We derive both time- and frequency-domain algorithms for the fast, approximate, numeric evaluation of the cross-correlation integral that appears in a variety of imaging applications. These algorithms possess a number of useful features. Their operation counts are linear in the amount (duration) of data to be processed, which allows them to be run quickly on small amounts of data, thereby allowing one to resolve time dependence in the sources being imaged. The algorithms also provide means by which to systematically increase or decrease their accuracy for increases and decreases in speed, respectively; that is to say, one can choose to obtain the result to lower accuracy and thereby obtain the result more quickly or with more modest computer requirements. The frequency-domain implementation is particularly fast and, on a 32-bit 1.8 GHz Pentium-M computer, has demonstrated the ability to synthesize full-sky cross-power images for a single baseline up to harmonic order 19, with a signal-to-noise ratio of 26 dB, at speeds of over $800\mathrm{k}\mathrm{\text{sample}}/\mathrm{s}$.

Topological interactions will generally occur in composite Higgs or little Higgs theories, extra-dimensional gauge theories in which $A_5$ plays the role of a Higgs boson, and amongst the (pseudo) Nambu-Goldstone bosons pNGB’s of technicolor. This phenomenon arises from the chiral and anomaly structure of the underlying UV completion theory, and/or through chiral delocalization in higher dimensions. These effects are described by a full Wess-Zumino-Witten term involving gauge fields and pNGB’s. We give a general discussion of these interactions, some of which may have novel signatures at future colliders, such as the LHC and ILC.

We analyze lepton flavor violating $\tau \to \mu \gamma$ and $\mu \to e\gamma$ processes in a supersymmetric grand unified theory model in which sfermions have a special mass spectrum. It is assumed that only third generation sfermions which are contained in $\mathbf{10}(\mathrm{Q},{\mathrm{U}}^{\mathrm{c}},{\mathrm{E}}^{\mathrm{c}})$ of SU(5) can have a different mass from the others. This mass spectrum is derived from the ${\mathrm{E}}_6$ grand unified theory model with horizontal symmetries. It is shown that branching ratios of $\tau \to \mu \gamma$ and $\mu \to e\gamma$ depend strongly on a right-handed stau mass. The weak scale stability requires a light stau, so large decay rates can be expected in this scenario. When the stau mass is around 150 GeV and $\tan \beta \sim 10$, the branching ratios can be larger than $\mathrm{Br}(\tau \to \mu \gamma )\simeq {10}^{-8}$ and $\mathrm{Br}(\mu \to e\gamma )\simeq 5\times {10}^{-12}$, which are within reach of future experiments. In addition, this model has an interesting feature that the final state charged lepton tends to have right-handed chirality.

A new economical way to understand neutrino mixings in the seesaw framework is proposed. We argue that its origin can be understood within the seesaw framework by a hidden condition on the mass matrix of heavy right-handed neutrinos under the transformation of the Abelian finite group $Z_3$ on the flavor basis. Ignoring $CP$ phases, we show that it can lead to the generic form of the effective light neutrino mass matrix from which the Harrison-Perkins-Scott mixing matrix appears naturally, as well as an experimentally allowed nonzero $\sin {\theta }_{13}$. Two examples are given to illustrate that the mass matrix based on our proposal is in good agreement with the current experimental data.

We reconcile seemingly conflicting statements in the literature about the behavior of cosmological solutions in modified theories of gravity where the Einstein-Hilbert Lagrangian for gravity is modified by the addition of a function of the Ricci scalar, $f(R)$. Using the example of $f(R)=\pm {\mu }^4/R$ we show that only such choices of $f(R)$ where ${\mathrm{d}}^{2}f/\mathrm{d}{R}^2>0$ have stable high-curvature limits and well-behaved cosmological solutions with a proper era of matter domination. The remaining models enter a phase dominated by both matter and scalar kinetic energy where the scalar curvature remains low.

We first investigate intersections of an $S$-brane with a single $p$-brane and show that in addition to the already known solutions, it is possible to place the $S$-brane so that the radial part of the $p$-brane is not included in its world volume. This leads to a new set of solutions. Second, we consider intersections of an $S$-brane with a supersymmetric $D{p}_1–D{p}_2$ intersection and find the list of allowed solutions for both positions of the $S$-brane. Among them there are $D1–D5–S1$ and $D1–D5–S5$ intersections which might be appropriate for studying time dependent $\mathrm{AdS}/\mathrm{CFT}$ correspondence.

