The possibility that extremely long-lived, time-dependent, and localized field configurations (“oscillons”) arise during the collapse of asymmetrical bubbles in (2+1)-dimensional ${\phi }^4$ models is investigated. It is found that oscillons can develop from a large spectrum of elliptically deformed bubbles. Moreover, we provide numerical evidence that such oscillons are (a) circularly symmetric and (b) linearly stable against small arbitrary radial and angular perturbations. The latter is based on a dynamical approach designed to investigate the stability of nonintegrable time-dependent configurations that is capable of probing slowly growing instabilities not seen through the usual “spectral” method.

We consider the $N=1\mathrm{}$ supersymmetric kink on a circle, i.e., on a finite interval with boundary or transition conditions which are locally invisible. For Majorana fermions, the single-particle Dirac Hamiltonian as a differential operator obeys simultaneously the three discrete symmetries of charge conjugation, parity, and time reversal. However, no single locally invisible transition condition can satisfy all three. When calculating sums over zero-point energies by mode number regularization, this gives a new rationale for a previous suggestion that one has to average over different choices of boundary conditions, such that for the combined set all three symmetries are obeyed. In particular it is shown that for twisted periodic or twisted antiperiodic boundary conditions separately both parity and time reversal are violated in the kink sector, as manifested by a delocalized momentum that cancels only in the average.

Gauge symmetry breaking through the Hosotani mechanism (the dynamics of nonintegrable phases) in softly broken supersymmetric QCD with $N_F^{\mathrm{fd}}$ flavors is studied. For $N=\mathrm{even},$ there is a single $\mathrm{SU}\left(N\right)\mathrm{}$ symmetric vacuum state, while for $N=\mathrm{odd},$ there is a doubly degenerate $\mathrm{SU}\left(N\right)\mathrm{}$ symmetric vacuum state in the model. We also study generalized supersymmetric QCD by adding $N_F^{\mathrm{adj}}$ numbers of massless adjoint matter. The gauge symmetry breaking pattern such as $\mathrm{SU}\left(3\right)\mathrm{}\to \mathrm{SU}\left(2\right)\mathrm{}\times U\left(1\right)\mathrm{}$ is possible for appropriate choices of the matter content and values of the supersymmetry breaking parameter. The massless state of the adjoint Higgs scalar is also discussed in the models.

We calculate conformal anomalies in noncommutative gauge theories by using the path integral method (Fujikawa’s method). Along with the axial anomalies and chiral gauge anomalies, conformal anomalies take the form of the straightforward Moyal deformation in the corresponding conformal anomalies in ordinary gauge theories. However, the Moyal star product leads to the difference in the coefficient of the conformal anomalies between noncommutative gauge theories and ordinary gauge theories. The β (Callan-Symanzik) functions which are evaluated from the coefficient of the conformal anomalies coincide with the result of perturbative analysis.

We study static spherically symmetric solutions of high derivative gravity theories, with 4, 6, 8 and even 10 derivatives. Except for isolated points in the space of theories with more than 4 derivatives, only solutions that are nonsingular near the origin are found. But these solutions cannot smooth out the Schwarzschild singularity without the appearance of a second horizon. This conundrum, and the possibility of singularities at finite r, leads us to study numerical solutions of theories truncated at four derivatives. Rather than two horizons we are led to the suggestion that the original horizon is replaced by a rapid nonsingular transition from weak to strong gravity. We also consider this possibility for the de Sitter horizon.

We present unified ways of handling the cosmological perturbations in a class of gravity theory covered by a general action. This gravity includes our previous generalized $f(\phi ,R)$ gravity and the gravity theory motivated by the tachyonic condensation. We present a general prescription to derive the power spectra generated from vacuum quantum fluctuations in the slow-roll inflation era. An application is made to a slow-roll inflation based on the tachyonic condensation with an exponential potential.

