We present explicit formulas for the matrix elements of the $SU(6)$ generators for totally symmetric spin-flavor states, relevant for baryon spectroscopy in large $N_c$ QCD. We rely on the interplay between two different methods to calculate these matrix elements. As an outcome, general analytic formulas of the corresponding $SU(6)$ isoscalar factors are derived for arbitrary $N_c$. These results can be used to study excited states of nonstrange and strange baryons.

Vector-boson fusion processes are an important tool for the study of electroweak symmetry breaking at hadron colliders, since they allow to distinguish a light Higgs boson scenario from strong weak-boson scattering. We here consider the channels $WW\to ZZ$ and $ZZ\to ZZ$ as part of electroweak $Z$ boson pair production in association with two tagging jets. We present the calculation of the NLO QCD corrections to the cross sections for $pp\to e^{+}{e}^{-}{\mu }^{+}{\mu }^{-}+2\mathrm{\text{jets}}$ and $pp\to e^{+}{e}^{-}{\nu }_{\mu }{\overline{\nu }}_{\mu }+2\mathrm{\text{jets}}$ via vector-boson fusion at order ${\alpha }_s{\alpha }^6$, which is performed in the form of a NLO parton-level Monte Carlo program. The corrections to the integrated cross sections are found to be modest, while the shapes of some kinematical distributions change appreciably at NLO. Residual scale uncertainties typically are at the few percent level.

Arkani-Hamed, Dimopoulous, and Dvali have proposed a model of low-scale quantum gravity featuring large extra dimensions. In this model, the exchange of Kaluza-Klein towers of gravitons can enhance the production rate of electron and photon pairs at high invariant mass in proton-antiproton collisions. The amount of enhancement is characterized by the parameter $M_S$, the fundamental Planck scale in the bulk extra dimensions. We have searched for this effect using $100{\mathrm{pb}}^{-1}$ of diphoton data and $110{\mathrm{pb}}^{-1}$ of dielectron data collected with the Collider Detector at Fermilab at $\sqrt{s}=1.8\mathrm{TeV}$ during the 1992–1996 run. In the absence of a signal, we place 95% confidence-level limits on $M_S$ of $905\mathrm{GeV}/c^2$ and $826\mathrm{GeV}/c^2$, for the case of constructive and destructive graviton interference, respectively.

We report a measurement of the branching fraction of the decay $B^0\to {\rho }^0{\pi }^0$, using $386\times {10}^6$ $B\overline{B}$ pairs collected at the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We detect ${51}_{-13}^{+14}$ signal events with a significance of 4.2 standard deviations, including systematic uncertainties, and measure the branching fraction to be $\mathcal{B}(B^0\to {\rho }^0{\pi }^0)=({3.12}_{-0.82}^{+0.88}(\mathrm{stat})\pm 0.33(\mathrm{syst}{)}_{-0.68}^{+0.50}(\mathrm{\text{model}}))\times {10}^{-6}$. We also perform the first measurement of direct $CP$ violating asymmetry in this mode.

We point out that 5D large radius doubly spinning black rings with rotation along $S^1$ and $S^2$ are afflicted by a robust instability. It is triggered by superradiant bound state modes. The Kaluza-Klein momentum of the mode along the ring is responsible for the bound state. This is shown by analyzing the boosted Kerr black string. The present kind of instability in black strings and branes was first suggested by Marolf and Palmer and studied in detail by Cardoso, Lemos and Yoshida. We find the frequency spectrum and time scale of this instability in the black ring background, and show that it is active for infinite-radius rings with large rotation along $S^2$. We identify the end point of the instability and argue that it provides a dynamical mechanism that introduces an upper bound in the rotation of the black ring. To estimate the upper bound, we use the recent black ring model of Hovdebo and Myers, with a minor extension to accommodate an extra small angular momentum. This dynamical bound can be smaller than the Kerr-like bound imposed by regularity at the horizon. Recently, the existence of higher-dimensional black rings has been conjectured. They will be stable against this mechanism.

We put forward a framework for cosmology that combines the string landscape with no boundary initial conditions. In this framework, amplitudes for alternative histories for the universe are calculated with final boundary conditions only. This leads to a top-down approach to cosmology, in which the histories of the universe depend on the precise question asked. We study the observational consequences of no boundary initial conditions on the landscape, and outline a scheme to test the theory. This is illustrated in a simple model landscape that admits several alternative inflationary histories for the universe. Only a few of the possible vacua in the landscape will be populated. We also discuss in what respect the top-down approach differs from other approaches to cosmology in the string landscape, like eternal inflation.

