We analyze the quantum dynamics of the Bianchi Type IX model, as described in the so-called polymer representation of quantum mechanics, to characterize the modifications that a discrete nature in the anisotropy variables of the Universe induces on the morphology of the cosmological singularity. We first perform a semiclassical analysis, to be regarded as the zeroth-order approximation of a WKB approximation of the quantum dynamics, and demonstrate how the features of polymer quantum mechanics are able to remove the chaotic properties of the Bianchi IX dynamics. The resulting evolution towards the cosmological singularity overlaps the one induced, in a standard Einsteinian dynamics, by the presence of a free scalar field. Then, we address the study of the full quantum dynamics of this model in the polymer representation and analyze the two cases in which the Bianchi IX spatial curvature does not affect the wave-packet behavior, as well as the instance for which it plays the role of an infinite potential confining the dynamics of the anisotropic variables. The main development of this analysis consists of investigating how, differently from the standard canonical quantum evolution, the high quantum number states are not preserved arbitrarily close to the cosmological singularity. This property emerges as a consequence, on one hand, of the no-longer-chaotic features of the classical dynamics (on which the Misner analysis is grounded), and, on the other hand, of the impossibility of removing the quantum effect due to the spatial curvature. In the polymer picture, the quantum evolution of the Bianchi IX model remains always significantly far from the semiclassical behavior, as far as both the wave-packet spread and the occupation quantum numbers are concerned. As a result, from a quantum point of view, the mixmaster dynamics loses any predictivity characterization for the discrete nature of the Universe’s anisotropy.

Massive spectroscopic redshift surveys open a promising window to accurately measure peculiar velocity at cosmological distances through redshift space distortion (RSD). In Paper I Zhang et al. [Phys. Rev. D 87, 063526 (2013)] of this series of work, we proposed decomposing peculiar velocity into three eigenmodes (${\mathbf{v}}_{\delta }$, ${\mathbf{v}}_S$, and ${\mathbf{v}}_B$) in order to facilitate the RSD modeling and peculiar velocity reconstruction. In the current paper we measure the dark matter RSD-related statistics of the velocity eigenmodes through a set of N-body simulations. These statistics include the velocity power spectra, correlation functions, one-point probability distribution functions, cumulants, and the damping functions describing the Finger of God effect. We have carried out a number of tests to quantify possible numerical artifacts in these measurements and have confirmed that these numerical artifacts are under control. Our major findings are as follows: (1) The power spectrum measurement shows that these velocity components have distinctly different spatial distribution and redshift evolution, consistent with predictions in Paper I. In particular, we measure the window function $\tilde{W}(k,z)$. $\tilde{W}$ describes the impact of nonlinear evolution on the ${\mathbf{v}}_{\delta }$-density relation. We confirm that the approximation $\tilde{W}=1$ can induce a significant systematic error of $O(10\%)$ in RSD cosmology. We demonstrate that $\tilde{W}$ can be accurately described by a simple fitting formula with one or two free parameters. (2) The correlation function measurement shows that the correlation length is $O(100)$, $O(10)$, and $O(1)\mathrm{Mpc}$ for ${\mathbf{v}}_{\delta }$, ${\mathbf{v}}_S$, and ${\mathbf{v}}_B$, respectively. These correlation lengths determine where we can treat the velocity fields as spatially uncorrelated. Hence, they are important properties in RSD modeling. (3) The velocity probability distribution functions and cumulants quantify non-Gaussianities of the velocity fields. We confirm speculation in Paper I that ${\mathbf{v}}_{\delta }$ is largely Gaussian, but with non-negligible non-Gaussianity. We confirm that ${\mathbf{v}}_B$ is significantly non-Gaussian. We also measure the damping functions. Despite the observed non-Gaussianities, the damping functions and hence the Finger of God effect are all well approximated as Gaussian ones at scales of interest.

