We study two-body $B$-meson decays to a charmonium state (${\eta }_c$, ${\eta }_c(2S)$ or $h_c$) and a $K^{+}$ or $K^{*0}(892)$ meson using a sample of $349{\mathrm{fb}}^{-1}$ of data collected with the BABAR detector at the PEP-II asymmetric-energy $B$ Factory at the Stanford Linear Accelerator Center. We measure $\mathcal{B}(B^0\to {\eta }_c{K}^{*0})=(5.7\pm 0.6(\mathrm{stat})\pm 0.9(\mathrm{syst}))\times {10}^{-4}$, $\mathcal{B}(B^0\to {\eta }_c(2S)K^{*0})<3.9\times {10}^{-4}$, $\mathcal{B}(B^{+}\to h_c{K}^{+})\times \mathcal{B}(h_c\to {\eta }_c\gamma )<4.8\times {10}^{-5}$ and $\mathcal{B}(B^0\to h_c{K}^{*0})\times \mathcal{B}(h_c\to {\eta }_c\gamma )<2.2\times {10}^{-4}$ at the 90% C.L., and $\mathcal{B}({\eta }_c(2S)\to K\overline{K}\pi )=(1.9\pm 0.4(\mathrm{stat})\pm 1.1(\mathrm{syst}))\%$. We also measure the mass and width of the ${\eta }_c$ meson to be $m({\eta }_c)=(2985.8\pm 1.5(\mathrm{stat})\pm 3.1(\mathrm{syst}))\mathrm{MeV}/c^2$ and $\Gamma ({\eta }_c)=({36.3}_{-3.6}^{+3.7}(\mathrm{stat})\pm 4.4(\mathrm{syst}))\mathrm{MeV}$.

We present the results of searches for decays of $B$ mesons to final states with a $b_1$ meson and a neutral pion or kaon. The data, collected with the BABAR detector at the Stanford Linear Accelerator Center, represent $465\times {10}^6$ $B\overline{B}$ pairs produced in $e^{+}{e}^{-}$ annihilation. The results for the branching fractions are, in units of ${10}^{-6}$, $\mathcal{B}(B^{+}\to b_1^{+}{K}^0)=9.6\pm 1.7\pm 0.9$, $\mathcal{B}(B^0\to b_1^0{K}^0)=5.1\pm 1.8\pm 0.5$ ($<7.8$), $\mathcal{B}(B^{+}\to b_1^{+}{\pi }^0)=1.8\pm 0.9\pm 0.2$ ($<3.3$), and $\mathcal{B}(B^0\to b_1^0{\pi }^0)=0.4\pm 0.8\pm 0.2$ ($<1.9$), with the assumption that $\mathcal{B}(b_1\to \omega \pi )=1$. We also measure the charge asymmetry ${\mathcal{A}}_{\mathrm{ch}}(B^{+}\to b_1^{+}{K}^0)=-0.03\pm 0.15\pm 0.02$. The first error quoted is statistical, the second systematic, and the upper limits in parentheses indicate the 90% confidence level.

We consider the problem of a degenerate electron gas in the background of a uniformly distributed positive charge, ensuring overall neutrality of the system, in the presence of noncommutativity. In contrast to previous calculations [F. S. Bemfica and H. O. Girotti, J. Phys. A 38, L539 (2005)] that did not include twisted formalism, we study the effects of noncommutativity from the points of view of both usual and braided twisted symmetry. We find corrections to the ground-state energy already at first order in perturbation theory when the usual twisted statistics is taken into account. The effects of noncommutativity, however, disappears if braided twisted symmetry is considered. In the former case these corrections arise since the interaction energy is sensitive to two-particle correlations, which are modified for the usual twisted anticommutation relations.

We study some of the roles for unparticles in an inflationary universe. Unparticles by themselves are not appropriate for generating the primordial perturbations since their power spectrum does not match what has been inferred from observations. In fact, when the scaling dimension for the unparticles exceeds three-halves, the unparticle power spectrum diverges. However, when a unparticle couples to an ordinary inflaton particle, loop corrections can produce a slight enhancement of the inflaton’s power spectrum at longer wavelengths. We examine these loop corrections from unparticles in some detail to learn how they scale in the wavelength of a perturbation and how they depend on the scaling dimension of the field.