Large scale structure introduces two different kinds of errors in the luminosity distance estimates from standardizable candles such as supernovae Ia (SNe)—a Poissonian scatter for each SN and a coherent component due to correlated fluctuations between different SNe. Increasing the number of SNe helps reduce the first type of error but not the second. The coherent component has been largely ignored in forecasts of dark energy parameter estimation from upcoming SN surveys. For instance it is commonly thought, based on Poissonian considerations, that peculiar motion is unimportant, even for a low redshift SN survey such as the Nearby Supernova Factory (SNfactory; $z=0.03–0.08$), which provides a useful anchor for future high redshift surveys by determining the SN zero point. We show that ignoring coherent peculiar motion leads to an underestimate of the zero-point error by about a factor of 2, despite the fact that SNfactory covers almost half of the sky. More generally, there are four types of fluctuations: peculiar motion, gravitational lensing, gravitational redshift and what is akin to the integrated Sachs-Wolfe effect. Peculiar motion and lensing dominates at low and high redshifts, respectively. Taking into account all significant luminosity distance fluctuations due to large scale structure leads to a degradation of up to 60% in the determination of the dark energy equation of state from upcoming high redshift SN surveys, when used in conjunction with a low redshift anchor such as the SNfactory. The most relevant fluctuations are the coherent ones due to peculiar motion and the Poissonian ones due to lensing, with peculiar motion playing the dominant role. We also discuss to what extent the noise here can be viewed as a useful signal, and whether corrections can be made to reduce the degradation.

This paper is concerned with a study of the analytic structure of a family of hyperboloidal beams introduced by Bondarescu and Thorne which generalizes the nearly-flat and nearly-concentric mesa beam configurations of interest for advanced LIGO. Capitalizing on certain results from the applied optics literature on flat-top beams, a physically-insightful and computationally-effective representation is derived in terms of rapidly-converging Gauss-Laguerre expansions. A generalization (involving fractional Fourier transform operators of complex order) of some recently discovered duality relations between the nearly-flat and nearly-concentric mesa configurations is obtained. Possible implications for the advanced-LIGO optical cavity design are discussed.

The decoupling of spurious states leads to linear relations among four-point functions in the high-energy limit of string theory. Recently it was shown that the linear relations uniquely determine ratios among four-point functions at the leading order. The purpose of this paper is to extend the validity of the same approach to the next-to-leading order and higher orders.

By twisting the commutation relations between creation and annihilation operators, we show that quantum conformal invariance can be implemented in the 2-d Moyal plane. This is an explicit realization of an infinite dimensional symmetry as a quantum algebra.

The infrared behavior of gluon and ghost propagators, ghost-gluon vertex, and three-gluon vertex is investigated for both the covariant Landau and the noncovariant Coulomb gauge. Assuming infrared ghost dominance, we find a unique infrared exponent in the $d=4$ Landau gauge, while in the $d=3+1$ Coulomb gauge we find two different infrared exponents. We also show that a finite dressing of the ghost-gluon vertex has no influence on the infrared exponents. Finally, we determine the infrared behavior of the three-gluon vertex analytically and calculate it numerically at the symmetric point in the Coulomb gauge.

We study vacuum solutions of five-dimensional Einstein equations generated by the inverse scattering method. We reproduce the black ring solution which was found by Emparan and Reall by taking the Euclidean Levi-Cività metric plus one-dimensional flat space as a seed. This transformation consists of two successive processes; the first step is to perform the three-solitonic transformation of the Euclidean Levi-Cività metric with one-dimensional flat space as a seed. The resulting metric is the Euclidean $C$-metric with extra one-dimensional flat space. The second is to perform the two-solitonic transformation by taking it as a new seed. Our result may serve as a stepping stone to find new exact solutions in higher dimensions.

In spherically symmetric charged dust, just like in neutral dust, two kinds of singularity may be present: the big bang/big crunch (BB/BC) singularity, and shell crossings. Quite unlike in neutral dust, the BB/BC singularity may be avoided. When the charge density ${\rho }_e$ and the mass-energy density $ϵ$ obey $|{\rho }_e|<D_e\stackrel{\mathrm{def}}{=}\sqrt{G}ϵ/c^2$, the conditions that allow the model to avoid the BB/BC singularity necessarily lead to shell crossings. However, when $|{\rho }_e|\to D_e$ at the center of symmetry while $|{\rho }_e|<D_e$ elsewhere, both kinds of singularity may be avoided for a sufficiently long period that a body of charged dust may go through the tunnel between the singularities in the maximally extended Reissner-Nordström spacetime, to emerge into another asymptotically flat region. An explicit example of such a configuration is presented and discussed. It does not contradict any astrophysical constraints.

We show that the use of the fourth-root trick in lattice QCD with staggered fermions corresponds to a nonlocal theory at nonzero lattice spacing, but argue that the nonlocal behavior is likely to go away in the continuum limit. We give examples of this nonlocal behavior in the free theory, and for the case of a fixed topologically nontrivial background gauge field. In both special cases, the nonlocal behavior indeed disappears in the continuum limit. Our results invalidate a recent claim that at nonzero lattice spacing an additive mass renormalization is needed because of taste-symmetry breaking.