By using the Euler-Lagrange equations, we find a static spherically symmetric solution in the Einstein-aether theory with the coupling constants restricted. The solution is similar to the Reissner-Nordstrom solution in that it has an inner Cauchy horizon and an outer black hole event horizon. But a remarkable difference from the Reissner-Nordstrom solution is that it is not asymptotically flat but approaches a two-dimensional sphere. The resulting electric potential is regular in the whole spacetime except for the curvature singularity. On the other hand, the magnetic potential is divergent on both the Cauchy horizon and the outer event horizon.

Asymptotic symmetries of the Einstein-Yang-Mills system with or without cosmological constant are explicitly worked out in a unified manner. In agreement with a recent conjecture, one finds a Virasoro-Kac-Moody type algebra not only in three dimensions but also in the four-dimensional asymptotically flat case.

Generic violations of Lorentz symmetry can be described by an effective field theory framework that contains both general relativity and the Standard Model of particle physics called the Standard-Model extension (SME). We obtain new constraints on the gravitational sector of the SME using recently published final results from Gravity Probe B. These include for the first time an upper limit at the ${10}^{-3}$ level on the time-time component of the new tensor field responsible for inducing local Lorentz violation in the theory, and an independent limit at the ${10}^{-7}$ level on a combination of components of this tensor field.

In the context of three-dimensional gravity with torsion, the concepts of standard and “exotic” Bañados–Teitelboim–Zanelli black holes are generalized by going over to black holes with torsion. This approach provides a unified insight into thermodynamics of black holes, with or without torsion.

Nucleon lifetimes for various decay modes via dimension-6 operators are calculated in the anomalous $U(1{)}_A$ grand unified theory (GUT) scenario, in which the unification scale ${\Lambda }_u$ becomes smaller than the usual supersymmetric (SUSY) unification scale ${\Lambda }_G=2\times {10}^{16}\mathrm{GeV}$ in general. Since the predicted lifetime $\tau (p\to {\pi }^0+e^c)$ falls around the experimental lower bound, though it is strongly dependent on the explicit models, the discovery of the this nucleon decay can be expected in the near future. We explain why the two ratios $R_1\equiv \frac{{\Gamma }_{n\to {\pi }^0+{\nu }^c}}{{\Gamma }_{p\to {\pi }^0+e^c}}$ and $R_2\equiv \frac{{\Gamma }_{p\to K^0+{\mu }^c}}{{\Gamma }_{p\to {\pi }^0+e^c}}$ are important in identifying the grand unification group, and we show that three anomalous $U(1{)}_A$ SUSY GUT models, with $SU(5)$, $SO(10)$ and $E_6$ grand unification groups, can be identified by measuring the two ratios. If $R_1$ is larger than 0.4, the grand unification group is not $SU(5)$, and moreover, if $R_2$ is larger than 0.3, the grand unification group is implied to be $E_6$.

We develop the holographic mean field approach in a bottom-up holographic QCD model including baryons and scalar mesons in addition to vector mesons and pions. We study the effect of parity doubling structure of baryons at nonzero density to the equation of state between the chemical potential and the baryon number density. We first show that we can adjust the amount of nucleon mass coming from the chiral symmetry breaking by changing the boundary value of the five-dimensional baryon fields. Then, introducing the mean field for the baryon fields, we calculate the equation of state between the baryon number density and its corresponding chemical potential. Then, comparing the predicted equation of state with the one obtained in a Walecka type model, we extract the density dependence of the effective nucleon mass. The result shows that the effective mass decreases with increasing density, and that the rate of decreasing is more rapid for a larger percentage of the mass from the chiral symmetry breaking.

We study Higgs couplings in the composite Higgs model based on the coset $SO(5)/SO(4)$. We show that the couplings to gluons and photons are insensitive to the elementary-composite mixings and thus not affected by light fermionic resonances. Moreover, at leading order in the mixings the Higgs couplings to tops and gluons, when normalized to the Standard Model (SM), are equal. These properties are shown to be direct consequences of the Goldstone symmetry, of the partial compositeness structure and of the assumption of $CP$ invariance. In particular, they are independent of the details of the elementary-composite couplings, and they are also insensitive to derivative interactions of the Higgs with the composite resonances. We support our conclusions with an explicit construction where the SM fermions are embedded in the 14-dimensional representation of $SO(5)$.

