We present numerical evidence for the existence of spinning generalizations for nontopological Q-ball solitons in the theory of a complex scalar field with a nonrenormalizable self-interaction. To the best of our knowledge, this provides the first explicit example of spinning solitons in $\mathrm{}(3+1)\mathrm{}$-dimensional Minkowski space. In addition, we find an infinite discrete family of radial excitations of nonrotating Q-balls, and construct also spinning Q-balls in $2+1$ dimensions.

We present a definition of the four-dimensional helicity (FDH) regularization scheme valid for two or more loops. This scheme was previously defined and utilized at one loop. It amounts to a variation on the standard ’t Hooft–Veltman scheme and is designed to be compatible with the use of helicity states for “observed” particles. It is similar to dimensional reduction in that it maintains an equal number of bosonic and fermionic states, as required for preserving supersymmetry. Supersymmetry Ward identities relate different helicity amplitudes in supersymmetric theories. As a check that the FDH scheme preserves supersymmetry, at least through two loops, we explicitly verify a number of these identities for gluon-gluon scattering $\left(g\overrightarrow{g}gg\right)$ in supersymmetric QCD. These results also cross-check recent nontrivial two-loop calculations in ordinary QCD. Finally, we compute the two-loop shift between the FDH coupling and the standard modified minimal subtraction $\left(\overline{\mathrm{MS}}\right)$ scheme coupling, ${\alpha }_s.$ The FDH shift is identical to the one for dimensional reduction. The two-loop coupling shifts are then used to obtain the three-loop QCD $\beta$ function in the FDH and dimensional reduction schemes.

I investigate the effect of the radion on cosmological perturbations in the brane world. The $S^1{/Z}_2$ compactified 5D anti–de Sitter spacetime bounded by positive and negative tension branes is considered. The radion is the relative displacement of the branes in this model. I find two different kinds of the radion at the linear perturbation order for a cosmological brane. One describes a “fluctuation” of the brane which does not couple to matter on the brane. The other describes a “bend” of the brane which couples to the matter. The bend determines the curvature perturbation on the brane. At large scales, the radion interacts with anisotopic perturbations in the bulk. By solving the bulk anisotropic perturbations, large scale metric perturbations and anisotropies of the cosmic microwave background (CMB) on the positive tension brane are calculated. I find an interesting fact that the radion contributes to the CMB anisotropies. The observational consequences of these effects are discussed.

A black hole attached to a brane in a higher-dimensional space emitting quanta into the bulk may leave the brane as a result of a recoil. We study this effect. We consider black holes which have a size much smaller than the characteristic size of extra dimensions. Such a black hole can be effectively described as a massive particle with internal degrees of freedom. We consider an interaction of such particles with a scalar massless field and prove that for a special choice of the coupling constant describing the transition of the particle to a state with smaller mass the probability of massless quanta emission takes the form identical to the probability of the black hole emission. Using this model we calculate the probability for a black hole to leave the brane and study its properties. The discussed recoil effect implies that, for black holes which might be created in the interaction of high energy particles in colliders, the thermal emission of the formed black hole could be terminated and the energy nonconservation can be observed in brane experiments.

We study non-Gaussian signatures on the cosmic microwave background (CMB) radiation predicted within inflationary models with non-vacuum initial states for cosmological perturbations. The model incorporates a privileged scale, which implies the existence of a feature in the primordial power spectrum. This broken-scale-invariant model predicts a vanishing three-point correlation function for the CMB temperature anisotropies (or any other odd-numbered-point correlation function) whilst an intrinsic non-Gaussian signature arises for any even-numbered-point correlation function. We thus focus on the first non-vanishing moment, the CMB four-point function at zero lag, namely the kurtosis, and compute its expected value for different locations of the primordial feature in the spectrum, as suggested in the literature to conform with observations of large scale structure. The excess kurtosis is found to be negative and the signal to noise ratio for the dimensionless excess kurtosis parameter is equal to $|S/N|\simeq 4\times {10}^{-4},$ almost independently of the free parameters of the model. This signature turns out to be undetectable. We conclude that, subject to current tests, Gaussianity is a generic property of single field inflationary models. The only uncertainty concerning this prediction is that the effect of back reaction has not yet been properly incorporated. The implications for the trans-Planckian problem of inflation are also briefly discussed.

We present numerical simulations for the two-point correlation function and the angular power spectrum of nucleons above ${10}^{19}\mathrm{eV}$ injected by a discrete distribution of continuously emitting sources which follow a simple approximation to the profile of the Local Supercluster. We develop a method to constrain the number of sources necessary to reproduce the observed sky distribution of ultrahigh energy cosmic rays, as a function of the strength of the large scale cosmic magnetic fields in the Local Supercluster. While for fields $B\lesssim 0.05\mu \mathrm{G}$ the Supercluster source distribution appears inconsistent with the data for any number of sources, fields of strength $B\simeq 0.3\mu \mathrm{G}$ could reproduce the observed data with a number of sources around 10.

