We study theoretically the quantum motion of a neutron in a horizontal waveguide in the gravitational field of the Earth. The waveguide in question is equipped with a mirror below and a rough surface absorber above. We show that such a system acts as a quantum filter, i.e. it effectively absorbs quantum states with sufficiently high transversal energy but transmits low-energy states. The states transmitted are determined mainly by the potential well formed by the gravitational field of the Earth and the mirror. The formalism developed for quantum motion in an absorbing waveguide is applied to the description of the recent experiment on the observation of the quantum states of neutrons in the Earth’s gravitational field.

The description of extreme-mass-ratio binary systems in the inspiral phase is a challenging problem in gravitational wave physics with significant relevance for the space interferometer LISA. The main difficulty lies in the evaluation of the effects of the small body’s gravitational field on itself. To that end, an accurate computation of the perturbations produced by the small body with respect the background geometry of the large object, a massive black hole, is required. In this paper we present a new computational approach based on finite element methods to solve the master equations describing perturbations of nonrotating black holes due to an orbiting pointlike object. The numerical computations are carried out in the time domain by using evolution algorithms for wave-type equations. We show the accuracy of the method by comparing our calculations with previous results in the literature. Finally, we discuss the relevance of this method for achieving accurate descriptions of extreme-mass-ratio binaries.

We explore the physics of a gas of particles interacting with a condensate that spontaneously breaks Lorentz invariance. The equation of state of this gas varies from $1/3$ to less than $-1$ and can lead to the observed cosmic acceleration without requiring a vacuum energy. The particles are always stable. In our particular class of models these particles are fermions with a chiral coupling to the condensate. They may behave as relativistic matter at early times, produce a brief period where they dominate the expansion with $w<0$ today, and behave as matter at late time. There are no small parameters in our models, which generically lead to dark energy clustering and, depending on the choice of parameters, smoothing of small scale power.

It is widely accepted that moduli in the mass range $10\mathrm{eV}–{10}^4\mathrm{GeV}$ which start to oscillate with an amplitude of the order of the Planck scale either jeopardize successful predictions of nucleosynthesis or overclose the Universe. It is shown that the moduli problem can be relaxed by making use of parametric resonance. A new nonperturbative decay channel for moduli oscillations is discussed. This channel becomes effective when the oscillating field results in a net negative mass term for the decay products. This scenario allows for the decay of the moduli much before nucleosynthesis and, therefore, leads to a complete solution of the cosmological moduli problem.

We investigate a kind of interacting Chaplygin gas model in which the Chaplygin gas plays the role of dark energy and interacts with cold dark matter particles. We find that there exists a stable scaling solution at late times with the Universe evolving into a phase of steady state. Furthermore, the effective equation of state of Chaplygin gas may cross the so-called phantom divide $w=-1$. The above results are derived from continuity equations, which means that they are independent of any gravity theories. Assuming standard general relativity and a spatially flat Friedamnn-Robertson-Walker (FRW) metric, we also find the deceleration parameter is well consistent with current observations.

A method to estimate the reliability of a perturbative expansion of the stochastic inflationary Langevin equation is presented and discussed. The method is applied to various inflationary scenarios, as large field, small field, and running mass models. It is demonstrated that the perturbative approach is more reliable than could be naïvely suspected and, in general, only breaks down at the very end of inflation.

A perturbative method for solving the Langevin equation of inflationary cosmology in the presence of backreaction is presented. In the Gaussian approximation, the method permits an explicit calculation of the probability distribution of the inflaton field for an arbitrary potential, with or without the volume effects taken into account. The perturbative method is then applied to various concrete models, namely, large field, small field, hybrid, and running mass inflation. New results on the stochastic behavior of the inflaton field in those models are obtained. In particular, it is confirmed that the stochastic effects can be important in new inflation while it is demonstrated they are negligible in (vacuum dominated) hybrid inflation. The case of stochastic running mass inflation is discussed in some details and it is argued that quantum effects blur the distinction between the four classical versions of this model. It is also shown that the self-reproducing regime is likely to be important in this case.

We extend our models for conformal sequestering of dynamical supersymmetry breaking with decoupling vectorlike matter in several different ways. These extensions enable us to simplify concrete model building, in particular, rendering large gauge group and ad hoc global symmetry for sequestering unnecessary. Conformal sequestering appears highly natural in such circumstances.

