We consider the quark-antiquark Green’s function in the Schwinger model with instanton contributions taken into account. Thanks to the fact that this function may analytically be found, we draw out singular terms, which arise due to the formation of the bound state in the theory—the massive Schwinger boson. The principal term has a pole character. The residue in this pole contains contributions from various instanton sectors: 0, $\pm 1$, $\pm 2$. It is shown that the nonzero ones change the factorizability property. The formula for the residue is compared to the Bethe-Salpeter wave function found as a field amplitude. Next, it is demonstrated, that apart from polar part, there appears in the Green’s function also the weak branch point singularity of the logarithmic and dilogarithmic nature. These results are not in variance with the universally adopted $S$-matrix factorization.

The nonequilibrium dynamics of mixing, oscillations, and equilibration is studied in a field theory of flavored neutral mesons that effectively models two flavors of mixed neutrinos, in interaction with other mesons that represent a thermal bath of hadrons or quarks and charged leptons. This model describes the general features of neutrino mixing and relaxation via charged currents in a medium. The reduced density matrix and the nonequilibrium effective action that describes the propagation of neutrinos is obtained by integrating out the bath degrees of freedom. We obtain the dispersion relations, mixing angles and relaxation rates of neutrino quasiparticles. The dispersion relations and mixing angles are of the same form as those of neutrinos in the medium, and the relaxation rates are given by ${\Gamma }_1(k)={\Gamma }_{ee}(k){cos}^2{\theta }_m(k)+{\Gamma }_{\mu \mu }(k){sin}^2{\theta }_m(k)$; ${\Gamma }_2(k)={\Gamma }_{\mu \mu }(k){cos}^2{\theta }_m(k)+{\Gamma }_{ee}(k){sin}^2{\theta }_m(k)$ where ${\Gamma }_{\alpha \alpha }(k)$ are the relaxation rates of the flavor fields in absence of mixing, and ${\theta }_m(k)$ is the mixing angle in the medium. A Weisskopf-Wigner approximation that describes the asymptotic time evolution in terms of a non-Hermitian Hamiltonian is derived. At long time $\gg {\Gamma }_{1,2}^{-1}$ neutrinos equilibrate with the bath. The equilibrium density matrix is nearly diagonal in the basis of eigenstates of an effective Hamiltonian that includes self-energy corrections in the medium. The equilibration of “sterile neutrinos” via active-sterile mixing is discussed.

We consider the possibility that a massive fourth family neutrino, predicted by a recently proposed minimal technicolor theory, could be the source of the dark matter in the Universe. The model has two techniflavors in the adjoint representation of a SU(2) techicolor gauge group and its consistency requires the existence of a fourth family of leptons. By a suitable hypercharge assignment the techniquarks together with the new leptons look like a conventional fourth standard model family. We show that the new (Majorana) neutrino $N$ can be the dark matter particle if $m_N\sim 100–500\mathrm{GeV}$ and the expansion rate of the Universe at early times is dominated by an energy component scaling as ${\rho }_{\varphi }\sim a^{-6}$ (kination), with ${\rho }_{\varphi }/{\rho }_{\mathrm{rad}}\sim {10}^{-6}$ during the nucleosynthesis era.

We consider the spacetime structure of Kerr-Gödel black holes, analyzing their parameter space in detail. We apply the tunnelling method to compute their temperature and compare the results to previous calculations obtained via other methods. We claim that it is not possible to have the closed timelike curve (CTC) horizon in between the two black hole horizons and include a discussion of issues that occur when the radius of the CTC horizon is smaller than the radius of both black hole horizons.

