By the Laplace-Runge-Lenz (LRL) vector, we analyzed perihelion precessions of orbit with arbitrary eccentricity from perturbations of 1) power law central force and 2) fThusmagnetic-like force. Exact and analytically closed expressions for the precession rate are derived in both cases. In the central force case, we give a further expansion expression of precession rate in orders of eccentricity, and a rule judging pro- or retrograde precession is also given. We applied the result of central force to precessions of a planet in 1) Schwarzschild space-time, for which the formula for the Mercury’s 43”/century is reproduced, and 2) spherically distributed dark matter, for which we find a formula that is a generalization of the result derived by others for circular orbit. In the magnetic case, the use of the LRL vector proves to be simple and efficient. An example of magnetic-like perturbation is also discussed.

We elaborated the gravitational collapse of a self-gravitating complex charged scalar field in the context of the low-energy limit of the string theory, the so-called dilaton gravity. We begin with the regular spacetime and follow the evolution through the formation of an apparent horizon and the final central singularity.

Physical decomposition of the non-Abelian gauge field has recently helped to achieve a meaningful gluon spin. Here we extend this approach to gravity and attempt a meaningful gravitational energy. The metric is unambiguously separated into a pure geometric term which contributes a null curvature tensor, and a physical term which represents the true gravitational effect and always vanishes in a flat space-time. By this decomposition the conventional pseudotensors of the gravitational stress-energy are easily rescued to produce a definite physical result. Our decomposition applies to any symmetric tensor, and has an interesting relation to the transverse-traceless decomposition discussed by Arnowitt, Deser and Misner, and by York.

The Laser Interferometer Space Antenna (LISA) is designed to detect gravitational wave signals from astrophysical sources, including those from coalescing binary systems of compact objects such as black holes. Colliding galaxies have central black holes that sink to the center of the merged galaxy and begin to orbit one another and emit gravitational waves. Some galaxy evolution models predict that the binary black hole system will enter the LISA band with significant orbital eccentricity, while other models suggest that the orbits will already have circularized. Using a full 17 parameter waveform model that includes the effects of orbital eccentricity, spin precession, and higher harmonics, we investigate how well the source parameters can be inferred from simulated LISA data. Defining the reference eccentricity as the value one year before merger, we find that for typical LISA sources, it will be possible to measure the eccentricity to an accuracy of parts in a thousand. The accuracy with which the eccentricity can be measured depends only very weakly on the eccentricity, making it possible to distinguish circular orbits from those with very small eccentricities. LISA measurements of the orbital eccentricity can help constraints theories of galaxy mergers in the early universe. Failing to account for the eccentricity in the waveform modeling can lead to a loss of signal power and bias the estimation of parameters such as the black hole masses and spins.

We propose a novel diagrammatic method for computing transport coefficients in relativistic quantum field theory. The self-consistent equation for summing the diagrams with pinch singularities has the form of a linearized kinetic equation as usual, but our formalism enables us to incorporate higher-order corrections of the coupling systematically for the first time. Furthermore, it is clarified that the higher-order corrections are nicely summarized into that of the vertex function, spectral function, and collision term. We identify the diagrams up to the next-to-next-leading-order corrections in the weak coupling expansion of ${\varphi }^4$ theory, which is a difficult task in kinetic approaches and other diagrammatic methods.

We propose singlet-stabilized minimal gauge mediation as a simple Intriligator, Seiberg and Shih-based model of direct gauge mediation which avoids both light gauginos and Landau poles. The hidden sector is a massive s-confining supersymmetric QCD that is distinguished by a minimal $SU(5)$ flavor group. The uplifted vacuum is stabilized by coupling the meson to an additional singlet sector with its own $U(1)$ gauge symmetry via nonrenormalizable interactions suppressed by a higher scale ${\Lambda }_{\mathrm{UV}}$ in the electric theory. This generates a nonzero vacuum expectation value for the singlet meson via the inverted hierarchy mechanism, but requires tuning to a precision $\sim (\Lambda /{\Lambda }_{\mathrm{UV}}{)}^2$, which is $\sim {10}^{-4}$. In the course of this analysis we also outline some simple model-building rules for stabilizing uplifted-ISS models, which lead us to conclude that meson deformations are required (or at least heavily favored) to stabilize the adjoint component of the magnetic meson.

