We study in this paper the perturbations of the quintom dark energy model and the effects of quintom perturbations on the current observations. Quintom describes a scenario of dark energy where the equation of state gets across the cosmological constant boundary $w=-1$ during evolution. We present a new method to show that the conventional dark energy models based on a single $k$-essence field and perfect fluid cannot act as the quintom due to the singularities and classical instabilities of perturbations around $w=-1$. One needs to add extra degrees of freedom for successful quintom model building. There are no singularities or classical instabilities in perturbations of realistic quintom models and they are potentially distinguishable from the cosmological constant. Basing on the realistic quintom models in this paper we provide one way to include the perturbations for dark energy models with parametrized equation of state across $-1$. Compared with those assuming no dark energy perturbations, we find that the parameter space which allows the equation of state to get across $-1$ will be enlarged, in general, when including the perturbations.

Using second-order gauge-invariant perturbation theory, a self-consistent framework describing the nonlinear coupling between gravitational waves and a large-scale homogeneous magnetic field is presented. It is shown how this coupling may be used to amplify seed magnetic fields to strengths needed to support the galactic dynamo. In situations where the gravitational wave background is described by an “almost“ Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology we find that the magnitude of the original magnetic field is amplified by an amount proportional to the magnitude of the gravitational wave induced shear anisotropy and the square of the field’s initial comoving scale. We apply this mechanism to the case where the seed field and gravitational wave background are produced during inflation and find that the magnitude of the gravitational boost depends significantly on the manner in which the estimate of the shear anisotropy at the end of inflation is calculated. Assuming a seed field of ${10}^{-34}\mathrm{G}$ spanning a comoving scale of about 10 kpc today, the shear anisotropy at the end of inflation must be at least as large as ${10}^{-40}$ in order to obtain a generated magnetic field of the same order of magnitude as the original seed. Moreover, contrasting the weak-field approximation to our gauge-invariant approach, we find that while both methods agree in the limit of high conductivity, their corresponding solutions are otherwise only compatible in the limit of infinitely long-wavelength gravitational waves.

We examine the importance of second order corrections to linearized cosmological perturbation theory in an inflationary background, taken to be a spatially flat FRW spacetime. The full second order problem is solved in the sense that we evaluate the effect of the superhorizon second order corrections on the inhomogeneous and homogeneous modes of the linearized fluctuations. These second order corrections enter in the form of a cumulative contribution from all of their Fourier modes. In order to quantify their physical significance we study their effective equation of state by looking at the perturbed energy density and isotropic pressure to second order. We define the energy density (isotropic pressure) in terms of the (averaged) eigenvalues associated with timelike (spacelike) eigenvectors of a total stress energy for the metric and matter fluctuations. Our work suggests that for many parameters of slow-roll inflation, the second order contributions to the energy density and pressures may dominate over the first order effects for the case of super-Hubble evolution. These results hold in our choice of first and second order coordinate conditions; however, we also argue that other “reasonable” coordinate conditions do not alter the relative importance of the second order terms. We find that these second order contributions approximately take the form of a cosmological constant in this coordinate gauge, as found by others using effective methods.

The gap caused by a strong electric field between the quark surface and nuclear crust of a strange star is studied in an improved model including gravity and pressure as well as electrostatic forces. The transition from gap to crust is followed in detail. The properties of the gap are investigated for a wide range of parameters assuming both color-flavor locked and noncolor-flavor locked strange star cores. The maximally allowed crust density is generally lower than that of neutron drip. Finite temperature is shown to increase the gap width, but the effect is significant only at extreme temperatures. Analytical approximations are derived and shown to provide useful fits to the numerical results.

The equations for the second-order gravitational perturbations produced by a compact object have highly singular source terms at the point particle limit. At this limit the standard retarded solutions to these equations are ill defined. Here we construct well defined and physically meaningful solutions to these equations. These solutions are important for practical calculations: the planned gravitational-wave detector LISA requires preparation of waveform templates for the expected gravitational waves. Construction of templates with desired accuracy for extreme mass-ratio binaries, in which a compact object inspirals towards a supermassive black hole, requires calculation of the second-order gravitational perturbations produced by the compact object.

We argue that the order of the chiral transition for $N_f=2$ is a sensitive probe of the QCD vacuum, in particular, of the mechanism of color confinement. A strategy is developed to investigate the order of the transition by use of finite size scaling analysis. An in-depth numerical investigation is performed with staggered fermions on lattices with $L_t=4$ and $L_s=12$, 16, 20, 24, 32 and quark masses $a{m}_q$ ranging from 0.01335 to 0.307036. The specific heat and a number of susceptibilities are measured and compared with the expectations of an $O(4)$ second order and of a first order phase transition. A detailed comparison with previous works, which all use similar techniques as ours, is performed. A second order transition in the $O(4)$ and $O(2)$ universality classes are incompatible with our data, which seem to prefer a first order transition. However we have $L_t=4$ and unimproved action, so that a check with improved techniques (algorithm and action) and possibly larger $L_t$ will be needed to assess this issue on a firm basis.

