A decay width calculation for a hybrid exotic meson $h$, with $J^{\mathrm{PC}}=1^{-+}$, is presented for the channel $h\to \pi a_1$. This quenched lattice QCD simulation employs Lüscher’s finite box method. Operators coupling to the $h$ and $\pi a_1$ states are used at various levels of smearing and fuzzing, and at four quark masses. Eigenvalues of the corresponding correlation matrices yield energy spectra that determine scattering phase shifts for a discrete set of relative $\pi a_1$ momenta. Although the phase shift data is sparse, fits to a Breit-Wigner model are attempted, resulting in a decay width of about 60 MeV when averaged over two lattice sizes having a lattice spacing of 0.07 fm.

We examine the anomalous dimension matrix appropriate for the phase space restricted $\overline{B}\to X_u\ell \overline{\nu }$ and $\overline{B}\to X_s\gamma$ decay spectra to subleading nonperturbative order. The time ordered products of the HQET Lagrangian with the leading order shape function operator are calculated, as are the anomalous dimensions of subleading operators. We establish the renormalizability and closure of a subset of the nonlocal operator basis, a requirement for the establishment of factorization theorems at this order. Operator mixing is found between the operators which occur to subleading order, requiring the subleading operator basis be extended. We comment on the requirement for new shape functions to be introduced to characterize the matrix elements of these new operators, and the phenomenological consequences for extractions of $|V_{ub}|$.

From $e^{+}{e}^{-}$ collision data acquired with the CLEO-c detector at CESR, we search for the non-$D\overline{D}$ decays $\psi (3770)\to \gamma {\chi }_{cJ}$, with ${\chi }_{cJ}$ reconstructed in four exclusive decays modes containing charged pions and kaons. We report the first observation of such decays for $J=0$ with a branching ratio of $(0.73\pm 0.07\pm 0.06)\%$. The rates for different $J$ are consistent with the expectations assuming $\psi (3770)$ is predominantly a $1^3{D}_1$ state of charmonium, but only if relativistic corrections are applied.

We construct a pair of black holes on the Eguchi-Hanson space as a solution in the five-dimensional Einstein-Maxwell theory.

An effective description of an initial state is a method for representing the signatures of new physics in the short-distance structure of a quantum state. The expectation value of the energy-momentum tensor for a field in such a state contains new divergences that arise when summing over this new structure. These divergences occur only at the initial time at which the state is defined and therefore can be cancelled by including a set of purely geometric counterterms that also are confined to this initial surface. We describe this gravitational renormalization of the divergences in the energy-momentum tensor for a free scalar field in an isotropically expanding inflationary background. We also show that the backreaction from these new short-distance features of the state is small when compared with the leading vacuum energy contained in the field.

Motivated by the problem of the evolution of bulk gravitational waves in Randall-Sundrum cosmology, we develop a characteristic numerical scheme to solve $1+1$ dimensional wave equations in the presence of a moving timelike boundary. The scheme exhibits quadratic convergence, is capable of handling arbitrary brane trajectories, and is easily extendible to non-AdS bulk geometries. We use our method to contrast two different prescriptions for the bulk fluctuation initial conditions found in the literature; namely, those of Hiramatsu et al. and Ichiki and Nakamura. We find that, if the initial data surface is set far enough in the past, the late-time waveform on the brane is insensitive to the choice between the two possibilities; and we present numeric and analytic evidence that this phenomenon generalizes to more generic initial data. Observationally, the main consequence of this work is to reaffirm previous claims that the stochastic gravitational wave spectrum is predominantly flat ${\Omega }_{\mathrm{GW}}\propto f^0$, in contradiction with naive predictions from the effective 4-dimensional theory. Furthermore, this flat spectrum result is predicted to be robust against uncertainties in (or modifications of) the bulk initial data, provided that the energy scale of brane inflation is high enough.

