The ghost and gluon propagator and the ghost-gluon and three-gluon vertex of two-dimensional SU(2) Yang-Mills theory in (minimal) Landau gauge are studied using lattice gauge theory. It is found that the results are qualitatively similar to the ones in three and four dimensions. The propagators and the Faddeev-Popov operator behave as expected from the Gribov-Zwanziger scenario. In addition, finite-volume effects affecting these Green’s functions are investigated systematically. The critical infrared exponents of the propagators, as proposed in calculations using stochastic quantization and Dyson-Schwinger equations, are confirmed quantitatively. For this purpose lattices of volume up to $(42.7\mathrm{fm}{)}^2$ have been used.

In terms of mass generation in the strong interaction without chiral symmetry breaking, we perform the first study for light scalar-quarks $\varphi$ (colored scalar particles with ${\mathbf{3}}_c$ or idealized diquarks) and their color-singlet hadronic states using quenched $\mathrm{SU}(3{)}_c$ lattice QCD with $\beta =5.70$ (i.e., $a\simeq 0.18\mathrm{fm}$) and lattice size ${16}^3\times 32$. We investigate “scalar-quark mesons” ${\varphi }^{†}\varphi$ and “scalar-quark baryons” $\varphi \varphi \varphi$ as the bound states of scalar-quarks $\varphi$. We also investigate the color-singlet bound states of scalar-quarks $\varphi$ and quarks $\psi$, i.e., ${\varphi }^{†}\psi$, $\psi \psi \varphi$, and $\varphi \varphi \psi$, which we name “chimera hadrons.” All the new-type hadrons including $\varphi$ are found to have a large mass even for zero bare scalar-quark mass $m_{\varphi }=0$ at $a^{-1}\simeq 1\mathrm{GeV}$. We find a “constituent scalar-quark/quark picture” for both scalar-quark hadrons and chimera hadrons. Namely, the mass of the new-type hadron composed of $m$ $\varphi$’s and $n$ $\psi$’s, $M_{m\varphi +n\psi }$, approximately satisfies $M_{m\varphi +n\psi }\simeq m{M}_{\varphi }+n{M}_{\psi }$, where $M_{\varphi }$ and $M_{\psi }$ are the constituent scalar-quark and quark masses, respectively. We estimate the constituent scalar-quark mass $M_{\varphi }$ for $m_{\varphi }=0$ at $a^{-1}\simeq 1\mathrm{GeV}$ as $M_{\varphi }\simeq 1.5–1.6\mathrm{GeV}$, which is much larger than the constituent quark mass $M_{\psi }\simeq 400\mathrm{MeV}$ in the chiral limit. Thus, scalar quarks acquire a large mass due to large quantum corrections by gluons in the systems including scalar quarks. Together with other evidences of mass generation of glueballs and charmonia, we conjecture that all colored particles generally acquire a large effective mass due to dressed gluon effects. In addition, the large mass generation of pointlike colored scalar particles indicates that plausible diquarks used in effective hadron models cannot be described as the pointlike particles and should have a much larger size than $a\simeq 0.2\mathrm{fm}$.

We present new sets of pion and kaon fragmentation functions obtained in next-to-leading order combined analyses of single-inclusive hadron production in electron-positron annihilation, proton-proton collisions, and deep-inelastic lepton-proton scattering with either pions or kaons identified in the final state. At variance with all previous fits, the present analyses take into account data where hadrons of different electrical charge are identified, which allow one to discriminate quark from antiquark fragmentation functions without the need of nontrivial flavor symmetry assumptions. The resulting sets are in good agreement with all data analyzed, which cover a much wider kinematical range than in previous fits. An extensive use of the Lagrange multiplier technique is made in order to assess the uncertainties in the extraction of the fragmentation functions and the synergy from the complementary data sets in our global analysis.