To avoid instabilities in the continuum semiclassical limit of loop quantum cosmology models, refinement of the underlying lattice is necessary. This lattice refinement leads to new dynamical difference equations which, in general, do not have a uniform step size, implying complications in their analysis and solutions. We propose a numerical method based on Taylor expansions, which can give us the necessary information to calculate the wave function at any given lattice point. The method we proposed can be applied in any lattice-refined model, while in addition the accuracy of the method can be estimated. Moreover, we confirm numerically the stability criterion which was earlier found following a von Neumann analysis. Finally, the “motion” of the wave function due to the underlying discreteness of the space-time is investigated, for both a constant lattice, as well as lattice refinement models.

We study the stability of neutron stars with toroidal magnetic fields by magnetohydrodynamic simulation in full general relativity under the assumption of axial symmetry. Nonrotating and rigidly rotating neutron stars are prepared for a variety of magnetic field configuration. For modeling the neutron stars, the polytropic equation of state with the adiabatic index $\Gamma =2$ is used for simplicity. It is found that nonrotating neutron stars are dynamically unstable for the case where toroidal magnetic field strength varies $\propto {\varpi }^{2k-1}$ with $k\ge 2$ (here $\varpi$ is the cylindrical radius), whereas for $k=1$ the neutron stars are stable. After the onset of the instability, unstable modes grow approximately in the Alfvén time scale and, as a result, a convective motion is excited to change the magnetic field profile until a new state, which is stable against axisymmetric perturbation, is reached. We also find that rotation plays a role in stabilization, although the instability still occurs in the Alfvén time scale when the ratio of magnetic energy to rotational kinetic energy is larger than a critical value $\sim 0.2$. Implication for the evolution of magnetized protoneutron stars is discussed.

The collective behavior of the $\mathrm{SL}(2,\mathbb{R})$ covariant brane states of noncritical $c=1$ string theory, found in a previous work, is studied in the Fermi liquid approximation. It is found that such states mimic the coset WZW model, whereas only by further restrictions one recovers the double-scaling limit which was purported to be equivalent to closed string models. Another limit is proposed, inspired by the tachyon condensation ideas, where the spectrum is the same of two-dimensional string theory. We close by noting some strange connections between vacuum states of the theory in their different interpretations.

We investigate the Hagedorn transitions of string networks with Y-junctions as may occur, for example, with $(p,q)$ cosmic superstrings. In a simplified model with three different types of string, the partition function reduces to three generalized coupled XY models. We calculate the phase diagram and show that, as the system is heated, the lightest strings first undergo the Hagedorn transition despite the junctions. There is then a second, higher, critical temperature above which infinite strings of all tensions, and junctions, exist. Conversely, on cooling to low temperatures, only the lightest strings remain, but they collapse into small loops.

The unification of gauge interactions in the context of adjoint $SU(5)$ and its phenomenological consequences are investigated. We show the allowed mass spectrum of the theory which is compatible with proton decay and discuss the possibility of having a cold dark matter candidate. Because of the upper bounds on the proton decay partial lifetimes, $\tau (p\to K^{+}\overline{\nu })\le 9.3\times {10}^{36}\mathrm{years}$ and $\tau (p\to {\pi }^{+}\overline{\nu })\le 3.0\times {10}^{35}\mathrm{years}$, the theory could be tested at future proton decay experiments. The theory predicts also light scalar color octets which could be produced at the Large Hadron Collider.

We extend the Fermilab method for heavy quarks to include interactions of dimensions 6 and 7 in the action. There are, in general, many new interactions, but we carry out the calculations needed to match the lattice action to continuum QCD at the tree level, finding six nonzero couplings. Using the heavy-quark theory of cutoff effects, we estimate how large the remaining discretization errors are. We find that our tree-level matching, augmented with one-loop matching of the dimension-5 interactions, can bring these errors below 1%, at currently available lattice spacings.