We examine the motion in Schwarzschild spacetime of a point particle endowed with a scalar charge. The particle produces a retarded scalar field which interacts with the particle and influences its motion via the action of a self-force. We assume that the magnitude of the scalar charge is small, and that the deviations from geodesic motion produced by the self-force are small. This problem is analogous to that of an electric charge moving under the action of its electromagnetic self-force, and to that of a small mass moving under the action of its gravitational self-force. We exploit the spherical symmetry of the Schwarzschild spacetime and decompose the scalar field in spherical-harmonic modes. Although each mode is bounded at the position of the particle, a mode-sum evaluation of the self-force requires regularization because the sum does not converge: the retarded field is infinite at the position of the particle. The regularization procedure involves the computation of regularization parameters, which are obtained from a mode decomposition of the Detweiler-Whiting singular field; these are subtracted from the modes of the retarded field, and the result is a mode-sum that converges to the actual self-force. We present such a computation in this paper. While regularization parameters have been presented before in the literature, there are two main aspects of our work that are new. First, we define the regularization parameters as scalar quantities by referring them to a tetrad decomposition of the singular field. This is different from standard practice, which is to define regularization parameters as vectorial quantities. The advantage of dealing with tetrad components is that these, unlike vector components, are naturally decomposed in scalar spherical harmonics. Second, we calculate, for any bound orbit around a Schwarzschild black hole, four sets of regularization parameters (denoted schematically by $A$, $B$, $C$, and $D$) instead of the usual three ($A$, $B$, and $C$). While only the first three regularization parameters are needed to produce a convergent mode-sum, the inclusion of a fourth parameter has the practically important consequence of accelerating the convergence. The focus of this paper is entirely on the computation of regularization parameters for the scalar self-force. The techniques that we introduce in this work are not, however, restricted to this context. They will readily be exported to the electromagnetic and gravitational cases, but we leave this generalization for future work. As proof of principle that our methods are reliable, we calculate the self-force acting on a scalar charge in circular motion around a Schwarzschild black hole, and compare our answers with those recorded in the literature. We leave for future work the generalization of this calculation to generic orbits.

In this paper we revisit thermodynamic constraints on primordial black hole (PBH) formation in the early universe. Under the assumption that PBH mass is equal to the cosmological horizon mass, one can use the 2nd Law of Thermodynamics to put a lower limit on the PBH mass. In models of PBH formation, however, PBHs are created at some fraction of the horizon mass. We show that this thermodynamic constraint still holds for subhorizon PBH formation.

We investigate the Selection of Original Universe Proposal (SOUP) of Tye et al and show that as it stands, this proposal is flawed. The corrections to the Euclidean gravity action that were to select a Universe with a sufficiently large value of the cosmological constant $\Lambda$ to allow for an inflationary phase only serve to renormalize the cosmological constant so that $\Lambda \to {\Lambda }_{\mathrm{eff}}$. SOUP then predicts a wave function that is highly peaked around ${\Lambda }_{\mathrm{eff}}\to 0$, thereby reintroducing the issue of how to select initial conditions allowing for inflation in the early Universe.

We obtain a complete set of free-field solutions of the Dirac equation in a (longitudinal) boost-invariant geometry with azimuthal symmetry and use these solutions to perform the canonical quantization of a free Dirac field of mass $M$. This coordinate system which uses the $1+1$ dimensional fluid rapidity $\eta =1/2\ln [(t-z)/(t+z)]$ and the fluid proper time $\tau =(t^2-z^2{)}^{1/2}$ is relevant for understanding particle production of quarks and antiquarks following an ultrarelativistic collision of heavy ions, as it incorporates the (approximate) longitudinal “boost invariance” of the distribution of outgoing particles. We compare two approaches to solving the Dirac equation in curvilinear coordinates, one directly using Vierbeins, and one using a “diagonal” Vierbein representation.