The idea of left-right symmetry with mirror fermions is very appealing from the symmetry point of view. In this picture, unlike the Standard Model, the symmetry is not only left-right symmetric, but each left-handed fermion multiplet is accompanied by a new right-handed fermion multiplet of opposite chirality. In this work, we consider a gauge symmetry, $SU(3{)}_c\otimes SU(2{)}_L\otimes SU(2{)}_R\otimes U(1{)}_{Y^{\prime }}$, supplemented by a discrete $Z_2$ symmetry. Instead of having right-handed multiplets for each left-handed multiplet of the same fermions as in the usual left-right model, the mirror model includes right- handed doublets involving new fermions (called mirrors), and similarly for each right- handed singlet, there are corresponding mirror singlets. Thus the gauge anomaly is naturally absent in this model, and the model also provides a solution for the strong $CP$ problem because of parity conservation. The first stage of symmetry breaking is achieved by a doublet mirror Higgs with a vacuum expectation value $\simeq {10}^7\mathrm{GeV}$, needed to explain the neutrino mass $\simeq {10}^{-11}\mathrm{GeV}$. The mirror fermions can mix with the ordinary fermions via a scalar that is singlet under the gauge symmetry. In this model, only light mirror particles, having masses in the few hundred GeV range, are $\widehat{e}$, $\widehat{u}$, $\widehat{d}$ with well-defined spectrum. $\widehat{u}$ and $\widehat{d}$ can be pair produced at the LHC and can be detected as ($uZ$) and ($dZ$) resonances. We discuss the signals of these mirror fermions at the LHC and find that the reach at the LHC can be as large as $m_{\widehat{q}}\simeq 800\mathrm{GeV}$.

We compute the isospin asymmetries in $B\to (K^{*},\rho )\gamma$ and $B\to (K,K^{*},\rho )l^{+}{l}^{-}$ for low lepton pair invariant mass $q^2$, within the Standard Model (SM) and beyond the SM in a generic dimension six operator basis. Within the SM the $CP$-averaged isospin asymmetries for $B\to (K,K^{*},\rho )ll$, between $1{\mathrm{GeV}}^2\le q^2\le 4m_c^2$, are predicted to be small (below 1.5%) though with significant cancellation. In the SM the non-$CP$-averaged asymmetries for $B\to \rho ll$ deviate by $\approx \pm 5\%$ from the $CP$-averaged ones. We provide physical arguments, based on resonances, of why isospin asymmetries have to decrease for large $q^2$ (towards the endpoint). Two types of isospin violating effects are computed: ultraviolet isospin violation due to differences between operators coupling to up and down quarks, and infrared isospin violation where a photon is emitted from the spectator quark and is hence proportional to the difference between the up- and down-quark charges. These isospin violating processes may be subdivided into weak annihilation (WA), quark loop spectator scattering, and a chromomagnetic contribution. Furthermore we discuss generic selection rules based on parity and angular momentum for the $B\to Kll$ transition as well as specific selection rules valid for WA at leading order in the strong coupling constant. We clarify that the relation between the $K$ and the longitudinal part of the $K^{*}$ only holds for leading twist and for left-handed currents. In general the $B\to \rho ll$ and $B\to K^{*}ll$ isospin asymmetries are structurally different yet the closeness of ${\alpha }_{\mathrm{CKM}}$ to $90°$ allows us to construct a (quasi)null test for the SM out of the respective isospin symmetries. We provide and discuss an update on $\mathcal{B}(B^0\to K^{*0}\gamma )/\mathcal{B}(B_s\to \varphi \gamma )$ which is sensitive to WA.