We study the possible origin of Friedberg-Lee symmetry. First, we propose the generalized Friedberg-Lee symmetry in the potential by including the scalar fields in the field transformations, which can be broken down to the Friedberg-Lee symmetry spontaneously. We show that the generalized Friedberg-Lee symmetry allows a typical form of Yukawa couplings, and the realistic neutrino masses and mixings can be generated via the seesaw mechanism. If the right-handed neutrinos transform nontrivially under the generalized Friedberg-Lee symmetry, we can have the testable TeV scale seesaw mechanism. Second, we present two models with the $SO(3)\times U(1)$ global flavor symmetry in the lepton sector. After the flavor symmetry breaking, we can obtain the charged lepton masses, and explain the neutrino masses and mixings via the seesaw mechanism. Interestingly, the complete neutrino mass matrices are similar to those of the above models with generalized Friedberg-Lee symmetry. So the Friedberg-Lee symmetry is the residual symmetry in the neutrino mass matrix after the $SO(3)\times U(1)$ flavor symmetry breaking.

Recently there has been growing evidence in favor of the presence of an intermediate mass black hole in the globular cluster G1, in Andromeda Galaxy. Under the assumption that formation of this globular cluster occurred within a dark matter halo, we explore whether the presence of a black hole could result in an observable gamma ray signal due to dark matter annihilation in this globular cluster. Starting from an initial Navarro-Frenk-White matter profile, with density parameters consistent with G1 observations, we find that indeed, if the spike in the density has been formed and has survived until the present, the signal could be observed by GLAST and current atmospheric Cerenkov telescope detectors.

We study the holographic map between long open strings, which stretch between $D$-branes separated in the bulk space-time, and operators in the dual boundary theory. We focus on a generalization of the Sakai-Sugimoto holographic model of QCD, where the simplest chiral condensate involves an operator of this type. Its expectation value is dominated by a semiclassical string world sheet, as for Wilson loops. We also discuss the deformation of the model by this operator, and, in particular, its effect on the meson spectrum. This deformation can be thought of as a generalization of a quark mass term to strong coupling. It leads to the first top-down holographic model of QCD with a non-Abelian chiral symmetry which is both spontaneously and explicitly broken, as in QCD. Other examples we study include half-supersymmetric open Wilson lines, and systems of $D$-branes ending on $NS5$-branes, which can be analyzed using world sheet methods.

We investigate the finite temperature quark antiquark problem in a compact space $S^{n-1}\times S^1$ by considering static strings in global ${\mathrm{AdS}}_{n+1}$ space with $n\ge 3$. For high temperatures we work in the black hole metric where two possible solutions show up : the big black hole and the small black hole. Using the AdS/CFT correspondence, we calculate the quark antiquark potential (free energy) as a function of the distance. We show that this potential can be intrepeted as confining for the anti-de Sitter (AdS) space and deconfining for the big black hole. We find for the small black hole a confining limit for the potential but this solution is instable following the Hawking-Page criteria. Our results for the free energy reinforce the Witten interpretation of the confinement/deconfinement transition as the dual of the well-known Hawking-Page transition.

In a recent paper Bender and Mannheim showed that the unequal-frequency fourth-order derivative Pais-Uhlenbeck oscillator model has a realization in which the energy eigenvalues are real and bounded below, the Hilbert-space inner product is positive definite, and time evolution is unitary. Central to that analysis was the recognition that the Hamiltonian $H_{\mathrm{PU}}$ of the model is $\mathcal{P}\mathcal{T}$ symmetric. This Hamiltonian was mapped to a conventional Dirac-Hermitian Hamiltonian via a similarity transformation whose form was found exactly. The present paper explores the equal-frequency limit of the same model. It is shown that in this limit the similarity transform that was used for the unequal-frequency case becomes singular and that $H_{\mathrm{PU}}$ becomes a Jordan-block operator, which is nondiagonalizable and has fewer energy eigenstates than eigenvalues. Such a Hamiltonian has no Hermitian counterpart. Thus, the equal-frequency $\mathcal{P}\mathcal{T}$ theory emerges as a distinct realization of quantum mechanics. The quantum mechanics associated with this Jordan-block Hamiltonian can be treated exactly. It is shown that the Hilbert space is complete with a set of nonstationary solutions to the Schrödinger equation replacing the missing stationary ones. These nonstationary states are needed to establish that the Jordan-block Hamiltonian of the equal-frequency Pais-Uhlenbeck model generates unitary time evolution.

