We propose a coherent method for detection and reconstruction of gravitational wave signals with a network of interferometric detectors. The method is derived by using the likelihood ratio functional for unknown signal waveforms. In the likelihood analysis, the global maximum of the likelihood ratio over the space of waveforms is used as the detection statistic. We identify a problem with this approach. In the case of an aligned pair of detectors, the detection statistic depends on the cross correlation between the detectors as expected, but this dependence disappears even for infinitesimally small misalignments. We solve the problem by applying constraints on the likelihood functional and obtain a new class of statistics. The resulting method can be applied to data from a network consisting of any number of detectors with arbitrary detector orientations. The method allows us reconstruction of the source coordinates and the waveforms of two polarization components of a gravitational wave. We study the performance of the method with numerical simulations and find the reconstruction of the source coordinates to be more accurate than in the standard likelihood method.

We present a universal formalism for transverse momentum resummation in the view of soft-collinear effective theory (SCET), and establish the relation between our SCET formula and the well known Collins-Soper-Sterman’s pQCD formula at the next-to-leading logarithmic order (NLLO). We also briefly discuss the reformulation of joint resummation in SCET.

The processes of muon (tau) and charged pion pair production at electron-positron annihilation with $\mathcal{O}(\alpha )$ radiative corrections are considered. The calculation results are presented assuming the energies of final particles (center of mass system implied) to be not far significantly from threshold production. The invariant mass distributions for the muon (tau) and pion pairs are obtained both for the initial and final state radiation. Some analytical calculations are illustrated numerically. The pions were assumed to be pointlike objects and scalar QED was applied for calculation. The QED radiative corrections related to the final state radiation, in addition to the well-known Coulomb factor, are treated near threshold region exactly.

We evaluate the problem of galaxy formation in the landscape approach to phenomenology of the axion sector. With other parameters of standard $\Lambda$CDM cosmology held fixed, the density of cold dark matter is bounded below relative to the density of baryonic matter by the requirement that structure should form before the era of cosmological constant domination of the universe. Galaxies comparable to the Milky Way can only form if the ratio also satisfies an upper bound. The resulting constraint on the density of dark matter is too loose to select a low axion decay constant or small initial displacement angle on anthropic grounds.

In the Randall-Sundrum model, the radion-Higgs mixing is weakly suppressed by the effective electroweak scale. A novel feature of the gravity-scalar mixing would be a sizable three-point vertex of $h_{\mu \nu }^{(n)}$-$h$-$\varphi$. We explore the potential of photon colliders, achieved by the laser back-scattering technique, in probing the radion-Higgs mixing via the associated production of the radion with the Higgs boson. The advantage of photon colliders is the capability of adjusting the polarization of the incoming photons such that the signal of the spin-2 graviton exchange can be largely enhanced. The enhancement factor is shown to be about 5, except for the small-$\xi$ region. We also study the corresponding backgrounds step by step in detail.

The origin of the breaking of conventional linear $k_{\perp }$ factorization for hard processes in a nuclear environment is by now well established. The realization of the nonlinear nuclear $k_{\perp }$ factorization which emerges instead was found to change from one jet observable to another. A basic ingredient of the master formula for the dijet spectrum is the $\mathsf{S}$ matrix for color-singlet multiparton states, and here we report on an important technical progress, the evaluation of the four-gluon color-dipole cross section operator. It describes the coupled seven-channel non-Abelian intranuclear evolution of the four-gluon color-singlet states. An exact diagonalization of this seven-channel problem is possible for large number of colors $N_c$ and allows a formulation of nonlinear $k_{\perp }$ factorization for production of gluon-gluon dijets. The momentum spectra for dijets in all possible color representations are reported in the form of explicit quadratures in terms of the collective nuclear unintegrated glue. Our results fully corroborate the concept of universality classes.