We clarify some aspects of the LSZ formalism and wave-function renormalization for unstable particles in the presence of electroweak interactions when mixing and $\mathrm{CP}$ violation are considered. We also analyze the renormalization of the Cabibbo-Kobayashi-Maskawa (CKM) mixing matrix which is closely related to wave-function renormalization. We critically review earlier attempts to define a set of “on-shell” wave-function renormalization constants. With the aid of extensive use of the Nielsen identities complemented by explicit calculations we corroborate that the counterterm for the CKM mixing matrix must be explicitly gauge independent and demonstrate that the commonly used prescription for the wave-function renormalization constants leads to gauge parameter dependent amplitudes, even if the CKM counterterm is gauge invariant as required. We show that a proper LSZ-compliant prescription leads to gauge independent amplitudes. The resulting wave-function renormalization constants necessarily possess absorptive parts, but we verify that they comply with the expected requirements concerning $\mathrm{CP}$ and $\mathrm{CPT}.\mathrm{}$ The results obtained using this prescription are different (even at the level of the modulus squared of the amplitude) from the ones neglecting the absorptive parts in the case of top decay. The difference is numerically relevant.

The most popular noncommutative field theories are characterized by a matrix parameter ${\theta }^{\mu \nu }$ that violates Lorentz invariance. We consider the simplest algebra in which the $\theta$ parameter is promoted to an operator and Lorentz invariance is preserved. This algebra arises through the contraction of a larger one for which explicit representations are already known. We formulate a star product and construct the gauge-invariant Lagrangian for Lorentz-conserving noncommutative QED. Three-photon vertices are absent in the theory, while a four-photon coupling exists and leads to a distinctive phenomenology.

A formalism for radiative correction (RC) calculation in exclusive pion electroproduction on the proton is presented. A FORTRAN code EXCLURAD is developed for the RC procedure. The numerical analysis is done in the kinematics of current Jefferson Lab experiments.

Because of two $3\sigma$ anomalies, the standard model (SM) fit of the precision electroweak data has a poor confidence level, $\mathrm{C}.\mathrm{L}.\mathrm{}=\mathrm{0.010.}\mathrm{}$ Since both anomalies involve challenging systematic issues, it might appear that the SM could still be valid if the anomalies resulted from underestimated systematic error. Indeed the C.L. of the global fit could then increase to 0.65, but that fit predicts a small Higgs boson mass, $m_H=43\mathrm{}\mathrm{GeV},$ that is only consistent at $\mathrm{C}.\mathrm{L}.\mathrm{}=0.035\mathrm{}$ with the lower limit, $m_H>114\mathrm{}\mathrm{GeV},$ established by direct searches. The data then favor new physics whether the anomalous measurements are excluded from the fit or not, and the Higgs boson mass cannot be predicted until the new physics is understood. Some measure of statistical fluctuation would be needed to maintain the validity of the SM, which is unlikely by broad statistical measures. New physics is favored, but the SM is not definitively excluded.

A one-parameter family of time-symmetric initial data for the radial infall of a particle into a Schwarzschild black hole is constructed within the framework of black-hole perturbation theory. The parameter measures the amount of gravitational radiation present on the initial spacelike surface. These initial data sets are then evolved by integrating the Zerilli-Moncrief wave equation in the presence of the particle. Numerical results for the gravitational waveforms and their power spectra are presented; we show that the choice of initial data strongly influences the waveforms, both in their shapes and their frequency content. We also calculate the total energy radiated by the particle-black-hole system, as a function of the initial separation between the particle and the black hole, and as a function of the choice of initial data. Our results confirm that for large initial separations, a conformally flat initial three-geometry minimizes the initial gravitational-wave content, so that the total energy radiated is also minimized. For small initial separations, however, we show that the conformally flat solution no longer minimizes the energy radiated.

The advent of high-resolution cosmic microwave background (CMB) experiments now allows studies on the temperature fluctuations at scales corresponding to a few arcminutes and below. Though the reported excess power at $l\sim 2000-6000$ by CBI and BIMA is roughly consistent with a secondary contribution resulting from the Sunyaev-Zeldovich effect, this requires a higher normalization for the matter power spectrum than measured by other means. In addition to a local redshift contribution, another strong possibility for anisotropies at very small scales involves nonstandard aspects of inflationary models. To distinguish between contributions from early universe and local structures, including a potential point source contribution, and to understand the extent to which structures at low redshifts contribute to small-scale temperature anisotropies, it may be necessary to perform a combined study involving CMB and the large-scale structure. We suggest a cross correlation of the temperature data with a map of the large-scale structure, such as the galaxy distribution. For next generation small angular scale CMB experiments, multifrequency observations may be a necessary aspect to allow an additional possibility to distinguish between these different scenarios.

We discuss the possibility that mass effects, beyond phase space, may have substantial influence on the direct determination of $V_{\mathrm{tq}}$ in decays of top quarks. In principle, our considerations are valid both for singly produced top and for $t\overline{t}$ pair production. The mass effect is practically irrelevant for the extraction of $V_{\mathrm{tb}}$ from Fermilab Tevatron data, but it may have implications for higher energy multijet top decay.

