We have searched for the di-pion transition ${\chi }_b(2\mathrm{P})\to \pi \pi {\chi }_b(1\mathrm{P})$ in the CLEO III sample of ${\rm Y}(3\mathrm{S})$ decays in the exclusive decay chain: ${\rm Y}(3\mathrm{S})\to \gamma {\chi }_b(2\mathrm{P})$, ${\chi }_b(2\mathrm{P})\to \pi \pi {\chi }_b(1\mathrm{P})$, ${\chi }_b(1\mathrm{P})\to \gamma {\rm Y}(1\mathrm{S})$, ${\rm Y}(1\mathrm{S})\to {\ell }^{+}{\ell }^{-}$. Our studies include both ${\pi }^{+}{\pi }^{-}$ and ${\pi }^0{\pi }^0$, each analyzed both in fully-reconstructed events and in events with one pion undetected. We show that the null hypothesis is not substantiated. Under reasonable assumptions, we find the partial decay width to be $\Gamma ({\chi }_b(2\mathrm{P})\to \pi \pi {\chi }_b(1\mathrm{P}))=(0.83\pm 0.22\pm 0.08\pm 0.19)\mathrm{keV}$, with the uncertainties being statistical, internal CLEO systematics, and common systematics from outside sources.

A typographical error in the Hamiltonian expression for the charges is corrected and the discussion on the integrability of the improved surface charges is rectified.

Recent numerical work on the fate of plasma instabilities in weakly-coupled non-Abelian gauge theory has shown the development of a cascade of energy from long to short wavelengths. This cascade has a steady-state spectrum, analogous to the Kolmogorov spectrum for turbulence in hydrodynamics or for energy cascades in other systems. In this paper, we theoretically analyze processes responsible for this cascade and find a steady-state spectrum $f_{\mathit{k}}\sim k^{-2}$, where $f_{\mathit{k}}$ is the phase-space density of particles with momentum $\mathit{k}$. The exponent $-2$ is consistent with results from numerical simulations. We also discuss implications of the emerging picture of instability development on the “bottom-up” thermalization scenario for (extremely high energy) heavy ion collisions, emphasizing fundamental questions that remain to be answered.

The standard Hartree-Fock approximation of the $O(N)$-invariant ${\varphi }^4$ model suffers from serious renormalization problems. In addition, when the symmetry is spontaneously broken, another shortcoming appears in relation to the Goldstone bosons: they fail to be massless in the intermediate states. In this work, within the framework of out-of-equilibrium Quantum Field Theory, we propose a class of systematic improvements of the Hartree-Fock resummation which overcomes all the above mentioned difficulties while ensuring also exact Renormalization-Group invariance to one loop.

We propose to consider the $\mathcal{N}=4,d=1$ supermultiplet with $(\mathbf{4},\mathbf{4},\mathbf{0})$ component content as a “root” one. We elaborate a new reduction scheme from the root multiplet to supermultiplets with a smaller number of physical bosons. Starting from the most general sigma-model-type action for the root multiplet, we explicitly demonstrate that the actions for the rest of linear and nonlinear $\mathcal{N}=4$ supermultiplets can be easily obtained by reduction. Within the proposed reduction scheme, there is a natural possibility to introduce Fayet-Iliopoulos terms. In the reduced systems, such terms give rise to potential terms, and in some cases also to terms describing the interaction with a magnetic field. We demonstrate that known $\mathcal{N}=4$ superconformal actions, together with their possible interactions, appear as results of the reduction from a free action for the root supermultiplet. As a by-product, we also construct an $\mathcal{N}=4$ supersymmetric action for the linear $(\mathbf{3},\mathbf{4},\mathbf{1})$ supermultiplet, containing both an interaction with a Dirac monopole and a harmonic oscillator-type potential, generalized for arbitrary conformally flat metrics.

We investigate the contribution of extra dimensions to the muon anomalous magnetic moment by using an Arkani-Hamed–Dimopoulos–Dvali-type (ADD-type) 6-dimensional model. This approach analyzes the extent of the influence of classical brane fluctuations on the magnetic moment. When we consider that the brane fluctuations are static in time, they add new potential terms to the Schrödinger equation through the induced vierbein. This paper shows that the brane fluctuation is responsible for the brane stretching effect. This effect would be capable of reproducing the appropriate order for recent Brookhaven National Laboratory (BNL) measurements of the muon (g-2) deviation.

We prove that the number of sphaleron instabilities of the $n$th $SU(2)$ Einstein-Yang-Mills-Dilaton soliton and black hole equals $n$.