We investigate the classical stability of nonsupersymmetric Freund-Rubin compactifications of Type IIB string theory on a product of three-dimensional Einstein spaces $A_3\times B_3$ with both Neveu-Schwarz (NS) and Ramond-Ramond (RR) three-form fluxes turned on through $A_3$ and $B_3$, and a zero axion. This results in a three parameter family of $\mathrm{Ad}{\mathrm{S}}_4$ vacua, with localized sources such as anti-three-branes or orientifold planes required to cancel the RR four-form tadpole. We scan the entire space of such solutions for perturbative stability and find that anti-three branes are unstable to a Jeans-like instability. For orientifold compactifications, we derive a precise criterion which the three-dimensional Einstein spaces have to satisfy in order to be stable.

We obtain an exact result for the nonperturbative quark (antiquark) production rate and its $p_T$ distribution from a constant SU(3) chromoelectric field $E^a$ with arbitrary color index $a$ by directly evaluating the path integral. Unlike the WKB tunneling result, which depends only on one gauge invariant quantity $|E|$, the strength of the chromoelectric field, we find that the exact result for the $p_T$ distribution for quark (antiquark) production rate depends on two independent Casimir (gauge) invariants, $E^a{E}^a$ and $[d_{abc}{E}^a{E}^b{E}^c{]}^2$.

A proof of the positive energy theorem of general relativity is given. In this proof the gravitational Lagrangian is identified with that of Lau and is equivalent to the teleparallel Lagrangian modulo, a boundary term. The approach adopted in this proof uses the two-spinor method and the extended Witten identities and then combines the Brown-York and the Nester-Witten approaches. At the same time the proof is extended to the case involving the contribution of angular momentum by choosing a special shift vector.

We have performed a comparative analysis of three recent and reliable SnIa datasets available in the literature: the Full Gold (FG) dataset (157 data points $0<z<1.75$), a Truncated Gold (TG) dataset (140 data points $0<z<1$) and the most recent Supernova Legacy Survey (SNLS) dataset (115 data points $0<z<1$). We have analyzed and compared the likelihood of cosmological constant and dynamical dark energy parametrizations allowing for crossing of the phantom divide line (PDL). We find that, even though the constraints obtained using the three datasets are consistent with each other at the 95% confidence level, the latest (SNLS) dataset shows distinct trends which are not shared by the Gold datasets. We find that the best fit dynamical $w(z)$ obtained from the SNLS dataset does not cross the PDL $w=-1$ and remains above and close to the $w=-1$ line for the whole redshift range $0<z<1$ showing no evidence for phantom behavior. The $\Lambda +\mathrm{\text{Cold}}\mathrm{\text{Dark}}\mathrm{\text{Matter}}$ (LCDM) parameter values ($w_0=-1$, $w_1=0$) almost coincide with the best fit parameters of the dynamical $w(z)$ parametrizations. In contrast, the best fit dynamical $w(z)$ obtained from the Gold datasets (FG and TG) clearly crosses the PDL and departs significantly from the PDL $w=-1$ line while the LCDM parameter values are about $2\sigma$ away from the best fit $w(z)$. In addition, the $({\Omega }_{0m},{\Omega }_{\Lambda })$ parameters in a LCDM parametrization without a flat prior, fit by the SNLS dataset, favor the minimal flat LCDM concordance model. The corresponding fit with the Gold datasets mildly favors a closed universe and the flat LCDM parameter values are $1\sigma –2\sigma$ away from the best fit $({\Omega }_{0m},{\Omega }_{\Lambda })$.

We study the non-Gaussianity in the simplest infrared model of the Dirac-Born-Infeld (DBI) inflation. We show that the non-Gaussianity in such a model is compatible with the current observational bound and is within the sensitivity of future experiments. We also discuss the scale dependence of the non-Gaussianity. In DBI inflation, such a feature can be used as a probe to the properties of the background geometry of the extra dimensions or internal space.