Single top production processes are usually regarded as the ones in which $V_{tb}$ can be directly measured at hadron colliders. We show that the analysis of the single top rapidity distribution in $t$-channel and $tW$ production can also set direct limits on $V_{td}$. At LHC with $10{\mathrm{fb}}^{-1}$ at 14 TeV, the combined limits on $V_{td}$ may be reduced by almost a factor of 2 when the top rapidity distribution is used. This also implies that the limits on $V_{tb}$ can also be reduced by $15\%$, since both parameters, as well as $V_{ts}$, must be simultaneously obtained from a global fit to data. At Tevatron, the exploitation of this distribution would require very high statistics.

In this note, we correct a mistake in the mass formula in [N. Okuyama and J. i. Koga, Phys. Rev. D 71, 084009 (2005).] which generalizes the Ashtekar-Magnon-Das method to incorporate extended gravities with quadratic curvature terms. The corrected mass formula confirms that the black hole masses for recently discovered critical gravities vanish.

We use the flat space limit of the AdS/CFT correspondence to derive a simple relation between the $2\to 2$ scattering amplitude of massless string states in type IIB superstring theory on ten-dimensional Minkowski space and a scaling limit of the $\mathcal{N}=4$ super Yang-Mills four-point functions. We conjecture that this relation holds nonperturbatively and at arbitrarily high energy.

We investigate the validity of the Dirac quantization condition for magnetic monopoles in noncommutative space-time. We use an approach which is based on an extension of the method introduced by Wu and Yang. To study the effects of noncommutativity of space-time, we consider the gauge transformations of $U_{\star }(1)$ gauge fields and use the corresponding deformed Maxwell’s equations. Using a perturbation expansion in the noncommutativity parameter $\theta$, we show that the Dirac quantization condition remains unmodified up to the first order in the expansion parameter. The result is obtained for a class of noncommutative source terms, which reduce to the Dirac delta function in the commutative limit.

We analytically show that mesonic bound states of confined monopoles appear inside a non-Abelian vortex string in massless three-flavor QCD at large quark chemical potential $\mu$. The orientational modes $\mathbb{C}{P}^2$ in the internal space of a vortex is described by the low-energy effective world-sheet theory. Mesons of confined monopoles are dynamically generated as bound states of kinks by the quantum effects in the effective theory. The mass of monopoles is shown to be an exponentially soft scale $M\sim \Delta \exp [-c(\mu /\Delta {)}^2]$, with the color superconducting gap $\Delta$ and some constant $c$. A possible quark-monopole duality between the hadron phase and the color superconducting phase is also discussed.

The Large Hadron Collider (LHC) has successfully run for a long period at half energy, 7 TeV. In this note, we update earlier full-energy LHC forward hadronic scattering predictions [M. M. Block, Phys. Rep. 436, 71 (2006).], giving new predictions, including errors, for the $pp$ total and inelastic cross sections, the $\rho$ value, the nuclear slope parameter $B$, $d{\sigma }_{\mathrm{el}}/dt$, and the large gap survival probability at the current 7 TeV energy.