Spin-weighted spheroidal harmonics are useful in a variety of physical situations, including light scattering, nuclear modeling, signal processing, electromagnetic wave propagation, black hole perturbation theory in four and higher dimensions, quantum field theory in curved space-time and studies of D-branes. We first review analytic and numerical calculations of their eigenvalues, and eigenfunctions in four dimensions, filling gaps in the existing literature when necessary. Then we compute the angular dependence of the spin-weighted spheroidal harmonics corresponding to slowly damped quasinormal mode frequencies of the Kerr black hole, providing numerical tables and approximate formulas for their scalar products. Finally we present an exhaustive analytic and numerical study of scalar spheroidal harmonics in ($n+4$) dimensions.

We calculate the first dynamical evolutions of merging black hole-neutron star binaries that construct the combined black hole-neutron star spacetime in a general relativistic framework. We treat the metric in the conformal flatness approximation, and assume that the black hole mass is sufficiently large compared to that of the neutron star so that the black hole remains fixed in space. Using a spheroidal spectral methods solver, we solve the resulting field equations for a neutron star orbiting a Schwarzschild black hole. The matter is evolved using a relativistic, Lagrangian, smoothed particle hydrodynamics (SPH) treatment. We take as our initial data recent quasiequilibrium models for synchronized neutron star polytropes generated as solutions of the conformal thin-sandwich (CTS) decomposition of the Einstein field equations. We are able to construct from these models relaxed SPH configurations whose profiles show good agreement with CTS solutions. Our adiabatic evolution calculations for neutron stars with low-compactness show that mass transfer, when it begins while the neutron star orbit is still outside the innermost stable circular orbit, is more unstable than is typically predicted by analytical formalisms. This dynamical mass loss is found to be the driving force in determining the subsequent evolution of the binary orbit and the neutron star, which typically disrupts completely within a few orbital periods. The majority of the mass transferred onto the black hole is accreted promptly; a significant fraction ($\sim 30\%$) of the mass is shed outward as well, some of which will become gravitationally unbound and ejected completely from the system. The remaining portion forms an accretion disk around the black hole, and could provide the energy source for short-duration gamma-ray bursts.

We consider the big-bang nucleosynthesis (BBN) in the brane world scenario, where all matter fields are confined on our 3-brane and the radion of the Brane evolves cosmologically. In the Einstein frame fundamental fermion masses vary and the results of standard BBN (SBBN) are modified. We can thus use the observational primordial element abundances to impose constraints on the possible variations of the radion. The possibility of using the evolving radion to resolve the discrepancies between the Wilkinson Microwave Anisotropy Probe and SBBN values of the baryon-to-photon ratio ($\eta$) is also discussed. The results and constraints presented here are applicable to other models in which fundamental fermion masses vary.

An alternative mechanism that dims high redshift supernovae without cosmic acceleration utilizes an oscillation of photons into a pseudoscalar particle during transit. Since angular diameter distance measures are immune to the loss of photons, this ambiguity in interpretation can be resolved by combining CMB acoustic peak measurements with the recent baryon oscillation detection in galaxy power spectra. This combination excludes a nonaccelerating dark energy species at the $4\sigma$ level regardless of the level of the pseudoscalar coupling. While solutions still exist with substantial noncosmological dimming of supernovae, they may be tested with future improvement in baryon oscillation experiments.

We discuss the variational method used in lattice spectroscopy calculations. In particular we address the role of ghost contributions which appear in quenched or partially quenched simulations and have a nonstandard euclidean time dependence. We show that the ghosts can be separated from the physical states. Our result is illustrated with numerical data for the scalar meson.

We study the phase structure of a 4-fermi model with three bare coupling constants, which potentially has three types of bound states. This model is a generalization of the model discussed previously by [A. Chodos, F. Cooper, W. Mao, H. Minakata, and A. Singh, Phys. Rev. D 61, 045011 (2000).], which contained both chiral condensates and Cooper pairs. For this generalization we find that there are two independent renormalized coupling constants which determine the phase structure at finite density and temperature. We find that the vacuum can be in one of three distinct phases depending on the value of these two renormalized coupling constants.

Based on the rainbow approximation of Dyson-Schwinger equation and the assumption that the inverse dressed fermion propagator at finite chemical potential is analytic in the neighborhood of $\mu =0$, A new method for calculating the dressed fermion propagator at finite chemical potential in ${\mathrm{QED}}_3$ is developed. From this the effects of the chemical potential on the critical number of the fermion flavors is evaluated.