We investigate in detail the flavor structure of the minimal 3-3-1 model and its implications for several flavor-changing neutral current (FCNC) processes. In this model, where the weak $SU(2{)}_L$ gauge group of the Standard Model is extended to a $SU(3{)}_L$, the by far dominant new contributions come from an additional neutral $Z^{\prime }$ gauge boson, that can transmit FCNCs at tree-level. At the same time, electroweak precision observables receive new contributions only at the loop level and do not constrain the model very strongly. In our analysis, we take into account new $CP$-violating effects that have been neglected in earlier analyses, and account for a general flavor structure without reference to a certain parametrization of the new mixing-matrix. We begin by studying the bounds obtained from quantities such as $\Delta M_K$, ${ϵ}_K$, $\Delta M_{d/s}$ as well as $\sin 2\beta {|}_{J/\psi K_S}$, and go on to explore the implications for several clean rare decay channels, namely, the decays $K^{+}\to {\pi }^{+}\nu \overline{\nu }$, $K_L\to {\pi }^0\nu \overline{\nu }$, $B_{d/s}\to {\mu }^{+}{\mu }^{-}$ and $K_L\to {\pi }^0{l}^{+}{l}^{-}$. We find sizeable effects in all these decays, but the most interesting quantity turns out to be the $B_s^0-{\overline{B}}_s^0$ mixing phase ${\beta }_s$, as measured in the mixing induced $CP$ asymmetry of $B_s^0\to J/\psi \varphi$, which can be large. In general, we find effects in purely hadronic channels to be larger than in (semi-)leptonic ones, due to a suppression of the $Z^{\prime }$-lepton couplings.

We present results for the static interquark potential, light meson and baryon masses, and light pseudoscalar meson decay constants obtained from simulations of domain wall QCD with one dynamical flavour approximating the $s$ quark, and two degenerate dynamical flavours with input bare masses ranging from $m_s$ to $m_s/4$ approximating the $u$ and $d$ quarks. We compare these quantities obtained using the Iwasaki and DBW2 improved gauge actions, and actions with larger rectangle coefficients, on ${16}^3\times 32$ lattices. We seek parameter values at which both the chiral symmetry breaking residual mass due to the finite lattice extent in the fifth dimension and the Monte Carlo time history for topological charge are acceptable for this set of quark masses at lattice spacings above 0.1 fm. We find that the Iwasaki gauge action is best, demonstrating the feasibility of using QCDOC to generate ensembles which are good representations of the QCD path integral on lattices of up to 3 fm in spatial extent with lattice spacings in the range 0.09–0.13 fm. Despite large residual masses and a limited number of sea quark-mass values with which to perform chiral extrapolations, our results for light hadronic physics scale and agree with experimental measurements within our statistical uncertainties.

We present the renormalization scheme used in and the characteristic features of $\mathtt{G}\mathtt{R}\mathtt{A}\mathtt{C}\mathtt{E}/\mathtt{S}\mathtt{U}\mathtt{S}\mathtt{Y}\mathtt{-}\mathtt{l}\mathtt{o}\mathtt{o}\mathtt{p}$, the package of the program for the automatic calculation of the minimal supersymmetric standard model processes including one-loop order corrections. The two-body and three-body decay widths of charginos in one-loop order evaluated by $\mathtt{G}\mathtt{R}\mathtt{A}\mathtt{C}\mathtt{E}/\mathtt{S}\mathtt{U}\mathtt{S}\mathtt{Y}\mathtt{-}\mathtt{l}\mathtt{o}\mathtt{o}\mathtt{p}$ are shown.

We revisit the problem of interplay between the strong and the Coulomb interaction in the charged-to-neutral yield ratio for $B\overline{B}$ and $D\overline{D}$ pairs near their respective thresholds in $e^{+}{e}^{-}$ annihilation. We consider here a realistic situation with a resonant interaction in the isospin $I=0$ channel and a nonresonant strong-scattering amplitude in the $I=1$ state. We find that the yield ratio has a smooth behavior depending on the scattering phase in the $I=1$ channel. The same approach is also applicable to the $K\overline{K}$ production at the $\varphi (1020)$ resonance, where the Coulomb effect in the charged-to-neutral yield ratio is generally sensitive to the scattering phases in both the isoscalar and the isovector channels. Furthermore, we apply the same approach to the treatment of the effect of the isotopic mass difference between the charged and neutral mesons and argue that the strong-scattering effects generally result in a modification to the pure kinematical effect of this mass difference.