We investigate $B\to K_0^{*}(1430)K^{*}$ decays in the perturbative QCD (pQCD) factorization approach, where $B$ denotes $B_u$, $B_d$, and $B_s$ mesons, respectively, and the scalar $K_0^{*}(1430)$ is considered as a meson based on the model of the conventional two-quark structure. With the light-cone distribution amplitude of $K_0^{*}(1430)$ defined in two scenarios, namely Scenario 1 and Scenario 2, we make the first estimation for the branching ratios and $CP$-violating asymmetries for those concerned decay modes in the pQCD factorization approach. For all considered $B\to K_0^{*}(1430)K^{*}$ decays in this paper, only one preliminary upper limit on the branching ratio of $B^0\to K_0^{*}(1430{)}^0{\overline{K}}^{*0}$ measured at 90% C.L. by the Belle Collaboration is available now. It is therefore of great interest to examine the predicted physical quantities at two $B$ factories, the Large Hadron Collider experiments, and the forthcoming Super-$B$ facility, and then to test the reliability of the pQCD approach employed to study the considered decay modes involving a $p$-wave scalar meson as one of the final state mesons. Furthermore, these pQCD predictions combined with the future precision measurements are also helpful to explore the complicated QCD dynamics involved in the light scalars.

In this paper, we have considered the possibility that the Standard Model, and its minimal extension with the addition of singlets, merges with a high-scale supersymmetric theory at a scale satisfying the Veltman condition and therefore with no sensitivity to the cutoff. The matching of the Standard Model is achieved at Planckian scales. In its complex singlet extension, the matching scale depends on the strength of the coupling between the singlet and Higgs fields. For order 1 values of the coupling, still in the perturbative region, the matching scale can be located in the TeV ballpark. Even in the absence of quadratic divergences, there remains a finite adjustment of the parameters in the high-energy theory, which should guarantee that the Higgs and the singlets in the low-energy theory are kept light. This fine-tuning (unrelated to quadratic divergences) is the entire responsibility of the ultraviolet theory and remains as the missing ingredient to provide a full solution to the hierarchy problem.

We present a measurement of the top-quark pair production cross section in proton-antiproton collisions at $\sqrt{s}=1.96\mathrm{TeV}$. The data were collected at the Fermilab Tevatron by the CDF II detector and correspond to an integrated luminosity of $8.8{\mathrm{fb}}^{-1}$, representing the complete CDF Run II data set. We select events consistent with the production of top-quark pairs by requiring the presence of two reconstructed leptons, an imbalance in the total event transverse momentum, and jets. At least one jet is required to be identified as consistent with the fragmentation of a bottom quark using a secondary-vertex-finding algorithm. The 246 candidate events are estimated to have a signal purity of 91%. We measure a cross section of ${\sigma }_{t\overline{t}}=7.09\pm 0.84\mathrm{pb}$, assuming a top-quark mass of $172.5\mathrm{GeV}/c^2$. The results are consistent with the standard model as predicted by next-to-leading-order calculations.

We examine the dynamics of scalar perturbations in closed Friedmann-Lemaître-Robertson-Walker universes in the framework of brane world theory with a timelike extra dimension. In this scenario, the unperturbed Friedmann equations contain additional terms arising from the bulk-brane interaction that implement nonsingular bounces in the models with a cosmological constant and noninteracting perfect fluids. The structure of the phase space of the models allows for two basic configurations, namely, one bounce solutions and eternal universes. Assuming that the matter content of the model is given by dust and radiation, we derive the dynamical field equations for scalar hydrodynamical perturbations considering either a conformally flat (de Sitter) bulk or a perturbed bulk. The dynamical system built with these equations is extremely involved. Nevertheless, in this paper we perform a numerical analysis which can shed some light on the study of cosmological scalar perturbations in bouncing brane world models. From a mathematical point of view we show that although the bounce enhances the amplitudes of scalar perturbations for one bounce models in the case of a de Sitter bulk, the amplitudes of the perturbations remain sufficiently small and bounded relative to the background values up to a certain scale. For one bounce models in the case of a perturbed bulk the amplitudes of all perturbations (apart from the Weyl fluid energy density) remain sufficiently small and bounded relative to the background values for any scale of the perturbations. We also discuss and compare the stability and bounded behavior of the perturbations in the late accelerated phase of one bounce solutions. For eternal universes we argue that some of these features are maintained only for early times (typically of the order of the first bounce). In this sense we show that eternal solutions are highly unstable configurations considering the background model of this paper.