In the framework of the topcolor assisted technicolor model we calculate the contributions from the pseudo Goldstone bosons and new gauge bosons to $e^{+}{e}^{-}\to b\overline{b}$. We find that, for reasonable ranges of the parameters, the top pions afford a dominate contribution, the corrections arising from technipions and new gauge bosons are negligibly small, the maximum of the total corrections is 43% with the c.m. energy $\sqrt{s}=500\mathrm{GeV}$; whereas in the case of $\sqrt{s}=1500\mathrm{GeV}$, the maximum of the relative corrections is only 3.1%. It might open a window to detect a topcolor assisted technicolor model in experiment of next generation linear colliders.

We consider $2+1$ flavor Wilson chiral perturbation theory including the lattice spacing contributions of $\mathrm{O}(a^2)$. We adopt a power counting appropriate for the unquenched lattice simulations carried out by the CP-PACS/JLQCD Collaboration and compute the pseudoscalar meson masses to one loop. These expression are required to perform the chiral extrapolation of the CP-PACS/JLQCD lattice data.

In equivariantly gauge-fixed $SU(N)$ Yang-Mills theories, the gauge symmetry is only partially fixed, leaving a subgroup $H\subset SU(N)$ unfixed. Such theories avoid Neuberger’s nogo theorem if the subgroup $H$ contains at least the Cartan subgroup $U(1{)}^{N-1}$, and they are thus nonperturbatively well defined if regulated on a finite lattice. We calculate the one-loop beta function for the coupling ${\tilde{g}}^2=\xi g^2$, where $g$ is the gauge coupling and $\xi$ is the gauge parameter, for a class of subgroups including the cases that $H=U(1{)}^{N-1}$ or $H=SU(M)\times SU(N-M)\times U(1)$. The coupling $\tilde{g}$ represents the strength of the interaction of the gauge degrees of freedom associated with the coset $SU(N)/H$. We find that $\tilde{g}$, like $g$, is asymptotically free. We solve the renormalization-group equations for the running of the couplings $g$ and $\tilde{g}$, and find that dimensional transmutation takes place also for the coupling $\tilde{g}$, generating an infrared scale $\tilde{\Lambda }$ which can be larger than or equal to the scale $\Lambda$ associated with the gauge coupling $g$, but not smaller. We speculate on the possible implications of these results.

The time-dependent $CP$ asymmetry in exclusive $B^0(t)\to K^{*0}\gamma$ decays has been proposed as a probe of new physics in B decays. Recently, this method was extended to radiative decays into multibody hadronic final states such as $B^0(t)\to K_S{\pi }^0\gamma$ and $B^0(t)\to {\pi }^{+}{\pi }^{-}\gamma$. The $CP$ asymmetry in these decays vanishes to the extent that the photon is completely polarized. In the standard model, the photon emitted in $b\to s\gamma$ has high left-handed polarization, but right-handed contamination enters already at leading order in $\Lambda /m_b$ even for vanishing light quark masses. We compute here the magnitude of this effect and the time-dependent $CP$ asymmetry parameter $S_{K_S{\pi }^0\gamma }$. We find that the standard model can easily accommodate values of $S$ as large as $10\%$, but a precise value cannot be obtained at present because of strong interactions uncertainties.

Heavy-to-light meson form factors at large recoil can be described using the same techniques as for hard exclusive processes involving only light hadrons. Two competing mechanisms appear in the large recoil regime, describing so-called “soft-overlap” and “hard-scattering” components of the form factors. It is shown how existing experimental data from $B$ and $D$ decays constrain the relative size of these components, and how lattice data can be used to study properties such as the energy-scaling laws obeyed by the individual components. Symmetry relations between different form factors ($F_{+}$, $F_0$ and $F_T$), and between different heavy initial-state mesons ($B$ and $D$) are derived in the combined heavy-quark and large-recoil limits, and are shown to generalize corresponding relations valid at small recoil. Form-factor parametrizations that are consistent with the large-recoil limit are discussed.

The $B\to K^{*}\rho$, $K^{*}\omega$ decays are useful to determine the Cabbibo-Kobayashi-Maskawa (CKM) angle ${\varphi }_3=\gamma$. Their polarization fractions are also interesting because of the polarization puzzle of the $B\to \varphi K^{*}$ decay. We study these decays in the perturbative QCD approach based on $k_T$ factorization. After calculating the nonfactorizable and annihilation type contributions, in addition to the conventional factorizable contributions, we find that the contributions from the annihilation diagrams are crucial. They give dominant contribution to the strong phases and suppress the longitudinal polarizations. Our results agree with the current existing data. We also predict sizable direct $CP$ asymmetries in $B^{+}\to K^{*+}{\rho }^0$, $B^0\to K^{*+}{\rho }^{-}$, and $B^{+}\to K^{*+}\omega$ decays, which can be tested by the oncoming measurements in the $B$ factory experiments.