We compute nonperturbatively the renormalization constants of composite operators on a quenched ${16}^3\times 28$ lattice with lattice spacing $a=0.20\mathrm{fm}$ for the overlap fermion by using the regularization-independent (RI) scheme. The quenched gauge configurations were generated with the Iwasaki action. We test the relations $Z_A=Z_V$ and $Z_S=Z_P$ and find that they agree well (less than 1%) above $\mu =1.6\mathrm{GeV}$. We also perform a Renormalization Group (RG) analysis at the next-to-next-to-leading order and match the renormalization constants to the $\overline{\mathrm{MS}}$ scheme. The wave function renormalization $Z_{\psi }$ is determined from the vertex function of the axial current and $Z_A$ from the chiral Ward identity. Finally, we examine the finite quark mass behavior for the renormalization factors of the quark bilinear operators. We find that the $(pa{)}^2$ errors of the vertex functions are small and the quark mass dependence of the renormalization factors to be quite weak.

We point out that nonleptonic $B$ decays driven by $b\to c\overline{c}s$ should provide a favorable environment for the production of hidden charm diquark-antidiquark bound states that have been suggested to explain the resonances with masses around 4 GeV recently observed by BABAR and BELLE. Studying their relative abundances in nonleptonic $B$ decays can teach us novel lessons about their structure and the strong interactions. Through their decay into $\psi$ they can provide a natural explanation of the excess of $B\to \psi X$ observed for $p_{\psi }<1\mathrm{GeV}$. Other phenomenological consequences are mentioned as well.

QCD sum rules for the nucleon are considered in complex $q^2$ plane with inclusion of the radiative corrections of the order ${\alpha }_s$. It is shown that the radiative corrections affect mainly the residue ${\lambda }^2$ of the nucleon pole. Their influence on the value of the nucleon mass is much smaller. Following the ideas of Ioffe and Zyablyuk we expand the analysis to complex values of $q^2$. This provides a more stable solution. Varying the weights of the contributions of different dimensions by changing the value of the angle in the complex plane we find the value of the six-quark condensate which insures the best consistency of the right hand sides and left-hand sides of the sum rules. The corresponding value of the six-quark condensate appears to be only about $10\%$ smaller then the one, provided by the factorization approximation. The value of the four-quark condensate also appears to be close to the one, corresponding to the factorization assumption. The role of the gluon condensate and its possible values are discussed.

We examine the question of the supersymmetric completion of the $R^4$ term in type IIB supergravity by using superfield methods. We show that, while there is an obstruction to constructing the full action, a subset of the terms in the action can be consistently analyzed independent of the other terms, and these can be obtained from the superfield. We find the complete type IIB action involving the curvature and five-form field strengths.

The $C$-metric is one of few known exact solutions of Einstein’s field equations which describes the gravitational field of moving sources. For a vanishing or positive cosmological constant, the $C$-metric represents two accelerated black holes in asymptotically flat or de Sitter spacetime. For a negative cosmological constant the structure of the spacetime is more complicated. Depending on the value of the acceleration, it can represent one black hole or a sequence of pairs of accelerated black holes in the spacetime with an anti-de Sitter-like infinity. The global structure of this spacetime is analyzed and compared with an empty anti-de Sitter universe. It is illustrated by 3D conformal-like diagrams.

The possibility that the scale-invariant inflationary spectrum may be modified due to the hidden assumptions about the Planck scale physics—dubbed as trans-Planckian inflation—has received considerable attention. To mimic the possible trans-Planckian effects, among various models, modified dispersion relations have been popular in the literature. In almost all the earlier analyses, unlike the canonical scalar field driven inflation, the trans-Planckian effects are introduced to the scalar/tensor perturbation equations in an ad hoc manner—without calculating the stress tensor of the cosmological perturbations from the covariant Lagrangian. In this work, we perform the gauge-invariant cosmological perturbations for the single scalar-field inflation with the Jacobson-Corley dispersion relation by computing the fluctuations of all the fields including the unit-timelike vector field which defines a preferred rest frame. We show that: (i) The nonlinear effects introduce corrections only to the perturbed energy density. The corrections to the energy density vanish in the super-Hubble scales. (ii) The scalar perturbations, in general, are not purely adiabatic. (iii) The equation of motion of the Mukhanov-Sasaki variable corresponding to the inflaton field is different from those presumed in the earlier analyses. (iv) The tensor perturbation equation remains unchanged. We perform the classical analysis for the resultant system of equations and also compute the power spectrum of the scalar perturbations in a particular limit. We discuss the implications of our results and compare with the earlier results.