Motivated by several recent data, we test the QCD spectral sum rules (QSSR) predictions based on different proposals ($\overline{q}q$, $\overline{q}\overline{q}qq$, and gluonium) for the nature of scalar mesons. In the $I=1$ and $1/2$ channels, the unusual wrong splitting between the $a_0(980)$ and $\kappa (900)$ and the $a_0(980)$ width can be understood from QSSR within a $\overline{q}q$ assignment. However, none of the $\overline{q}q$ and $\overline{q}\overline{q}qq$ results can explain the large $\kappa$ width, which may suggest that it can result from a strong interference with nonresonant backgrounds. In the $I=0$ channel, QSSR and some low-energy theorems (LET) require the existence of a low mass gluonium ${\sigma }_B(1\mathrm{GeV})$ coupled strongly to Goldstone boson pairs which plays in the $U(1{)}_V$ channel, a similar role as the ${\eta }^{\prime }$ for the value of the $U(1{)}_A$ topological charge. The observed $\sigma (600)$ and $f_0(980)$ mesons result from a maximal mixing between the gluonium ${\sigma }_B$ and $\overline{q}q$ (1 GeV) mesons, a mixing scheme which passes several experimental tests. Okubo-Zweig-Izuki (OZI) violating $J/\psi \to \varphi {\pi }^{+}{\pi }^{-}$, $D_s\to 3\pi$ decays, and $J/\psi \to \gamma S$ glueball filter processes may indicate that the $f_0(1500)$, $f_0(1710)$, and $f_0(1790)$ have significant gluonium components in their wave functions, while the $f_0(1370)$ is mostly $\overline{q}q$. Tests of these results can be provided by the measurements of the pure gluonium ${\eta }^{\prime }\eta$ and $4\pi$ specific $U(1{)}_A$ decay channels.

We calculate the electric dipole moments (EDM) of the neutral ${}^{199}\mathrm{Hg}$ atom, neutron and deuteron within a generic $R$-parity violating SUSY model (${\mathrm{R̸}}_p$ SUSY) on the basis of a one-pion-exchange model with $CP$-odd pion-nucleon interactions. We consider two types of the ${\mathrm{R̸}}_p$ SUSY contributions to the above hadronic EDMs: via the quark chromoelectric dipole moments (CEDM) and $CP$-violating 4-quark interactions. We demonstrate that the former contributes to all the three studied EDMs while the latter appears only in the nuclear EDMs via the $CP$-odd nuclear forces. We find that the ${\mathrm{R̸}}_p$ SUSY induced 4-quark interactions arise at tree level through the sneutrino exchange and involve only $s$ and $b$ quarks. Therefore, their effect in hadronic EDMs is determined by the strange and bottom-quark sea of the nucleon. From the null experimental results on the hadronic EDMs we derive the limits on the imaginary parts of certain products $\mathrm{Im}({\lambda }^{\prime }{\lambda }^{\prime *})$ of the trilinear ${\mathrm{R̸}}_p$-couplings and show that the currently best limits come from the ${}^{199}\mathrm{Hg}$ EDM experiments. We demonstrate that some of these limits are better than those existing in the literature. We argue that future storage ring experiments on the deuteron EDM are able to improve these limits by several orders of magnitude.

We consider five-dimensional Einstein-dilaton gravity with antisymmetric forms. Assuming staticity and a restriction on the dilaton coupling parameters, we derive a four-dimensional sigma model with a target space $SL(2,R)/SO(1,1)\times SL(2,R)/SO(1,1)$. On this basis, using the symmetries of the target space, we develop a solution-generating technique and employ it to construct new asymptotically flat and nonflat dyonic black rings solutions. The solutions are analyzed and the basic physical quantities are calculated.

We study the spectrum of gravitational waves generated from inflation in the Randall-Sundrum braneworld. Since the inflationary gravitational waves are of quantum-mechanical origin, the initial configuration of perturbations in the bulk includes Kaluza-Klein quantum fluctuations as well as fluctuations in the zero mode. We show, however, that the initial fluctuations in Kaluza-Klein modes have no significant effect on the late time spectrum, irrespective of the energy scale of inflation and the equation of state parameter in the post-inflationary stage. This is done numerically, using the Wronskian formulation.

Stability of self-similar solutions for gravitational collapse is an important problem to be investigated from the perspectives of their nature as an attractor, critical phenomena, and instability of a naked singularity. In this paper we study spherically symmetric non-self-similar perturbations of matter and metrics in spherically symmetric self-similar backgrounds. The collapsing matter is assumed to be a perfect fluid with the equation of state $P=\alpha \rho$. We construct a single wave equation governing the perturbations, which makes their time evolution in arbitrary self-similar backgrounds analytically tractable. Further we propose an analytical application of this master wave equation to the stability problem by means of the normal mode analysis for the perturbations having the time dependence given by $\exp (i\omega \log |t|)$, and present some sufficient conditions for the absence of nonoscillatory unstable normal modes with purely imaginary $\omega$.