We show that the effective field theory of low energy modes in dense QCD has a positive Euclidean path integral measure. The complexity of the measure of QCD at the finite chemical potential can be ascribed to modes which are irrelevant to the dynamics at sufficiently high density. Rigorous inequalities follow at asymptotic density. Lattice simulations of dense QCD should be possible using the quark determinant calculated in the effective theory.

We describe how mirror symmetry of three-dimensional $\mathcal{N}=1\mathrm{}$ supersymmetric gauge theories can be used to determine the theory on the world volume of a D2-brane probe of manifolds with $G_2$ holonomy.

The formation and late time decays of Q balls are generic consequences of the Affleck-Dine (AD) baryogenesis. A substantial number of the lightest supersymmetry (SUSY) particles (LSPs) are produced nonthermally as the decay products of these Q balls. This requires a significantly large annihilation cross section of the LSP so as not to overclose the universe, which predicts a Higgsino- or W-ino-like LSP instead of the standard B-ino LSP. We have reexamined the AD baryogenesis with special attention to the late-time decays of the Q balls, and then specified the parameter regions where the LSPs produced by the Q ball decays result in a cosmologically interesting mass density of dark matter by adopting several SUSY breaking models. This reveals new cosmologically interesting parameter regions, which have not attracted much attention so far. We have also investigated the prospects of direct and indirect detection of these dark matter candidates, and found that there is an intriguing possibility to detect them in various next generation dark matter searches.

In earlier work, the planar diagrams of ${SU(N}_c)$ gauge theory have been regulated on the light cone by a scheme involving both discrete $p^{+}$ and $\tau {=ix}^{+}.$ The transverse coordinates remain continuous, but even so all diagrams are rendered finite by this procedure. In this scheme quartic interactions are represented as two cubics mediated by short-lived fictitious particles whose detailed behavior could be adjusted to retain properties of the continuum theory, at least at one loop. Here we use this setup to calculate the one loop three gauge boson triangle diagram, and so complete the calculation of diagrams renormalizing the coupling to one loop. In particular, we find that the cubic vertex is correctly renormalized once the couplings to the fictitious particles are chosen to keep the gauge bosons massless.

Conventional lattice gauge theory assigns the lowest spin compatible with the symmetry channel of a given operator to the state coupling to that operator. Operators on a cubic lattice, however, are only defined on angles of $\pi /2;$ hence states with equal spin modulo 4 may overlap significantly. This paper explores a new technique for generating lattice operators that may be placed onto the lattice at angles other than $\pi /2,$ thereby resolving this modulo 4 ambiguity. Calculations of the mass of states with spin equal to 0, 2, and 4 are performed in the positive parity and charge conjugation channel and compared to the spectrum from previous lattice calculations. These masses compare well for spin 0 and 2, and for spin 4 the mass agrees with a state conventionally assigned spin 0, raising the possibility of misidentification of the spin of states coupling to some traditional operators.

We have searched for lepton flavor violating decays of the $\tau$ lepton with one or two $K_S^0$ mesons in the final state. The data used in the search were collected with the CLEO II and II.V detectors at the Cornell Electron Storage Ring (CESR) and correspond to an integrated luminosity of $13.9{\mathrm{fb}}^{-1}$ at the ${\rm Y}\mathrm{}\left(4S\right)\mathrm{}$ resonance. No evidence for signals were found; therefore, we have set 90% confidence level (C.L.) upper limits on the branching fractions $\mathcal{B}({\tau }^{-}\to e^{-}{K}_S^0)<\mathrm{}9.1\mathrm{}\times {10}^{-7},$ $\mathcal{B}({\tau }^{-}\to {\mu }^{-}{K}_S^0)<\mathrm{}9.5\mathrm{}\times {10}^{-7},$ $\mathcal{B}({\tau }^{-}\to e^{-}{K}_S^0{K}_S^0)<\mathrm{}2.2\mathrm{}\times {10}^{-6},$ and $\mathcal{B}({\tau }^{-}\to {\mu }^{-}{K}_S^0{K}_S^0)<\mathrm{}3.4\mathrm{}\times {10}^{-6}.$ These represent significantly improved upper limits on the two-body decays and first upper limits on the three-body decays.

The dynamically generated fermion mass is investigated in a flat brane world with (4+δ)-dimensional bulk space-time, and in the Randall-Sundrum (RS) brane world. We consider the bulk Yang-Mills theory interacting with a fermion confined on a four-dimensional brane. Based on the effective theory below a reduced cutoff scale on the brane, we formulate the Schwinger-Dyson equation of the brane fermion propagator. By using the improved ladder approximation we numerically solve the Schwinger-Dyson equation and find that the dynamical fermion mass is near the reduced cutoff scale on the brane for the flat brane world with $\delta >~3$ and for the RS brane world. In the RS brane world Kaluza-Klein excited modes of the bulk gauge field localize around the $y=\pi R$ brane and this enhances dynamical symmetry breaking on the brane. The decay constant of the fermion and the antifermion composite operator can be taken to be of the order of the electroweak scale, much smaller than the Planck scale. Therefore the electroweak mass scale can be realized from only the Planck scale in the RS brane world due to fermion and antifermion pair condensation. That is a dynamical realization of the Randall-Sundrum model which solves the weak-Planck hierarchy problem.