We describe searches for decays of $B$ mesons to the charmless final states ${\eta }^{\prime }{\eta }^{\prime }K$. The data consist of $228\times {10}^6$ $B\overline{B}$ pairs produced in $e^{+}{e}^{-}$ annihilation, collected with the BABAR detector at the Stanford Linear Accelerator Center. The 90% confidence level upper limits for the branching fractions are $\mathcal{B}(B^0\to {\eta }^{\prime }{\eta }^{\prime }{K}^0)<31\times {10}^{-6}$ and $\mathcal{B}(B^{+}\to {\eta }^{\prime }{\eta }^{\prime }{K}^{+})<25\times {10}^{-6}$.

We show that the cosmological constant at late-time places a bound on the entropy of microwave background radiation deposited in the future event horizon of a given observer, $S\le S_{{\Lambda }_0}^{3/4}$. This bound is independent of the energy scale of reheating and the FRW evolution after reheating. We also discuss why the entropy of microwave background in our observable universe has its present value.

We continue the study of a local, gauge invariant Yang-Mills action containing a mass parameter, which we constructed in a previous paper starting from the nonlocal gauge invariant mass dimension two operator $F_{\mu \nu }(D^2{)}^{-1}{F}_{\mu \nu }$. We return briefly to the renormalizability of the model, which can be proven to all orders of perturbation theory by embedding it in a more general model with a larger symmetry content. We point out the existence of a nilpotent Becchi-Rouet-Stora-Tyutin (BRST) symmetry. Although our action contains extra (anti)commuting tensor fields and coupling constants, we prove that our model in the limit of vanishing mass is equivalent with ordinary massless Yang-Mills theories. The full theory is renormalized explicitly at two loops in the $\overline{\mathrm{MS}}$ scheme and all the renormalization group functions are presented. We end with some comments on the potential relevance of this gauge model for the issue of a dynamical gluon mass generation.

We consider $\mathcal{N}=2$ supersymmetric quantum electrodynamics with two flavors, the Fayet-Iliopoulos parameter, and a mass term $\beta$ which breaks the extended supersymmetry down to $\mathcal{N}=1$. The bulk theory has two vacua; at $\beta =0$ the Bogomol’nyi-Prasad-Sommerfield (BPS) monopoles-saturated domain wall interpolating between them has a moduli space parameterized by a $U(1)$ phase $\sigma$ which can be promoted to a scalar field in the effective low-energy theory on the wall world-volume. At small nonvanishing $\beta$ this field gets a sine-Gordon potential. As a result, only two discrete degenerate BPS domain walls survive. We find an explicit solitonic solution for domain lines—stringlike objects living on the surface of the domain wall which separate wall I from wall II. The domain line is seen as a BPS kink in the world-volume effective theory. We expect that the wall with the domain line on it saturates both the $\{1,0\}$ and the $\{\frac{1}{2},\frac{1}{2}\}$ central charges of the bulk theory. The domain line carries a magnetic flux which is exactly $\frac{1}{2}$ of the flux carried by the flux tube living in the bulk on each side of the wall. Thus, the domain lines on the wall confine charges living on the wall, resembling Polyakov’s three-dimensional confinement.

We evaluate the isovector nucleon electromagnetic form factors in quenched and unquenched QCD on the lattice using Wilson fermions. In the quenched theory we use a lattice of spatial size 3 fm at $\beta =6.0$ enabling us to reach low momentum transfers and a lowest pion mass of about 400 MeV. In the unquenched theory we use two degenerate flavors of dynamical Wilson fermions on a lattice of spatial size 1.9 fm at $\beta =5.6$ and lowest pion mass of about 380 MeV enabling comparison with the results obtained in the quenched theory. that unquenching effects are small for the pion masses considered in this work. We compare our lattice results to the isovector part of the experimentally measured form factors.

The mass spectrum of baryons in the spin-$3/2$ sector is computed in quenched lattice QCD using a tadpole-improved anisotropic action. Both isospin $1/2$ and $3/2$ (the traditional decuplet) are considered, as well as members that contain strange quarks. States with positive and negative parities are isolated by parity projection, while states with spin-$3/2$ and spin-$1/2$ are separated by spin projection. The extent to which spin projection is needed is examined. The issue of optimal interpolating field is also investigated. The results are discussed in relation to previous calculations and experiment.