In this work we calculate the corrections to the amputated Green’s functions of four-fermion operators, in 1-loop lattice perturbation theory. One of the novel aspects of our calculations is that they are carried out to second order in the lattice spacing, $\mathcal{O}(a^2)$. We employ the Wilson/clover action for massless fermions (also applicable for the twisted mass action in the chiral limit) and a family of Symanzik improved actions for gluons. Our calculations have been carried out in a general covariant gauge. Results have been obtained for several popular choices of values for the Symanzik coefficients (Plaquette, Tree-level Symanzik, Iwasaki, TILW and DBW2 action). While our Green’s function calculations regard any pointlike four-fermion operators which do not mix with lower dimension ones, we pay particular attention to $\Delta F=2$ operators, both parity conserving and parity violating ($F$ stands for flavor: $S$, $C$, $B$). By appropriately projecting those bare Green’s functions we compute the perturbative renormalization constants for a complete basis of four-fermion operators and we study their mixing pattern. For some of the actions considered here, even $\mathcal{O}(a^0)$ results did not exist in the literature to date. The correction terms which we calculate (along with our previous $\mathcal{O}(a^2)$ calculation of $Z_{\Psi }$ [M. Constantinou, V. Lubicz, H. Panagopoulos, and F. Stylianou, J. High Energy Phys. 10 (2009) 064.][M. Constantinou, P. Dimopoulos, R. Frezzotti, G. Herdoiza, K. Jansen, V. Lubicz, H. Panagopoulos, G. C. Rossi, S. Simula, F. Stylianou, and A. Vladikas, J. High Energy Phys. 08 (2010) 068.][C. Alexandrou, M. Constantinou, T. Korzec, H. Panagopoulos, and F. Stylianou (unpublished).]) are essential ingredients for minimizing the lattice artifacts which are present in nonperturbative evaluations of renormalization constants with the $\mathrm{R}{\mathrm{I}}^{\prime }-\mathrm{MOM}$ method. Our perturbative results, for the matrix elements of $\Delta F=2$ operators and for the corresponding renormalization matrices, depend on a large number of parameters: coupling constant, number of colors, lattice spacing, external momentum, clover parameter, Symanzik coefficients, gauge parameter. To make these results most easily accessible to the reader, we have included them in the distribution package of this paper, as an ASCII file named: 4-fermi.m; the file is best perused as Mathematica input. The main results of this work have been applied to improve nonperturbative estimates of the $B_K$-parameter in $N_F=2$ twisted mass lattice QCD [M. Constantinou, P. Dimopoulos, R. Frezzotti, K. Jansen, V. Gimenez, V. Lubicz, F. Mescia, H. Panagopoulos, M. Papinutto, G. C. Rossi, S. Simula, A. Skouroupathis, F. Stylianou, and A. Vladikas, arXiv:1009.5606.].

We analyze the problem of spin decomposition for an interacting system from a natural perspective of constructing angular-momentum eigenstates. We split, from the total angular-momentum operator, a proper part which can be separately conserved for a stationary state. This part commutes with the total Hamiltonian and thus specifies the quantum angular momentum. We first show how this can be done in a gauge-dependent way, by seeking a specific gauge in which part of the total angular-momentum operator vanishes identically. We then construct a gauge-invariant operator with the desired property. Our analysis clarifies what is the most pertinent choice among the various proposals for decomposing the nucleon spin. A similar analysis is performed for extracting a proper part from the total Hamiltonian to construct energy eigenstates.

Nonthermal scaling phenomena can exhibit a characteristic dependence on the dimensionality $d$ of space. For $d=3$ and 4 we simulate a relativistic scalar field theory on a lattice and compute turbulent scaling exponents. We recover Kolmogorov or weak wave-turbulence in the perturbative high-momentum regime, where it exhibits the scaling exponent ${\kappa }_w=d-3/2$. In the nonperturbative infrared regime, we find a different scaling exponent ${\kappa }_s=4(5)$ for $d=3(4)$, which is in agreement with the recently predicted anomalously large values ${\kappa }_s=d+1$ of strong turbulence. We show how the latter can be seen to characterize stationary transport of a conserved effective particle number.

The properties of the ground state of relativistic matter in a magnetic field are examined within the framework of a Nambu-Jona-Lasinio model. The main emphasis of this study is the normal ground state, which is realized at sufficiently high temperatures and/or sufficiently large chemical potentials. In contrast to the vacuum state, which is characterized by the magnetic catalysis of chiral symmetry breaking, the normal state is accompanied by the dynamical generation of the chiral shift parameter $\Delta$. In the chiral limit, the value of $\Delta$ determines a relative shift of the longitudinal momenta (along the direction of the magnetic field) in the dispersion relations of opposite chirality fermions. We argue that the chirality remains a good approximate quantum number even for massive fermions in the vicinity of the Fermi surface and, therefore, the chiral shift is expected to play an important role in many types of cold dense relativistic matter, relevant for applications in compact stars. The qualitative implications of the revealed structure of the normal ground state on the physics of protoneutron stars are discussed. A noticeable feature of the $\Delta$ parameter is that it is insensitive to temperature when $T\ll {\mu }_0$, where ${\mu }_0$ is the chemical potential, and increases with temperature for $T>{\mu }_0$. The latter implies that the chiral shift parameter is also generated in the regime relevant for heavy ion collisions.