Perfect magnetic conductor (PMC) boundary conditions are dual to the more familiar perfect electric conductor (PEC) conditions and can be viewed as the electromagnetic analog of the boundary conditions in the bag model for hadrons in QCD. Recent advances and requirements in communication technologies have attracted great interest in PMC’s, and Casimir experiments involving structures that approximate PMC’s may be carried out in the not-too-distant future. In this paper, we make a study of the zero-temperature PMC Casimir piston in $d+1$ dimensions. The PMC Casimir energy is explicitly evaluated by summing over $p+1$-dimensional Dirichlet energies where $p$ ranges from 2 to $d$ inclusively. We derive two exact $d$-dimensional expressions for the Casimir force on the piston and find that the force is negative (attractive) in all dimensions. Both expressions are applied to the case of $2+1$ and $3+1$ dimensions. A spin-off from our work is a contribution to the PEC literature: we obtain a useful alternative expression for the PEC Casimir piston in $3+1$ dimensions and also evaluate the Casimir force per unit area on an infinite strip, a geometry of experimental interest.

We construct a new type of S-matrix in quantum field theory using the general boundary formulation. In contrast to the usual S-matrix the space of free asymptotic states is located at spatial rather than at temporal infinity. Hence, the new S-matrix applies to situations where interactions may remain important at all times, but become negligible with distance. We show that the new S-matrix is equivalent to the usual one in situations where both apply. This equivalence is mediated by an isomorphism between the respective asymptotic state spaces that we construct. We introduce coherent states that allow us to obtain explicit expressions for the new S-matrix. In our formalism crossing symmetry becomes a manifest rather than a derived feature of the S-matrix.

The equation which governs the temporal evolution of a gravitational wave (GW) in curved space-time can be treated as the Schrödinger equation for a particle moving in the presence of an effective potential. When GWs propagate in an expanding universe with constant effective potential, there is a critical value $(k_c)$ of the comoving wave number which discriminates the metric perturbations into oscillating $(k>k_c)$ and nonoscillating $(k<k_c)$ modes. As a consequence, if the nonoscillatory modes are outside the horizon they do not freeze out. The effective potential is reduced to a nonvanishing constant in a cosmological model which is driven by a two-component fluid, consisting of radiation (dominant) and cosmic strings (subdominant). It is known that the cosmological evolution gradually results in the scaling of a cosmic-string network and, therefore, after some time $(\Delta \tau )$ the Universe becomes radiation dominated. The evolution of the nonoscillatory GW modes during $\Delta \tau$ (while they were outside the horizon), results in the distortion of the GW power spectrum from what it is anticipated in a pure radiation model, at present-time frequencies in the range ${10}^{-16}\mathrm{Hz}<f\lesssim {10}^5\mathrm{Hz}$.

The presence of Kaluza-Klein (KK) particles in the universe is a potential manifestation of string theory cosmology. In general, they can be present in the high temperature bath of the early universe. In particular examples, string theory inflation often ends with brane-antibrane annihilation followed by the energy cascading through massive closed string loops to KK modes which then decay into lighter standard model particles. However, massive KK modes in the early universe may become dangerous cosmological relics if the inner manifold contains warped throat(s) with approximate isometries. In the complimentary picture, in the AdS/CFT dual gauge theory with extra isometries, massive glueballs of various spins become the dangerous cosmological relics. The decay of these angular KK modes/glueballs, located around the tip of the throat, is caused by isometry breaking which results from gluing the throat to the compact Calabi-Yau (CY) manifold. We address the problem of these angular KK particles/glueballs, studying their interactions and decay channels, from the theory side, and the resulting cosmological constraints on the warped compactification parameters, from the phenomenology side. The abundance and decay time of the long-lived nonrelativistic angular KK modes depend strongly on the parameters of the warped geometry, so that observational constraints rule out a significant fraction of the parameter space. In particular, the coupling of the angular KK particles can be weaker than gravitational.

In light of the five-year data from the Wilkinson Microwave Anisotropy Probe (WMAP), we discuss models of inflation based on the pseudo Nambu-Goldstone potential predicted in five-dimensional gauge theories for different backgrounds: flat Minkowski, anti–de Sitter, and dilatonic spacetime. In this framework, the inflaton potential is naturally flat due to shift symmetries and the mass scales associated with it are related to 5D geometrical quantities.