We continue the analysis of the ghost wedge states in the oscillator formalism by studying the spectral properties of the ghost matrices of Neumann coefficients. We show that the traditional spectral representation is not valid for these matrices and propose a new heuristic formula that allows one to reconstruct them from the knowledge of their eigenvalues and eigenvectors. It turns out that additional data, which we call boundary data, are needed in order to actually implement the reconstruction. In particular our result lends support to the conjecture that there exists a ghost three strings vertex with properties parallel to those of the matter three strings vertex.

We calculate the free-streaming length and the phase space density of dark-matter sterile neutrinos produced from decays, at the electroweak scale, of a gauge singlet in the Higgs sector. These quantities, which depend on the dark-matter production mechanism, are relevant to the study of small-scale structure formation and may be used to constrain or rule out dark-matter candidates.

We consider generalized self-duality equations for $U(2r)$ Yang-Mills theory on ${\mathbb{R}}^8$ with quaternionic structure. We employ the extended ADHM method in eight dimensions to construct exact soliton solutions of the low-energy effective theory of the heterotic string.

In a 4D chiral Thirring model we analyze the possibility that radiative corrections may produce spontaneous breaking of Lorentz and $CPT$ symmetry. By studying the effective potential, we verified that the chiral current $\overline{\psi }{\gamma }^{\mu }{\gamma }_5\psi$ may assume a nonzero vacuum expectation value which triggers Lorentz and $CPT$ violations. Furthermore, by making fluctuations on the minimum of the potential we dynamically induce a bumblebee-like model containing a Chern-Simons term.

We study numerically gravitational collapse of a spherically symmetric instanton particle in five dimensions. We show that the late stages of the process are characterized by a nearly constant “free energy,” the value of which matches (within numerical uncertainties) the value obtained from standard black-hole thermodynamics. This suggests a purely classical interpretation of the free energy of a black hole.

We consider a scalar charge travelling in a curved background space-time. We calculate the quasilocal contribution to the scalar self-force experienced by such a particle following a geodesic in a general space-time. We also show that if we assume a massless field and a vacuum background space-time, the expression for the self-force simplifies significantly. We consider some specific cases whose gravitational analogs are of immediate physical interest for the calculation of radiation-reaction corrected orbits of binary black hole systems. These systems are expected to be detectable by the LISA space based gravitational wave observatory. We also investigate how alternate techniques may be employed in some specific cases and use these as a check on our own results.

The Kerr metric outside the ergosphere is transformed into Arnowitt-Deser-Misner coordinates up to the orders $1/r^4$ and $a^2$, respectively, in radial coordinate $r$ and reduced angular momentum variable $a$, starting from the Kerr solution in quasi-isotropic as well as harmonic coordinates. The distributional source terms for the approximate solution are calculated. To leading order in linear momenta, higher-order-in-spin interaction Hamiltonians for black hole binaries are derived.

We present an analysis of a scalar field model of dark energy with an exponential potential using the Dark Energy Task Force (DETF) simulated data models. Using Markov Chain Monte Carlo sampling techniques we examine the ability of each simulated data set to constrain the parameter space of the exponential potential for data sets based on a cosmological constant and a specific exponential scalar field model. We compare our results with the constraining power calculated by the DETF using their “$w_0-w_a$” parametrization of the dark energy. We find that respective increases in constraining power from one stage to the next produced by our analysis give results consistent with DETF results. To further investigate the potential impact of future experiments, we also generate simulated data for an exponential model background cosmology which cannot be distinguished from a cosmological constant at DETF “Stage 2,” and show that for this cosmology good DETF Stage 4 data would exclude a cosmological constant by better than $3\sigma$.

We analyze the constraining power of future dark energy experiments for pseudo-Nambu-Goldstone-boson (PNGB) quintessence. Following the Dark Energy Task Force (DETF) methodology, we forecast data for three experimental stages: Stage 2 represents in-progress projects relevant to dark energy; Stage 3 refers to medium-sized experiments; Stage 4 comprises larger projects. We determine the posterior probability distribution for the parameters of the PNGB model using Markov Chain Monte Carlo analysis. Utilizing data generated on a $\Lambda \mathrm{CDM}$ cosmology, we find that the relative power of the different data stages on PNGB quintessence is roughly comparable to the DETF results for the $w_0-w_a$ parametrization of dark energy. We also generate data based on a PNGB cosmological model that is consistent with a $\Lambda \mathrm{CDM}$ fiducial model at Stage 2. We find that Stage 4 data based on this PNGB fiducial model will rule out a cosmological constant by at least $3\sigma$.