Noncommutative geometry may be a starting point to a quantum gravity. We study the influence of the spacetime noncommutative parameter on the strong field gravitational lensing in the noncommutative Schwarzschild black-hole spacetime and obtain the angular position and magnification of the relativistic images. Supposing that the gravitational field of the supermassive central object of the galaxy can be described by this metric, we estimate the numerical values of the coefficients and observables for strong gravitational lensing. In comparison to the Reissner-Norström black hole, we find that the influences of the spacetime noncommutative parameter is similar to those of the charge, but these influences are much smaller. This may offer a way to distinguish a noncommutative black hole from a Reissner-Norström black hole, and may permit us to probe the spacetime noncommutative constant $\vartheta$ by the astronomical instruments in the future.

We investigate existence, uniqueness, and the asymptotic properties of constant mean curvature (CMC) slicings in vacuum Kantowski-Sachs spacetimes with positive cosmological constant. Since these spacetimes violate the strong energy condition, most of the general theorems on CMC slicings do not apply. Although there are in fact Kantowski-Sachs spacetimes with a unique CMC foliation or CMC time function, we prove that there also exist Kantowski-Sachs spacetimes with an arbitrary number of (families of) CMC slicings. The properties of these slicings are analyzed in some detail.

Plausibly spacetime is foamy on small distance scales, due to quantum fluctuations. We elaborate on the proposal to detect spacetime foam by looking for seeing disks in the images of distant quasars and active galactic nuclei. This is a null test in the sense that the continued presence of unresolved point sources at the milliarcsecond level in samples of distant compact sources puts severe constraints on theories of quantized spacetime foam at the Planckian level. We discuss the geometry of foamy spacetime, and the appropriate distance measure for calculating the expected angular broadening. We then deal with recent data and the constraints they put on spacetime foam models. While time lags from distant pulsed sources such as gamma ray bursts have been posited as a possible test of spacetime foam models, we demonstrate that the time-lag effect is rather smaller than has been calculated, due to the equal probability of positive and negative fluctuations in the speed of light inherent in such models. Thus far, images of high-redshift quasars from the Hubble ultra-deep field provide the most stringent test of spacetime foam theories. While random-walk models ($\alpha =1/2$) have already been ruled out, the holographic ($\alpha =2/3$) model remains viable. Here $\alpha \sim 1$ parametrizes the different spacetime foam models according to which the fluctuation of a distance $l$ is given by $\sim l^{1-\alpha }{l}_P^{\alpha }$ with $l_P$ being the Planck length. Indeed, we see a slight wavelength-dependent blurring in the ultra-deep field images selected for this study. Using existing data in the Hubble Space Telescope (HST) archive we find it is impossible to rule out the $\alpha =2/3$ model, but exclude all models with $\alpha <0.65$. By comparison, current gamma ray burst time-lag observations only exclude models with $\alpha <0.3$.

We introduce a method for conducting a targeted, coherent search for compact binary coalescences. The search is tailored to be used as a follow-up to electromagnetic transients such as gamma-ray bursts. We derive the coherent search statistic for Gaussian detector noise and discuss the benefits of a coherent, multidetector search over coincidence methods. To mitigate the effects of nonstationary data, we introduce a number of signal consistency tests, including the null signal-to-noise ratio, amplitude consistency, and several ${\chi }^2$ tests. We demonstrate the search performance on Gaussian noise and on data from LIGO’s fourth science run and verify that the signal consistency tests are capable of removing the majority of noise transients, giving the search an efficiency comparable to that achieved in Gaussian noise.