$B\to K\pi$ and related decays are studied in the heavy quark limit of QCD using the soft collinear effective theory (SCET). We focus on results that follow solely from integrating out the scale $m_b$, without expanding the amplitudes for the physics at smaller scales such as ${\alpha }_s(\sqrt{E_{\pi }{\Lambda }_{\mathrm{QCD}}})$. The reduction in the number of hadronic parameters in SCET leads to multiple predictions without the need of SU(3). We find that the $CP$-asymmetry in $B^{-}\to {\pi }^0{K}^{-}$ should have a similar magnitude and the same sign as the well measured asymmetry in ${\overline{B}}^0\to {\pi }^{+}{K}^{-}$. Our prediction for $\mathrm{Br}(K^{+}{\pi }^{-})$ exceeds the current experimental value at the $2\sigma$ level. We also use our results to determine the corrections to the Lipkin and $CP$-asymmetry sum rules in the standard model and find them to be quite small, thus sharpening their utility as a tool to look for new physics.

We present the first search for the decay $B^0\to K_S^0{K}_S^0{K}_L^0$ using a data sample of $232\times {10}^6$ $B\overline{B}$ pairs. We find no statistically significant evidence for the nonresonant component of this decay. Our central value for the branching fraction, assuming the true Dalitz distribution is uniform and excluding the $\varphi$ resonance, is $\mathcal{B}(B^0\to K_S^0{K}_S^0{K}_L^0)=({2.4}_{-2.5}^{+2.7}\pm 0.6)\times {10}^{-6}$ where the errors are statistical and systematic, respectively. We set a single-sided Bayesian upper limit of $\mathcal{B}(B^0\to K_S^0{K}_S^0{K}_L^0)<7.4\times {10}^{-6}$ at 90% confidence level using a uniform prior probability for physical values. Assuming the worst-case true Dalitz distribution, where the signal is entirely in the region of lowest efficiency, the 90% confidence level upper limit is $\mathcal{B}(B^0\to K_S^0{K}_S^0{K}_L^0)<16\times {10}^{-6}$.

We present a search for the rare $B$-meson decay $B^0\to a_1^{\pm }{\rho }^{\mp }$ with $a_1^{\pm }\to {\pi }^{+}{\pi }^{-}{\pi }^{\pm }$. We use $(110\pm 1.2)\times {10}^6\mathit{{\rm Y}}(4S)\to B\overline{B}$ decays collected with the BABAR detector at the PEP-II asymmetric-energy $B$ Factory at SLAC. We obtain an upper limit of $30\times {10}^{-6}(90\%\mathrm{C}.\mathrm{L}.)$ for the branching fraction product $\mathcal{B}(B^0\to a_1^{\pm }{\rho }^{\mp })\mathcal{B}(a_1^{\pm }\to {\pi }^{+}{\pi }^{-}{\pi }^{\pm })$, where we assume that the $a_1^{\pm }$ decays exclusively to ${\rho }^0{\pi }^{\pm }$.

In this paper we investigate the cosmological effects of modified gravity with string curvature corrections added to the Einstein-Hilbert action in the presence of a dynamically evolving scalar field coupled to Riemann invariants. The scenario exhibits several features of cosmological interest for the late universe. We show that higher-order stringy corrections can lead to a class of dark energy models consistent with recent observations. The models can give rise to quintessence without recourse to a scalar field potential. The detailed treatment of the reconstruction program for general scalar-Gauss-Bonnet gravity is presented for any given cosmology. The explicit examples of reconstructed scalar potentials are given for an accelerated (quintessence, cosmological constant, or phantom) universe. Finally, the relation with modified $F(G)$ gravity is established at the classical level and is extended to include third order terms on the curvature.