We study the stability of black holes that are solutions of the dilaton gravity derived from string-theoretical models in two and five dimensions under scalar field perturbations, using the Quasinormal Modes (QNMs) approach. In order to find the QNMs corresponding to a black hole geometry, we consider perturbations described by a massive scalar field nonminimally coupled to gravity. We find that the QNMs frequencies turn out to be pure imaginary leading to purely damped modes, in the range $0<\zeta <1/4$ of nonminimal coupling constant ($\zeta$), and the QNMs acquires a real part if $\zeta >1/4$ that is in agreement with the literature of dilatonic black holes. Our result exhibits the unstable behavior of the considered geometry against scalar perturbations. We study the instability for different values of nonminimal coupling constant. We extend our results to the $4+1$ dimensional dilatonic black hole, where the metric is the product of a two-dimensional asymptotically flat geometry and a three-sphere with constant radius, which are completely decoupled from each other. The exact solution for the QNMs was obtained in the five-dimensional case.

The Larmor formula for scalar and gravitational radiation from a pointlike particle is derived in any even higher-dimensional flat spacetime. General expressions for the field in the wave zone and the energy flux are obtained in closed form. The explicit results in four and six dimensions are used to illustrate the effect of extra dimensions on linear and uniform circular motion. Prospects for detection of bulk gravitational radiation are briefly discussed.

We study the geometry and dynamics of both isolated and dynamical trapping horizons by considering the allowed variations of their foliating two-surfaces. This provides a common framework that may be used to consider both their possible evolutions and their deformations as well as derive the well-known flux laws. Using this framework, we unify much of what is already known about these objects as well as derive some new results. In particular we characterize and study the “almost isolated” trapping horizons known as slowly evolving horizons. It is for these horizons that a dynamical first law holds and this is analogous and closely related to the Hawking-Hartle formula for event horizons.

We consider quantum backreaction of the quantized scalar field with an arbitrary mass and curvature coupling on ultraextremal horizons. The problem is distinguished in that (in contrast to nonextremal or extremal black holes) the WKB approximation remains valid near $r_{+}$ (which is the radius of the horizon) even in the massless limit. We examine the behavior of the stress-energy tensor of the quantized field near $r_{+}$ and show that quantum-corrected objects under discussion do exist. In the limit of the large mass our results agree with previous ones known in literature.

Models with interacting dark energy can alleviate the cosmic coincidence problem by allowing dark matter and dark energy to evolve in a similar fashion. At a fundamental level, these models are specified by choosing a functional form for the scalar potential and for the interaction term. However, in order to compare to observational data it is usually more convenient to use parametrizations of the dark energy equation of state and the evolution of the dark matter energy density. Once the relevant parameters are fitted, it is important to obtain the shape of the fundamental functions. In this paper I show how to reconstruct the scalar potential and the scalar interaction with dark matter from general parametrizations. I give a few examples and show that it is possible for the effective equation of state for the scalar field to cross the phantom barrier when interactions are allowed. I analyze the uncertainties in the reconstructed potential arising from foreseen errors in the estimation of fit parameters and point out that a Yukawa-like linear interaction results from a simple parametrization of the coupling.

$B$-modes of cosmic microwave background (CMB) polarization can be created by a primordial gravitational wave background. If this background was created by inflation, then the amplitude of the polarization signal is proportional to the energy density of the universe during inflation. The primordial signal will be contaminated by polarized foregrounds including dust and synchrotron emission within the galaxy. In light of the WMAP polarization maps, we consider the ability of several hypothetical CMB polarization experiments to separate primordial CMB $B$-mode signal from galactic foregrounds. We also study the optimization of a CMB experiment with a fixed number of detectors in the focal plane to determine how the detectors should be distributed in different frequency bands to minimize foreground confusion. We show that the optimal configuration requires observations in at least 5 channels spread over the frequency range between 30 and 500 GHz with substantial coverage around 150 GHz. If a low-resolution space experiment using 1000 detectors to reach a noise level of about $1000{\mathrm{nK}}^2$ concentrates on roughly 66% of the sky with the least foreground contamination, the minimum detectable level of the tensor-to-scalar ratio would be about 0.002 at the 99% confidence level for an optical depth of 0.1.