The low energy effective theory for the Randall-Sundrum two-brane system is investigated with an emphasis on the role of the nonlinear radion in the brane world. The equations of motion in the bulk are solved using a low energy expansion method. This allows us, through the junction conditions, to deduce the effective equations of motion for gravity on the brane. It is shown that the gravity on the brane world is described by a quasi-scalar-tensor theory with a specific coupling function $\omega \left(\Psi \right)=3\mathrm{}\Psi /2\left(1\mathrm{}-\Psi \right)$ on the positive tension brane and $\omega \left(\Phi \right)=-3\Phi /2(1+\Phi )$ on the negative tension brane, where $\Psi$ and $\Phi$ are nonlinear realizations of the radion on the positive and negative tension branes, respectively. In contrast with the usual scalar-tensor gravity, the quasi-scalar-tensor gravity couples with two kinds of matter; namely, the matter on both positive and negative tension branes, with different effective gravitational coupling constants. In particular, the radion disguised as the scalar fields $\Psi$ and $\Phi$ couples with the sum of the traces of the energy-momentum tensor on both branes. In the course of the derivation, it is revealed that the radion plays an essential role in converting the nonlocal Einstein gravity with generalized dark radiation to local quasi-scalar-tensor gravity. For completeness, we also derive the effective action for our theory by substituting the bulk solution into the original action. It is also shown that quasi-scalar-tensor gravity works as a hologram at low energy in the sense that the bulk geometry can be reconstructed from the solution of quasi-scalar-tensor gravity.

We investigate the constraint on the split fermions in extra dimensions by considering the universality of W leptonic decays $\overrightarrow{W}{l}_i{\nu }_i,$ the charged lepton decays $l_i\to l_j{\nu }_i{\overline{\nu }}_j,$ and the lepton flavor violating process $l_i\to l_j{l}_k{l}_h$ where $l_i=e,\mu$ or $\tau .$ For the standard model (SM) background of $\overrightarrow{W}{l}_i{\nu }_i,$ we extended the one loop quantum correction to include effects of order $m_l^2{/M}_W^2$ and the Higgs boson mass dependence. We find that in general the split fermion scenarios giving rise to 4D effective Yukawa matrices of the Kaluza-Klein Higgs bosons which are misaligned with respect to the fermion mass matrix. This holds true also for gauge bosons as well. This leads to decays of $l_i\to l_j{l}_k{l}_h$ at the tree level and muonium antimuonium conversion. Interestingly the leptonic universality of W boson decays are not affected at this level.

We derive constraints on the Randall-Sundrum scenario with the standard model fields in the bulk. These result from tree level effects associated with the deformation of the zero mode wave functions of the W and the Z once electroweak symmetry is broken. Recently Csáki, Erlich and Terning pointed out that this implies large contributions to electroweak oblique parameters. Here we find that when fermions are allowed in the bulk the couplings of the W and the Z to zero-mode fermions are also affected. We perform a fit to electroweak observables, assuming universal bulk fermion masses and including all effects, and find constraints that are considerably stronger than for the case with fermions localized in the low energy boundary. These put the lowest Kaluza-Klein excitation out of reach of the CERN Large Hadron Collider. We then relax the universality assumption and study the effects of flavor violation in the bulk and its possible signatures.

We consider a recent proposal by Dimopoulos and Kaplan to embed the electroweak $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\times \mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_Y$ into a larger group $\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}_W\times \mathrm{SU}\mathrm{}\left(2\right)\mathrm{}\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ at a scale above a TeV. This idea is motivated by the prediction for the weak mixing angle ${\sin }^2{\theta }_W=1/4,$ which naturally appears in these models so long as the gauge couplings of the high energy SU(2) and U(1) groups are moderately large. The extended gauge dynamics results in new effective operators that contribute to four-fermion interactions and Z pole observables. We calculate the corrections to these electroweak precision observables and carry out a global fit of the new physics to the data. For SU(2) and U(1) gauge couplings larger than $1,$ we find that the 95% C.L. lower bound on the matching (heavy gauge boson mass) scale is 11 TeV. We comment on the fine-tuning of the high energy parameters needed to allow matching scales above our bounds. The remnants of $\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}_W$ breaking include multi-TeV $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L$ doublets with electric charge $(\pm 2,\pm 1).$ The lightest charged gauge boson is stable, leading to cosmological difficulties.

Supersymmetric models often predict a lightest superpartner (LSP) which is electrically charged and stable on the time scales of collider experiments. If such a particle were to be observed experimentally, is it possible to determine whether or not it is stable on cosmological time scales? Charged, stable particles are usually considered to be excluded by cosmological arguments coupled with terrestrial searches for anomalously heavy water molecules. But when the cosmology is significantly altered, as can happen in models with large extra dimensions, these arguments are in turn significantly weakened. In this paper we suggest an alternate way to use searches for superheavy water to constrain the lifetimes of long-lived, charged particles, independent of most cosmological assumptions. By considering supersymmetric production by cosmic rays in the upper atmosphere, we are able to use current bounds on superheavy water to constrain the mass scale of squarks and gluinos to be greater than about $230\mathrm{GeV},$ assuming a stable, charged LSP. This bound can be increased, but only by significantly increasing the size of the initial water sample tested.