Lorentz invariance is one of the fundamental principles of physics, and, as such, it must be experimentally tested. The purpose of this work is to obtain, within the Standard-Model Extension, the dynamics of a Lorentz-violating spinor in a uniform Newtonian gravitational field. This is achieved by treating the spinor as a test particle and introducing the gravitational field through a uniformly accelerated observer. The nonrelativistic Hamiltonian is obtained, and some experimental consequences are discussed. One unexpected outcome of this work is that the gravitational field helps disentangle bounds on coefficients for Lorentz violation.

Bipartite field theories (BFTs) are a new class of 4D $\mathcal{N}=1$ quantum field theories defined by bipartite graphs on bordered Riemann surfaces. In this paper we derive, purely in terms of the gauge theory, the cluster transformations of face weights under square moves in the graph. In this context, we obtain them by connecting regular parametrizations of the master space of the associated BFTs. For BFTs on a disk, these transformations follow from the properties of coordinates in the Grassmannian. This represents a new addition to the list of combinatorial objects for the Grassmannian, such as matching and matroid polytopes, that have been shown to emerge from BFT dynamics.

We derive a suite of generalized Boltzmann equations, based on the density-matrix formalism, that incorporates the physics of neutrino oscillations for two- and three-flavor oscillations, matter refraction, and self-refraction. The resulting equations are straightforward extensions of the classical transport equations that nevertheless contain the full physics of quantum oscillation phenomena. In this way, our broadened formalism provides a bridge between the familiar neutrino transport algorithms employed by supernova modelers and the more quantum-heavy approaches frequently employed to illuminate the various neutrino oscillation effects. We also provide the corresponding angular-moment versions of this generalized equation set. Our goal is to make it easier for astrophysicists to address oscillation phenomena in a language with which they are familiar. The equations we derive are simple and practical, and are intended to facilitate progress concerning oscillation phenomena in the context of core-collapse supernova theory.

We consider the decay of cosmic strings that are trapped in the false vacuum in a theory of scalar electrodynamics in $3+1$ dimensions. This paper is the $3+1$-dimensional generalization of the $2+1$-dimensional decay of false vortices which we have recently completed [2]. We restrict our analysis to the case of thin-walled cosmic strings which occur when large magnetic flux is trapped inside the string. Thus the string looks like a tube of fixed radius, at which it is classically stable. The core of the string contains magnetic flux in the true vacuum, while outside the string, separated by a thin wall, is the false vacuum. The string decays by tunneling to a configuration which is represented by a bulge, where the region of true vacuum within is ostensibly enlarged. The bulge can be described as the meeting of a kink soliton-antisoliton pair along the length of the string. It can be described as a bulge appearing in the initial string, starting from the string of small, classically stable radius, expanding to a fat string of large, classically unstable (to expansion) radius and then returning back to the string of small radius along its length. This configuration is the bounce point of a corresponding $O(2)$ symmetric instanton, which we can determine numerically. Once the bulge appears it explodes in real time. The paired soliton and antisoliton recede from each other along the length of the string with a velocity that quickly approaches the speed of light, leaving behind a fat tube. At the same time the radius of the fat tube that is being formed expands (transversely) as it is no longer classically stable, converting false vacuum to the true vacuum with ever-diluting magnetic field within. The rate of this expansion is determined by the energy difference between the true vacuum and the false vacuum. Our analysis could be applied to a network of cosmic strings formed in the very early Universe or vortex lines in a superheated superconductor.