We consider the coupling of quintessence to observable matter in supergravity and study the dynamics of both supersymmetry breaking and quintessence in this context. We investigate how the quintessence potential is modified by supersymmetry breaking and analyze the structure of the soft supersymmetry-breaking terms. We pay attention to their dependence on the quintessence field and to the electroweak symmetry breaking, i.e. the pattern of fermion masses at low energy within the minimal supersymmetric standard model (MSSM) coupled to quintessence. In particular, we compute explicitly how the fermion masses generated through the Higgs mechanism depend on the quintessence field for a general model of quintessence. Fifth force and equivalence principle violations are potentially present as the vacuum expectation values of the Higgs bosons become quintessence field dependent. We emphasize that equivalence principle violations are a generic consequence of the fact that, in the MSSM, the fermions couple differently to the two Higgs doublets. Finally, we also discuss how the scaling of the cold dark and baryonic matter energy density is modified and comment on the possible variation of the gauge coupling constants, among which is the fine structure constant, and of the proton-electron mass ratio.

We investigate the signals of a supersymmetric scenario where the lighter tau-sneutrino is the lightest supersymmetric particle, while the lighter stau-state is the next lightest. We confirm that such a scenario can be motivated within the framework of minimal supergravity, with just the addition of a right-chiral neutrino superfield. Such a spectrum leads to rather unusual signals of supersymmetry, showing stable tracks of the stau in the muon chambers. We have studied two types of signals, namely, (a) two or more hard jets and two stau tracks, and (b) hard jets with two muons and two stau tracks. We demonstrate that the stau tracks can be distinguished from the muonic ones through proper kinematic cuts which also enable one to remove all standard model backgrounds.

We present the new analysis of the semileptonic $B$ decays in the framework of the relativistic quark model based on the quasipotential approach. Decays both to heavy $D^{(*)}$ and light $\pi (\rho )$ mesons are considered. All relativistic effects are systematically taken into account including contributions of the negative-energy states and the wave function transformation from the rest to moving reference frame. For heavy-to-heavy transitions the heavy quark expansion is applied. Leading and subleading Isgur-Wise functions are determined as the overlap integrals of initial and final meson wave functions. For heavy-to-light transitions the explicit relativistic expressions are used to determine the dependence of the form factors on the momentum transfer squared. Such treatment significantly reduces theoretical uncertainties and increases reliability of obtained predictions. All results for form factors, partial and total decay rates agree well with recent experimental data and unquenched lattice calculations. From this comparison we find the following values of the Cabibbo-Kobayashi-Maskawa matrix elements: $|V_{cb}|=(3.85\pm 0.15\pm 0.20)\times {10}^{-2}$ and $|V_{ub}|=(3.82\pm 0.20\pm 0.20)\times {10}^{-3}$, where the first error is experimental and the second one is theoretical.

We reexamine $CP$ violation in the $\Delta S=0$ decays $\tau \to N\pi {\nu }_{\tau }$ ($N=2,3,4$). We assume that the new physics (NP) is a charged Higgs boson. We show that there is no NP contribution to $\tau \to \pi \pi {\nu }_{\tau }$, which means that no $CP$ violation is expected in this decay. On the other hand, NP can contribute to $\tau \to N\pi {\nu }_{\tau }$ ($N=3,4$). These are dominated by the intermediate resonant decays $\tau \to \omega \pi {\nu }_{\tau }$, $\tau \to \rho \pi {\nu }_{\tau }$, and $\tau \to a_1\pi {\nu }_{\tau }$. We show that the only sizeable $CP$-violating effects which are possible are in $\tau \to a_1\pi {\nu }_{\tau }\to 4\pi {\nu }_{\tau }$ (polarization-dependent rate asymmetry) and $\tau \to \omega \pi {\nu }_{\tau }$ (triple-product asymmetry).