In a previous work we have shown that a general two-Higgs-doublet model with a very light $\mathrm{CP}$-odd scalar can be compatible with electroweak precision data, such as the $\rho$ parameter, $\mathrm{BR}\left(\overrightarrow{b}s\gamma \right),$ $R_b,$ $A_b,$ $\mathrm{BR}\left(\overrightarrow{{\rm Y}}A\gamma \right),$ $\mathrm{BR}\left(\overrightarrow{\eta }A\gamma \right),$ and $\left(g-2\right)$ of the muon. Prompted by the recent significant change in the theoretical status of the latter observable, we comment on the consequences for this model and update the allowed parameter region. It is found that the presence of a very light scalar with a mass of 0.2 GeV is still compatible with the new theoretical prediction of the muon anomalous magnetic moment.

We study the rate and $\phi$ momentum distribution in semi-inclusive decays $\overrightarrow{B}\phi X_s$ induced by the quark level processes $\overrightarrow{b}\phi s$ and $\overrightarrow{b}\phi sg,$ in which the gluon is radiated from the internal charm quark loop or emitted from the virtual gluon of the strong penguin (inner bremsstrahlung) process. We find $\mathcal{B}\left(\overrightarrow{b}\phi s\right)=6.7\mathrm{}\times {10}^{-5}$ and $\mathcal{B}\left(\overrightarrow{b}\phi sg\right)=3.8\mathrm{}\times {10}^{-5}.$ The momentum spectrum of $\phi$ produced by $\overrightarrow{b}\phi \mathrm{sg}$ is very broad. With the cut $|{\mathbf{k}}_{\phi }|>~2.0\mathrm{GeV},$ $\mathcal{B}\left(\overrightarrow{b}\phi s\right)=6.1\mathrm{}\times {10}^{-5}$ (where the Fermi motion of the b quark in the B meson is described by a Gaussian), and $\mathcal{B}\left(\overrightarrow{b}\phi sg\right)=1.0\mathrm{}\times {10}^{-5}.$ Because of the special nature of $\phi ,$ many difficulties that hindered a reliable theoretical prediction for $\overrightarrow{B}{\eta }^{\prime }{X}_s$ decay are absent in the process $\overrightarrow{B}\phi X_s.$ Therefore, theoretical predictions for $\overrightarrow{B}\phi X_s$ are relatively clean. Moreover, the clear experimental signature of the $\phi$ is of great help. Data for $\overrightarrow{B}\phi X_s,$ both the branching ratio and the $\phi$ momentum distribution, would teach us about the strength of strong penguin processes which might be of great importance in the search for $\mathrm{CP}$ violation and for new physics at B factories.

The nonperturbative effects in the quark form factor are considered in the Wilson loop formalism. The properties of the Wilson loops with cusp singularities are studied taking into account the perturbative and nonperturbative contributions, where the latter are considered within the framework of the instanton liquid model. For the integration path corresponding to this form factor—the angle with infinite sides—the explicit expression for the vacuum expectation value of the Wilson operator is found to leading order. The calculations are performed in the weak-field limit for the instanton vacuum contribution and compared with the one- and two-loop order results for the perturbative part. It is shown that the instantons produce the powerlike corrections to the perturbative result, which are comparable in magnitude with the perturbative part at the scale of order of the inverse average instanton size. It is demonstrated that the instanton contributions to the quark form factor are exponentiated to high orders in the small instanton density parameter.

The perturbative expression of the running strong coupling constant ${\alpha }_{\mathrm{s}}{(Q}^2)$ has an unphysical singularity for $Q^2={\Lambda }_{\mathrm{QCD}}^2.$ Various modification have been proposed for the infrared region. The effect of some of such proposals on the quark-antiquark spectrum is tested on a Bethe-Salpeter (second order) formalism which was successfully applied in previous papers to an overall evaluation of the spectrum in the light-light, light-heavy and heavy-heavy sectors (the only serious discrepancy with data being for the light pseudoscalar meson masses). In this paper only the $c\overline{c},$ $b\overline{b}$ and $q\overline{q}$ $(q=u$ or $d)$ cases are considered and fine structure is neglected. It is found that in the $b\overline{b}$ and $c\overline{c}$ cases the results are little sensitive to the specific choice. In the light-light case the Dokshitzer et al. prescription is again essentially equivalent to the truncation prescription used in the previous calculation and it is consistent with the same a priori fixing of the light quark masses on the typical current values $m_{\mathrm{u}}{=m}_{\mathrm{d}}=10\mathrm{}\mathrm{MeV}$ (only the pion mass resulting completely out of scale at about 500 MeV). With the Shirkov-Solovtsov prescription, on the contrary, a reasonable agreement with the data is obtained only at the price of using a phenomenological momentum dependent effective mass for the quark. The use of such an effective mass amounts to a correction of the free quark propagator. It is remarkable that this also has the effect of bringing the pion mass into the correct range.