Considering corrections from two-loop Feynman diagrams which involve a gluino at large $\tan \beta$, we analyze the effects of possible $CP$ phases on the rare $B$ decays: ${\overline{B}}_s\to l^{+}{l}^{-}$ and $\overline{B}\to K{l}^{+}{l}^{-}$ in the $CP$ violating minimal supersymmetric extension of the standard model. It is shown that the results of exact two-loop calculations obviously differ from those including one-loop contributions plus threshold radiative corrections. The numerical analysis indicates that the possibly large $CP$ phases strongly affect the theoretical estimation of the branching ratios, and these results coincide with the conclusion of some other works appearing in recent literature.

We calculate $B_{(s)}$ and $D_{(s)}$ to $K_0^{*}(1430)$ transition form factors, and study semileptonic decays of $B_{(s)}$ and $D_{(s)}\to K_0^{*}(1430)\overline{\ell }\nu$ based on QCD sum rule. Measuring these semileptonic decays with high statistics will give valuable information on the nature of light scalar mesons.

We analyze the $B\to \varphi K^{*}$ polarization puzzle in the minimal supersymmetric standard model (MSSM) including the neutral Higgs boson (NHB) contributions. To calculate the nonfactorizable contributions to the hadronic matrix elements of operators, we have used the QCD factorization framework to the ${\alpha }_s$ order. It is shown that the recent experimental results of the polarization fractions in $B\to \varphi K^{*}$ decays, which are difficult to be explained in SM, could be explained in MSSM if there are flavor nondiagonal squark mass matrix elements of 2nd and 3rd generations, which also satisfy all relevant constraints from known experiments ($B\to X_s\gamma ,B_s\to {\mu }^{+}{\mu }^{-},B\to X_s{\mu }^{+}{\mu }^{-},B\to X_{s}g,\Delta M_s$, etc.). We have shown in detail that the experimental results can be accommodated with the flavor nondiagonal mass insertion of chirality RL, $\mathrm{RL}+\mathrm{LR}$, RR, or $\mathrm{LL}+\mathrm{RR}$ when the NHB contributions as well as $\mathcal{O}({\alpha }_s)$ corrections of hadronic matrix elements of operators are included. However, the branching ratios for the decay are smaller than the experimental measurements.

We study the effect of neutrino trapping on the phase diagram of dense, locally neutral three-flavor quark matter within the framework of a Nambu–Jona-Lasinio model. In the analysis, dynamically generated quark masses are taken into account self-consistently. The phase diagrams in the plane of temperature and quark chemical potential, as well as in the plane of temperature and lepton-number chemical potential are presented. We show that neutrino trapping favors two-flavor color superconductivity and disfavors the color-flavor-locked phase at intermediate densities of matter. At the same time, the location of the critical line separating the two-flavor color-superconducting phase and the normal phase of quark matter is little affected by the presence of neutrinos. The implications of these results for the evolution of protoneutron stars are briefly discussed.

We investigate the feasibility of probing the neutrino mass hierarchy and the mixing angle ${\varphi }_{13}$ with the neutrino burst from a future supernova. An inverse power-law density $\rho \sim r^n$ with varying $n$ is adopted in the analysis as the density profile of a typical core-collapse supernova. The survival probabilities of ${\nu }_e$ and ${\overline{\nu }}_e$ are shown to reduce to two-dimensional functions of $n$ and ${\varphi }_{13}$. It is found that in the $n-{sin}^2{\varphi }_{13}$ parameter space, the 3D plots of the probability functions exhibit highly nontrivial structures that are sensitive to the mass hierarchy, the mixing angle ${\varphi }_{13}$, and the value of $n$. The conditions that lead to observable differences in the 3D plots are established. With the uncertainty of $n$ considered, a qualitative analysis of the Earth matter effect is also included.

The little Higgs scenario may provide an interesting framework to accommodate TeV scale leptogenesis, because a TeV Majorana mass of the right-handed neutrino that we employ for the latter may find a natural place near the ultraviolet cutoff of the former. In this work we study how a light neutrino spectrum, generated radiatively, and TeV scale leptogenesis can be embedded in the simplest little Higgs framework. Alternatively, we highlight how the neutrino Yukawa textures of the latter are constrained.