Possible effects due to nonequilibrium dynamics in the Affleck-Dine mechanism of baryogenesis are examined. Using the closed-time-path formalism, the quantum fluctuation and the backreaction of the Affleck-Dine scalar field are incorporated self-consistently into the dynamical equations of the system by invoking a nonperturbative Hartree approximation. It is found that such nonequilibrium effects can significantly affect the amount of baryon asymmetry that can be generated. In particular, it is possible to generate the observed baryon asymmetry with suitable initial conditions. The methodology described in this paper as well as some of the results obtained are quite general, and can be applied to any complex scalar field in a cosmological background.

Recently a mechanism was proposed whereby the primordial density perturbations are generated at the end of inflation. We continue the analysis of the proposed model of this mechanism and calculate the maximum extent to which the density perturbations produced via this model can dominate over those of the standard inflationary paradigm. In addition, we provide a straightforward variation of this model which allows for greater amplification of the density perturbations. Finally, we show that a variation in the implementation of the original model results in significant non-Gaussianities in the resulting spectrum of density perturbations. The level of non-Gaussianities can be made to saturate the current observational bound.

In inflationary models gravitational waves are produced in the early universe and generate $B$-type polarization in the cosmic microwave background (CMB). Since $B$ polarization is only generated by gravity waves it does not suffer from the usual cosmic variance. A perfect decomposition of the CMB into $B$-modes and $E$-modes would require data from the entire sky, which in practice is not possible because of the foreground contaminants. This leads to mixing of $E$ polarization into $B$, which introduces cosmic variance contamination of $B$ polarization and reduces sensitivity to gravity wave amplitude even in absence of detector noise. We present numerical results for the uncertainty in the tensor-to-scalar ratio using the Fisher matrix formalism for various resolutions and considering several cuts of the sky, using the foreground model based on dust maps and assuming 90 GHz operating frequency. We find that the usual scaling $△(\frac{T}{S})\propto f_{\mathrm{sky}}^{-1/2}$ is significantly degraded and becomes $△(\frac{T}{S})\propto f_{\mathrm{sky}}^{-2}$ for $f_{\mathrm{sky}}>0.7$. This dependence is affected only weakly by the choice of sky cuts. To put this into a context of what is required level of foreground cleaning, to achieve a $T/S={10}^{-3}$ detection at $3\sigma$ one needs to observe 15% of the sky as opposed to naive expectation of 0.3%. To prevent contamination over this large sky area at required level one must be able to remove polarized dust emission at or better than 0.1% of unpolarized intensity, assuming the cleanest part of the sky has been chosen. To achieve $T/S={10}^{-4}$ detection at $3\sigma$ one needs to observe 70% of the sky, which is only possible if dust emission is removed everywhere over this region at 0.01% level. Reaching $T/S={10}^{-2}$ should be easier: 1% of the sky is needed over which polarized emission needs to be removed at 1% of unpolarized intensity if the cleanest region is chosen. These results suggest that foreground contamination may make it difficult to achieve levels below $T/S={10}^{-3}$.

We examine the effects of the extended gauge sector of the littlest Higgs model in high energy $e^{+}{e}^{-}$ collisions. We find that the search reach in $e^{+}{e}^{-}\to f\overline{f}$ at a $\sqrt{s}=500\mathrm{GeV}$ International Linear Collider covers essentially the entire parameter region where the littlest Higgs model is relevant to the gauge hierarchy problem. In addition, we show that this channel provides an accurate determination of the fundamental model parameters, to the precision of a few percent, provided that the CERN LHC measures the mass of the heavy neutral gauge field. Additionally, we show that the couplings of the extra gauge bosons to the light Higgs can be observed from the process $e^{+}{e}^{-}\to Zh$ for a significant region of the parameter space. This allows for confirmation of the structure of the cancellation of the Higgs mass quadratic divergence and would verify the little Higgs mechanism.

With the aim of resolving theoretical issues associated with the fourth root prescription for dynamical staggered fermions in lattice QCD simulations, we consider the problem of finding a viable lattice Dirac operator $D$ such that $(\det D_{\mathrm{staggered}}{)}^{1/4}=\det D$. Working in the flavor field representation we show that in the free field case there is a simple and natural candidate $D$ satisfying this relation, and we show that it has acceptable locality behavior: exponentially local with a localization range vanishing $\sim \sqrt{a/m}$ for lattice spacing $a\to 0$. Prospects for the interacting case are also discussed, although we do not solve this case here.