We consider the effect of future dark energy experiments on “Albrecht-Skordis” (AS) models of scalar field dark energy using the Monte Carlo Markov chain method. We deal with the issues of parametrization of these models, and have included spatial curvature as a parameter, finding it to be important. We use the Dark Energy Task Force (DETF) simulated data to represent future experiments and report our results in the form of likelihood contours in the chosen parameter space. Simulated data is produced for cases where the background cosmology has a cosmological constant, as well as cases where the dark energy is provided by the AS model. The latter helps us demonstrate the power of DETF Stage 4 data in the context of this specific model. Though the AS model can produce equations of state functions very different from what is possible with the $w_0-w_a$ parametrization used by the DETF, our results are consistent with those reported by the DETF.

We present the first fully relativistic long-term numerical evolutions of three equal-mass black holes in a system consisting of a third black hole in a close orbit about a black-hole binary. These close-three-black-hole systems have very different merger dynamics from black-hole binaries; displaying complex trajectories, a redistribution of energy that can impart substantial kicks to one of the holes, distinctive waveforms, and suppression of the emitted gravitational radiation. In one configuration the binary is quickly disrupted and the individual holes follow complicated trajectories and merge with the third hole in rapid succession, while in another, the binary completes a half-orbit before the initial merger of one of the members with the third black hole, and the resulting two-black-hole system forms a highly elliptical, well separated binary that shows no significant inspiral for (at least) the first $t\sim 1000M$ of evolution.

A primordial gravitational wave background with positive (blue) spectral index is expected in several nonstandard inflationary cosmologies where the stress-energy tensor violates the null energy condition. Here we show that a sizable amount of blue gravitational waves is compatible with current cosmological and astrophysical data. So far most of the works on parameter estimation from cosmic microwave background data have assumed a negative or negligible spectral index. The present limits on cosmological parameters, especially on the scalar spectral index, widen up considerably when one allows also for blue tilts of the tensor spectrum. Since the amplitude of the cosmic microwave background (CMB) B-mode polarization is larger in these models, future data from Planck are likely to provide crucial measurements.

Consequences of a specific class of two Higgs doublet models in which the Higgs induced tree level flavor changing neutral currents (FCNC) display minimal flavor violation are considered. These FCNC are fixed in terms of the Cabibbo Kobayashi Maskawa (CKM) matrix elements and the down quark masses. The minimal model in this category with only two Higgs doublets has no extra $CP$ violating phases, but such a phase can be induced by adding a complex singlet Higgs. The FCNC contribute significantly to $B$ meson mixing and $CP$ violation, but similar contributions in case of the $K$ mesons are suppressed. Detailed numerical analysis to determine the allowed Higgs contributions to neutral meson mixings and the CKM parameters $\overline{\rho }$, $\overline{\eta }$ in their presence is presented. The Higgs induced phase in the $B_{d,s}^0-{\overline{B}}_{d,s}^0$ transition amplitude $M_{12}^{d,s}$ is predicted to be equal for the $B_d$ and the $B_s$ systems. There is a strong correlation between $|V_{ub}|$ and phases ${\varphi }_{d,s}$ in $M_{12}^{d,s}$. A measurable $CP$ violating phase ${\varphi }_s=-0.18\pm 0.08$ is predicted on the basis of the observed phase ${\varphi }_d$ in the $B_d$ system if $|V_{ub}|$ is large and close to its value determined from the inclusive $b$ decays.

Using the general factorization approach, we present a detailed investigation for the branching ratios, $CP$ asymmetries and longitudinal polarization fractions in all charmless hadronic $B\to VV$ decays (except for the pure annihilation processes) within the most general two-Higgs-doublet model with spontaneous $CP$ violation. It is seen that such a new physics model only has very small contributions to the branching ratios and longitudinal polarization fractions. However, as the model has rich $CP$-violating sources, it can lead to significant effects on the $CP$ asymmetries, especially on those of penguin-dominated decay modes, which provides good signals for probing new physics beyond the SM in the future $B$-physics experiments.

