and their phenomenological implications for this model is underway.