We present regular solutions for a brane world scenario in the form of a ’t Hooft–Polyakov monopole living in the three-dimensional spherically symmetric transverse space of a seven-dimensional space-time. In contrast with the cases of a domain wall in five dimensions and a string in six dimensions, there exist gravity-localizing solutions for both signs of the bulk cosmological constant. A detailed discussion of the parameter space that leads to localization of gravity is given. A pointlike monopole limit is discussed.

We examine the first order Fermi acceleration on the presumption that supernova remnant shocks cross ambient magnetic fields with various angles. These oblique shocks accelerate particles more efficiently than the parallel shocks and elevate the maximum energies achievable by the particles. The primary cosmic ray spectrum is strongly dependent upon these energies. We also consider the dependence of the injection efficiency and of spectral indices on obliquity. When indices and absolute fluxes at ${10}^{12}$ eV are given for six nuclear groups from balloon-borne data, each energy spectrum develops a smooth rigidity dependent knee structure. The resultant total spectrum also behaves similarly and fits well with ground-based experimental data up to several ${10}^{17}$ eV. It is shown as well that the chemical composition changes significantly from lighter to heavier nuclei as the energies of particles exceed the knee region. Other predicted curves are compared with the experimental data which they reproduce rather well.

Finite temperature Euclidean $\mathrm{SU}\left(2\right)\mathrm{}$ lattice gauge fields generated in the confinement phase close to the deconfinement phase transition are subjected to cooling. The aim is to identify long-living, almost-classical local excitations which carry (generically noninteger) topological charge. Two kinds of spatial boundary conditions (fixed holonomy and standard periodic boundary conditions) are applied. For the lowest-action configurations we find that their relative probability semi-quantitatively agrees for both types of boundary conditions. We find calorons with unit topological charge as well as (anti-)self-dual lumps of noninteger (equal or opposite sign) topological charge (Bogomol’nyi-Prasad-Sommerfield monopoles or dyons) combined in pairs. For calorons and separated pairs of equal-sign dyons we have found (i) the gluon field to be well-described by Kraan–van Baal solutions of the field equations and (ii) the real Wilson-fermion modes to be well approximated by analytic solutions of the corresponding Dirac equation. For metastable configurations found at higher action, the multicenter structure can also be interpreted in terms of dyons and antidyons, using the gluonic and fermionic indicators as for the dyon-pair case. We argue that an improvement of the semiclassical caloron approach to the nonzero temperature path integral should take into account superpositions of solutions with nontrivial holonomy.

The value of the bottom quark mass at ${Q=M}_Z$ in the $\overline{\mathrm{DR}}$ scheme is an important input for the analysis of supersymmetric models with a large value of $\tan \beta .$ Conventionally, however, the running bottom quark mass extracted from experimental data is quoted in the $\overline{\mathrm{MS}}$ scheme at the scale ${Q=m}_b.$ We describe a two loop procedure for the conversion of the bottom quark mass from the $\overline{\mathrm{MS}}$ to $\overline{\mathrm{DR}}$ scheme. The Particle Data Group value $m_b^{\overline{\mathrm{MS}}}{(m}_b^{\overline{\mathrm{MS}}})=4.2\mathrm{}\pm 0.2\mathrm{GeV}$ corresponds to a range of 2.65–3.03 GeV for $m_b^{\overline{\mathrm{DR}}}{(M}_Z).\mathrm{}$

We investigate the effect of axions on the polarization of electromagnetic waves as they propagate through astronomical distances. We analyze the change in the dispersion of the electromagnetic wave due to its mixing with axions. We find that this leads to a shift in polarization and turns out to be the dominant effect for a wide range of frequencies. We analyze whether this effect or the decay of photons into axions can explain the large scale anisotropies which have been observed in the polarizations of quasars and radio galaxies. We also comment on the possibility that the axion-photon mixing can explain the dimming of distant supernovae.