Color-octet scalars, if present at the TeV scale, will be produced in abundance at the LHC. We discuss in some detail the phenomenology of scalars in the $(8,2{)}_{1/2}$ representation, recently identified by Manohar and Wise as an addition to the standard model Higgs sector consistent with the principle of minimal flavor violation. Couplings of this multiplet to the Higgs lift the mass degeneracy among its states, possibly allowing for two-body decays of a heavier colored scalar to a lighter one and a gauge boson. We perform a renormalization group analysis of these couplings and find that limits from Tevatron searches leave little room for these decays. This fact, and the assumption of minimal flavor violation, lead us to study the case where the octets decay to the heaviest kinematically accessible fermion pairs. Focusing on pair-production events leading to $t\overline{t}t\overline{t}$, $b\overline{b}b\overline{b}$, and $b\overline{b}t\overline{t}$ final states, we find that discovery at the LHC should be possible up to masses exceeding 1 TeV.

We investigate the prospects for the discovery at the CERN Large Hadron Collider or at the Fermilab Tevatron of neutral Higgs bosons through the channel where the Higgs are produced together with a single bottom quark and the Higgs decays into a pair of tau leptons, $bg\to b{\varphi }^0\to b{\tau }^{+}{\tau }^{-}$, ${\varphi }^0=h^0$, $H^0$, $A^0$. We work within the framework of the minimal supersymmetric model. The dominant physics background from the production of $b{\tau }^{+}{\tau }^{-}$, $j{\tau }^{+}{\tau }^{-}$ ($j=g,u,d,s,c$), $b\overline{b}{W}^{+}{W}^{-}$, $W+2j$, and $Wbj$ is calculated with realistic acceptance cuts and efficiencies. Promising results are found for the $CP$-odd pseudoscalar ($A^0$) and the heavier CP-even scalar ($H^0$) Higgs bosons with masses up to one TeV.

A new over-improved stout-link smearing algorithm, designed to stabilize instanton-like objects, is presented. A method for quantifying the selection of the over-improvement parameter, $ϵ$, is demonstrated. The new smearing algorithm is compared with the original stout-link smearing, and Symanzik improved smearing through calculations of the topological charge and visualizations of the topological charge density. We find the incorporation of improvement in stout-link smearing to be essential for the accurate study of QCD vacuum structure.

We derive a second-order linear differential equation for the leading-order gluon distribution function $G(x,Q^2)=xg(x,Q^2)$ which determines $G(x,Q^2)$ directly from the proton structure function $F_2^p(x,Q^2)$. This equation is derived from the leading-order evolution equation for $F_2^p(x,Q^2)$, and does not require knowledge of either the individual quark distributions or the gluon evolution equation. Given an analytic expression that successfully reproduces the known experimental data for $F_2^p(x,Q^2)$ in a domain $x_{\min }(Q^2)\le x\le x_{\max }(Q^2)$, $Q_{\min }^2\le Q^2\le Q_{\max }^2$ of the Bjorken variable $x$ and the virtuality $Q^2$ in deep inelastic scattering, $G(x,Q^2)$ is uniquely determined in the same domain. We give the general solution and illustrate the method using the recently proposed Froissart-bound-type parametrization of $F_2^p(x,Q^2)$ of E. L. Berger, M. M. Block and C.-I. Tan [Phys. Rev. Lett. 98, 242001 (2007)]. Existing leading-order gluon distributions based on power-law descriptions of individual parton distributions agree roughly with the new distributions for $x\gtrsim {10}^{-3}$ as they should, but are much larger for $x\lesssim {10}^{-3}$.

The dimensionless parameter $\xi =M_{\pi }^2/(16{\pi }^2{F}_{\pi }^2)$, where $F_{\pi }$ is the pion decay constant and $M_{\pi }$ is the pion mass, is expected to control the convergence of chiral perturbation theory applicable to QCD. Here we demonstrate that a strongly coupled lattice gauge theory model with the same symmetries as two-flavor QCD but with a much lighter $\sigma$-resonance is different. We first confirm that the leading low-energy constants appearing in the chiral Lagrangian are the same when calculated from the $p$-regime and the $ϵ$-regime as expected. However, $\xi \lesssim 0.002$ is necessary before 1-loop chiral perturbation theory predicts the data within 1%. For $\xi >0.0035$ the data begin to deviate dramatically from 1-loop chiral perturbation theory predictions. We argue that this qualitative change is due to the presence of a light $\sigma$-resonance in our model. Our findings may be useful for lattice QCD studies.