A model-independent partial-wave analysis of the $S$-wave component of the $K\pi$ system from decays of $D^{+}$ mesons to the three-body $K^{-}{\pi }^{+}{\pi }^{+}$ final state is described. Data come from the Fermilab E791 experiment. Amplitude measurements are made independently for ranges of $K^{-}{\pi }^{+}$ invariant mass, and results are obtained below $825\mathrm{MeV}/c^2$, where previous measurements exist only in two mass bins. This method of parametrizing a three-body decay amplitude represents a new approach to analyzing such decays. Though no model is required for the $S$-wave, a parametrization of the relatively well-known reference $P$- and $D$-waves, optimized to describe the data used, is required. In this paper, a Breit-Wigner model is adopted to describe the resonances in these waves. The observed phase variation for the $S$-, $P$-, and $D$-waves do not match existing measurements of $I=\frac{1}{2}$ $K^{-}{\pi }^{+}$ scattering in the invariant mass range in which scattering is predominantly elastic. If the data are mostly $I=\frac{1}{2}$, this observation indicates that the Watson theorem, which requires these phases to have the same dependence on invariant mass, may not apply to these decays without allowing for some interaction with the other pion. The production rate of $K^{-}{\pi }^{+}$ from these decays, if assumed to be predominantly $I=\frac{1}{2}$, is also found to have a significant dependence on invariant mass in the region above $1.25\mathrm{GeV}/c^2$. These measurements can provide a relatively model-free basis for future attempts to determine which strange scalar amplitudes contribute to the decays.

We introduce a simple scenario where, by starting with a five-dimensional $SU(3)$ gauge theory, we end up with several 4-D parallel branes with localized fermions and gauge fields. Similar to the split fermion scenario, the confinement of fermions is generated by the nontrivial topological solution of a $SU(3)$ scalar field. The 4-D fermions are found to be chiral, and to have interesting properties coming from their 5-D group representation structure. The gauge fields, on the other hand, are localized by loop corrections taking place at the branes produced by the fermions. We show that these two confining mechanisms can be put together to reproduce the basic structure of the electroweak model for both leptons and quarks. A few important results are: Gauge and Higgs fields are unified at the 5-D level; and new fields are predicted: One left-handed neutrino with zero-hypercharge, and one massive vector field coupling together the new neutrino with other left-handed leptons. The hierarchy problem is also addressed.

Using the anti-de Sitter (AdS)/conformal field theories correspondence, we establish a correspondence between the intricate thermal phases of $R$-charged ${\mathrm{AdS}}_5$ black holes and the $R$-charge sector of the $N=4$ gauge theory, in the large $N$ limit. Integrating out all fields in the gauge theory, except the thermal Polyakov line, leads to an effective unitary matrix model. In the canonical ensemble, a logarithmic term is generated in the nonzero charge sector of the matrix model. This term is important for discussing various supergravity properties like (i) the nonexistence of a thermal AdS phase as a solution, (ii) the existence of a point of cusp catastrophe in the phase diagram, and (iii) the matching of saddle points and the critical exponents of supergravity and those of the effective matrix model. Our study is restricted to a unitary matrix model where the action depends only on $\mathrm{Tr}U\mathrm{Tr}{U}^{†}$.

Having in mind applications to gravitational wave theory (in connection with the radiation reaction problem), stochastic semiclassical gravity (in connection with the regularization of the noise kernel) and quantum field theory in higher-dimensional curved spacetime (in connection with the Hadamard regularization of the stress-energy tensor), we improve the DeWitt-Schwinger and Hadamard representations of the Feynman propagator of a massive scalar field theory defined on an arbitrary gravitational background by deriving higher-order terms for the covariant Taylor series expansions of the geometrical coefficients—i.e., the DeWitt and Hadamard coefficients—that define them.

Gravitational effects in relativistic quantum mechanics are investigated. The Dirac particle in general space-time metrics is considered and the Dirac Hamiltonian is constructed in terms of the Newman-Penrose formalism. To discuss the physical meaning of the Dirac Hamiltonian, it is necessary to perform the Foldy-Wouthuysen transformation. In most cases this transformation exists only in an approximate form. In this paper we show that for supersymmetric Dirac Hamiltonians not depending explicitly on time the exact Foldy-Wouthuysen transformation can always be constructed. Further, we derive criteria for spin coefficients for which the accompanying Dirac Hamiltonian is supersymmetric. These criteria are fulfilled by the class of static axisymmetric space-time metrics. For the subclass of stationary metrics, the exact Foldy-Wouthuysen transformation is calculated and the transformed Dirac Hamiltonian is derived. Recently, Obukhov constructed a different exact Foldy-Wouthuysen transformation for that class of space-time metrics and calculated the Dirac Hamiltonian in the Foldy-Wouthuysen representation. We show that the expansion series in orders of $1/m{c}^2$ of our and Obukhov’s Dirac Hamiltonians coincide.

We extend the classical and quantum treatment of the Lemaître-Tolman-Bondi (LTB) model to the nonmarginal case (defined by the fact that the shells of the dust cloud start with a nonvanishing velocity at infinity). We present the classical canonical formalism and address with particular care the boundary terms in the action. We give the general relation between dust time and Killing time. Employing a lattice regularization, we then derive and discuss for particular factor orderings exact solutions to all quantum constraints.