Generalized parton distributions with helicity flip are studied in the quark sector, within a simple version of the MIT bag model, assuming an SU(6) wave function for the proton target. In the framework under scrutiny, it turns out that only the generalized transversity distribution, $H_T^q$, is nonvanishing. For this quantity, the forward limit is properly recovered and numerical results are found to underestimate recent lattice data for its first moment. Positivity bounds recently proposed are fulfilled by the obtained distribution. The relevance of the analysis for the planning of measurements of the quark generalized transversity is addressed.

We consider the capability of the $e^{+}{e}^{-}$ linear collider (which has recently been called the International Linear Collider, or ILC) for studying the properties of the heavy Higgs bosons in the supersymmetric standard model. We pay special attention to the large $\tan \beta$ region which is motivated, in particular, by explaining the dark-matter density of the universe (i.e., so-called “rapid-annihilation funnels”). We perform a systematic analysis to estimate expected uncertainties in the masses and widths of the heavy Higgs bosons assuming an energy and integrated luminosity of $\sqrt{s}=1\mathrm{TeV}$ and $L=1{\mathrm{ab}}^{-1}$. We also discuss its implication to the reconstruction of the dark-matter density of the universe.

We propose a generalization of the upgraded Karl-Sehgal formula which relates baryon magnetic moments to the spin structure of constituent quarks, by adding anomalous magnetic moments of quarks. We first argue that the relativistic nature of quarks inside baryons requires the introduction of two kinds of magnetisms, one axial and the other tensorial. The first one is associated with integrated quark helicity distributions ${\Delta }_i-{\Delta }_{\overline{i}}$ (standard) and the second with integrated transversity distributions ${\delta }_i-{\delta }_{\overline{i}}$. The weight of each contribution is controlled by the combination of two parameters, $x_i$ the ratio of the quark mass to the average kinetic energy and $a_i$ the quark anomalous magnetic moment. The quark anomalous magnetic moment is correlated to transversity, and both are necessary ingredients in describing relativistic quarks. The proposed formula, when confronted with baryon magnetic moments data with reasonable inputs, yields, besides quark magnetic densities, anomalous magnetic moments large enough not to be ignored.

It has been argued that the mystery boson $X(3872)$ is a molecule state consisting of primarily $D^0{\overline{D}}^{*0}+{\overline{D}}^0{D}^{*0}$. In contrast, apparent puzzles and potential difficulties have been pointed out for the charmonium assignment of $X(3872)$. We examine several aspects of these alternatives by semiquantitative methods since quantitatively accurate results are often hard to reach on them. We point out that some of the observed properties of $X(3872)$, in particular the binding and the production rates, are incompatible with the molecule interpretation. Despite puzzles and obstacles, $X(3872)$ may fit more likely to the excited ${}^{3}P_1$ charmonium than to the molecule after the mixing of $c\overline{c}$ with $D{\overline{D}}^{*}+\overline{D}{D}^{*}$ is taken into account.

We report a search for the decays $B^0\to D_s^{-}{D}_s^{+}$, $B^0\to D_s^{*-}{D}_s^{+}$, and $B^0\to D_s^{*-}{D}_s^{*+}$ in a sample of $232\times {10}^6$ ${\rm Y}(4S)$ decays to $B\overline{B}$ pairs collected with the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}$ storage ring. We find no significant signal and set upper bounds for the branching fractions: $\mathcal{B}(B^0\to D_s^{-}{D}_s^{+})<1.0\times {10}^{-4}$, $\mathcal{B}(B^0\to D_s^{*-}{D}_s^{+})<1.3\times {10}^{-4}$, and $\mathcal{B}(B^0\to D_s^{*-}{D}_s^{*+})<2.4\times {10}^{-4}$ at 90% confidence level.

In this work, we are motivated by previous attempts to derive the vacuum contribution to the bag energy in terms of familiar Casimir energy calculations for spherical geometries. A simple infrared modified model is introduced which allows studying the effects of the analytic structure as well as the geometry in a clear manner. In this context, we show that if a class of infrared vanishing effective gluon propagators is considered, then the renormalized vacuum energy for a spherical bag is attractive, as required by the bag model to adjust hadron spectroscopy.