In the littlest Higgs model with $T$ parity, which predicts a pair of $T$-even and $T$-odd partners for the top quark, the top-quark interactions are altered with respect to the standard model predictions and the deviation will manifest in various top-quark processes. In this work we examine the effects in $ht\overline{t}$ productions at the International Linear Collider and CERN LHC. We find that, in the allowed parameter space, the cross sections can be significantly deviated from the standard model predictions and thus provide a good test for the littlest Higgs model with $T$ parity. We also examine the new production channel, $ht\overline{T}$ or $hT\overline{t}$ production, at the LHC, which gives the same final states as $ht\overline{t}$ production due to the dominant decay $T\to Wb$. We find that, compared with $ht\overline{t}$ production, this new production channel can have a sizable production rate for a $T$ quark below the TeV scale. Such a production will be counted into $ht\overline{t}$ events or possibly extracted from $ht\overline{t}$ events, depending on if we can distinguish the $T$ quark from the top quark from mass reconstructions.

The parent action method is utilized to the Born-Infeld and $Dp$-brane theories. Various new forms of Born-Infeld and $Dp$-brane actions are derived by using this systematic approach, in which both the already known 2-metric and newly proposed 3-metric prescriptions are considered. An auxiliary worldvolume tensor field, denoted by ${\omega }_{\mu \nu }$, is introduced and treated probably as an additional worldvolume metric because it plays a similar role to that of the auxiliary worldvolume (also called intrinsic) metric ${\gamma }_{\mu \nu }$. Some properties, such as duality, permutation and Weyl invariance as a local worldvolume symmetry of the new forms are analyzed. In particular, a new symmetry, i.e. the double Weyl invariance is discovered in 3-metric forms.

Models where the dark matter component of the Universe interacts with the dark energy field have been proposed as a solution to the cosmic coincidence problem, since in the attractor regime both dark energy and dark matter scale in the same way. In these models the mass of the cold dark matter particles is a function of the dark energy field responsible for the present acceleration of the Universe, and different scenarios can be parametrized by how the mass of the cold dark matter particles evolves with time. In this article we study the impact of a constant coupling $\delta$ between dark energy and dark matter on the determination of a redshift dependent dark energy equation of state $w_{\mathrm{DE}}(z)$ and on the dark matter density today from SNIa data. We derive an analytical expression for the luminosity distance in this case. In particular, we show that the presence of such a coupling increases the tension between the cosmic microwave background data from the analysis of the shift parameter in models with constant $w_{\mathrm{DE}}$ and SNIa data for realistic values of the present dark matter density fraction. Thus, an independent measurement of the present dark matter density can place constraints on models with interacting dark energy.

We present a new constraint for the axion monopole-dipole coupling in the range of $1\mu \mathrm{m}$–a few mm, previously unavailable for experimental study. The constraint was obtained using our recent results on the observation of neutron quantum states in the Earth’s gravitational field. We exploit the ultimate sensitivity of ultracold neutrons (UCN) in the lowest gravitational states above a material surface to any additional interaction between the UCN and the matter, if the characteristic interaction range is within the mentioned domain.

We consider a technicolor model in which the expectation value of an additional, possibly composite, scalar field is responsible for the generation of fermion masses. We define the dynamics of the strongly coupled sector by constructing its holographic dual. Using the AdS/CFT correspondence, we study the $S$ parameter and the phenomenology of the light technihadrons. We find that the $S$ parameter is small over a significant region of the model’s parameter space. The particle spectrum is distinctive and includes a nonstandard Higgs boson as well as heavier hadronic resonances. Technihadron masses and decay rates are calculated holographically, as a function of the model’s parameters.

We study the lepton sector in the model based on the local gauge group $SU(3{)}_c\otimes SU(3{)}_L\otimes U(1{)}_X$, which does not contain particles with exotic electric charges. The seesaw mechanism and discrete $A_4$ symmetry are introduced into the model to help us understand why neutrinos are especially light and have the observed pattern of neutrino mixing. The model provides a method for obtaining the tribimaximal mixing matrix in the leading order. A nonzero mixing angle $V_{e3}$ is presented in the modified mixing matrix.