In an effort to clarify the significance of the recent observation of long-range topological charge coherence in QCD gauge configurations, we study the local topological charge distributions in two-dimensional $C{P}^{N-1}$ sigma models, using the overlap Dirac operator to construct the lattice topological charge. We find long-range sign coherence of topological charge along extended one-dimensional structures in two-dimensional spacetime. We discuss the connection between the long-range topological structure found in $C{P}^{N-1}$ and the observed sign coherence along three-dimensional sheets in four-dimensional QCD gauge configurations. In both cases, coherent regions of topological charge form along membranelike surfaces of codimension one. We show that the Monte Carlo results, for both two-dimensional and four-dimensional gauge theory, support a view of topological charge fluctuations suggested by Lüscher and Witten. In this framework, the observed membranes are associated with boundaries between “k-vacua,” characterized by an effective local value of $\theta$ which jumps by $\pm 2\pi$ across the boundary.

We consider three-body $\Delta s=1$ $B\to f$ decays with $f=KKK$. The deviations of $-{\eta }_f{S}_f$ from $S_{\psi K_S}$ and of $C_f$ from zero can be bounded using the approximate $SU(3)$ flavor symmetry of the strong interactions and branching ratios of various $\Delta s=0$ modes. We present the most promising $SU(3)$ amplitude relations that can be used to obtain these bounds.

We use the invariance of a physical picture under a change of Lagrangian, the reparameterization invariance in the space of Lagrangians and its particular case—the rephrasing invariance—for analysis of the two-Higgs-doublet extension of the standard model. We found that some parameters of theory like $\tan \beta$ are reparameterization dependent and therefore cannot be fundamental. We use the $Z_2$ symmetry of the Lagrangian, which prevents a ${\varphi }_1\leftrightarrow {\varphi }_2$ transition, and the different levels of its violation, soft and hard, to describe the physical content of the model. In general, the broken $Z_2$ symmetry allows for a $CP$ violation in the physical Higgs sector. We argue that the two-Higgs-doublet model with a soft breaking of $Z_2$ symmetry is a natural model in the description of electroweak symmetry breaking. To simplify the analysis, we choose among different forms of Lagrangian describing the same physical reality a specific one, in which the vacuum expectation values of both Higgs fields are real. A possible $CP$ violation in the Higgs sector is described by using a two-step procedure with the first step identical to a diagonalization of the mass matrix for $CP$-even fields in the $CP$-conserving case. We find a very simple, necessary, and sufficient condition for a $CP$ violation in the Higgs sector. We determine the range of parameters for which $CP$ violation and flavor-changing neutral current effects are naturally small—it corresponds to a small dimensionless mass parameter $\nu =\mathrm{Re}{m}_{12}^2/(2v_1{v}_2)$. We show that for small $\nu$ some Higgs bosons can be heavy—with mass up to about 0.6 TeV—without violating of the unitarity constraints. If $\nu$ is large, all Higgs bosons except one can be arbitrarily heavy. We discuss, in particular, main features of this case, which corresponds for $\nu \to \infty$ to a decoupling of heavy Higgs bosons. In the model II for Yukawa interactions we obtain the set of relations among the couplings to gauge bosons and to fermions which allows us to analyze different physical situations (including $CP$ violation) in terms of these very couplings, instead of the parameters of Lagrangian.

We discuss an extension of a map between BPS states and free fermions. The extension involves states associated with a full two matrix problem which are constructed using a sequence of integral equations. A two parameter set of matrix model eigenstates is then related to states in SUGRA. Their wave functions are characterized by nontrivial dependence on the radial coordinate of AdS and of the Sphere, respectively. A kernel defining a one to one map between these states is then constructed.