By introducing the generalized uncertainty principle (GUP) on quantum density states, we obtain a consistent entropy of a scalar field on the $(1+1)$-dimensional Maxwell-dilaton background without an artificial cutoff in contrast to the results of the brick wall model, which depends on the choice of the Hawking temperature for the extremal case.

The matrix model formulation of two dimensional string theory has been shown to admit time dependent classical solutions whose closed string duals are geodesically incomplete space-times with spacelike boundaries. We investigate some aspects of the dynamics of fermions in one such background. We show that even though the background solution appears pathological, the time evolution of the system is smooth in terms of open string degrees of freedom, viz. the fermions. In particular, an initial state of fermions evolves smoothly into a well-defined final state over an infinite open string time interval, while the time perceived by closed strings appears to end abruptly. We outline a method of calculating fermion correlators exactly using symmetry properties. The result for the two-point function is consistent with the semiclassical picture.

Using the AdS/CFT duality, we analytically evaluate the high momentum (or short distance) behavior of the color field strength due to a moving quark in an $\mathcal{N}=4$ SYM plasma. We find a fireball-like behavior in the near quark vicinity as predicted in the literature on general grounds, in the context of heavy ion collisions. Our approach to analytically solving the problem is based on a WKB approximation which may be extended to other setups as well.

We study Z(2) lattice gauge theory on triangulations of compact d-manifolds. We reformulate the theory algebraically, describing it in terms of the structure constants of a bidimensional vector space $\mathcal{H}$ equipped with algebra and coalgebra structures, and prove that in the low-temperature limit $\mathcal{H}$ reduces to a Hopf algebra, in which case the theory becomes equivalent to a topological field theory. The degeneracy of the ground state is shown to be a topological invariant. This fact is used to compute the zeroth- and first-order terms in the low-temperature expansion of $Z$ for arbitrary triangulations. In finite temperatures, the algebraic reformulation gives rise to new duality relations among classical spin models, related to changes of basis of $\mathcal{H}$.

We discuss static axially symmetric solutions of $SU(2)$ Einstein-Yang-Mills-Higgs theory for large scalar coupling $\lambda$. These regular asymptotically flat solutions represent monopole-antimonopole chain and vortex ring solutions, as well as new configurations, present only for larger values of $\lambda$. When gravity is coupled to the Yang-Mills-Higgs system, branches of gravitating solutions emerge from the flat-space solutions, and extend up to critical values of the gravitational coupling constant. For small scalar coupling only two branches of gravitating solutions exist, where the second branch connects to a generalized Bartnik-McKinnon solution. For large scalar coupling, however, a plethora of gravitating branches can be present and indicate the emergence of new flat-space branches.

Gravitational waves from the inspiral of a stellar-size black hole to a supermassive black hole can be accurately approximated by a point particle moving in a Kerr background. This paper presents progress on finding the electromagnetic and gravitational field of a point particle in a black-hole spacetime and on computing the self-force in a “radiation gauge.” The gauge is chosen to allow one to compute the perturbed metric from a gauge-invariant component ${\psi }_0$ (or ${\psi }_4$) of the Weyl tensor and follows earlier work by Chrzanowski, Cohen, and Kegeles (we correct a minor, but propagating, error in the Cohen-Kegeles formalism). The electromagnetic field tensor and vector potential of a static point charge and the perturbed gravitational field of a static point mass in a Schwarzschild geometry are found, surprisingly, to have closed-form expressions. The gravitational field of a static point charge in the Schwarzschild background must have a strut, but ${\psi }_0$ and ${\psi }_4$ are smooth except at the particle, and one can find local radiation gauges for which the corresponding spin $\pm 2$ parts of the perturbed metric are smooth. Finally a method for finding the renormalized self-force from the Teukolsky equation is presented. The method is related to the Mino, Sasaki, Tanaka and Quinn and Wald (MiSaTaQuWa) renormalization and to the Detweiler-Whiting construction of the singular field. It relies on the fact that the renormalized ${\psi }_0$ (or ${\psi }_4$) is a source-free solution to the Teukolsky equation; and one can therefore reconstruct a nonsingular renormalized metric in a radiation gauge.