We investigate the unpolarized virtual photon structure functions $F_2^{\gamma }(x,Q^2,P^2)$ and $F_L^{\gamma }(x,Q^2,P^2)$ in perturbative QCD for the kinematical region ${\Lambda }^2\ll P^2\ll Q^2$, where $-Q^2$ ($-P^2$) is the mass squared of the probe (target) photon and $\Lambda$ is the QCD scale parameter. Using the framework of the operator product expansion supplemented by the renormalization group method, we derive the definite predictions for the moments of $F_2^{\gamma }(x,Q^2,P^2)$ up to the next-to-next-to-leading order (NNLO) (the order $\alpha {\alpha }_s$) and for the moments of $F_L^{\gamma }(x,Q^2,P^2)$ up to the next-to-leading order (NLO) (the order $\alpha {\alpha }_s$). The NNLO corrections to the sum rule of $F_2^{\gamma }(x,Q^2,P^2)$ are negative and found to be 7%–10% of the sum of the LO and NLO contributions, when $P^2=1{\mathrm{GeV}}^2$ and $Q^2=30\sim 100{\mathrm{GeV}}^2$ or $P^2=3{\mathrm{GeV}}^2$ and $Q^2=100{\mathrm{GeV}}^2$, and the number of active quark flavors $n_f$ is three or four. The NLO corrections to $F_L^{\gamma }$ are also negative. The moments are inverted numerically to obtain the predictions for $F_2^{\gamma }(x,Q^2,P^2)$ and $F_L^{\gamma }(x,Q^2,P^2)$ as functions of $x$.

We analyze soliton solutions in the two-family Calogero model. There are two types of solutions, a one-soliton–antisoliton solution and a wave solution. It is shown that there is no finite number of solitons at finite distances in the limit when the period of wave solutions tends to infinity.

A scenario in which inflation, dark energy, and dark matter can be unified into a single scalar field, the inflaton field $\varphi$, is studied. The inflaton is identified with the sneutrino, the scalar partner of the neutrino. I determine the conditions needed for avoiding the gravitino problem and not having negligible plasma effects, and I obtain the allowed range for the sneutrino coupling.

We investigate the dynamics and gravitational-wave (GW) emission in the binary merger of equal-mass black holes as obtained from numerical relativity simulations. The simulations were performed with an evolution code based on generalized harmonic coordinates developed by Pretorius, and used quasiequilibrium initial-data sets constructed by Cook and Pfeiffer. Results from the evolution of three sets of initial data are explored in detail, corresponding to different initial separations of the black holes, and exhibit between 2–8 GW cycles before coalescence. We find that to a good approximation the inspiral phase of the evolution is quasicircular, followed by a “blurred, quasicircular plunge” lasting for about 1–1.5 GW cycles. After this plunge the GW frequency decouples from the orbital frequency, and we define this time to be the start of the merger phase. Roughly 10–15 M separates the time between the beginning of the merger phase and when we are able to extract quasinormal ring-down modes from gravitational waves emitted by the newly formed black hole. This suggests that the merger lasts for a correspondingly short amount of time, approximately 0.5–0.75 of a full GW cycle. We present first-order comparisons between analytical models of the various stages of the merger and the numerical results—more detailed and accurate comparisons will need to await numerical simulations with higher accuracy, better control of systemic errors (including coordinate artifacts), and initial configurations where the binaries are further separated. During the inspiral, we find that if the orbital phase is well modeled, the leading order Newtonian quadrupole formula is able to match both the amplitude and phase of the numerical GW quite accurately until close to the point of merger. We provide comparisons between the numerical results and analytical predictions based on the adiabatic post-Newtonian (PN) and nonadiabatic resummed-PN models (effective-one-body and Padé models). For all models considered, 3PN and 3.5PN orders match the inspiral numerical data the best. From the ring-down portion of the GW, we extract the fundamental quasinormal mode and several of the overtones. Finally, we estimate the optimal signal-to-noise ratio (SNR) for typical binaries detectable by GW experiments. We find that, when the merger and ring-down phases are included, binaries with total mass larger than $40M_{\odot }$ (sources for ground-based detectors) are brought in band and can be detected with signal-to-noise up to $\approx 15$ at 100 Mpc, whereas for binaries with total mass larger than $2\times {10}^6{M}_{\odot }$ (sources for space-based detectors) the SNR can be $\approx {10}^4$ at 1 Gpc.

The ringdown phase following a binary black hole merger is usually assumed to be well described by a linear superposition of complex exponentials (quasinormal modes). In the strong-field conditions typical of a binary black hole merger, nonlinear effects may produce mode coupling. Artificial mode coupling can also be induced by the black hole’s rotation, if the radiation field is expanded in terms of spin-weighted spherical harmonics (rather than spin-weighted spheroidal harmonics). Observing deviations from the predictions of linear black hole perturbation theory requires optimal fitting techniques to extract ringdown parameters from numerical waveforms, which are inevitably affected by numerical error. So far, nonlinear least-squares fitting methods have been used as the standard workhorse to extract frequencies from ringdown waveforms. These methods are known not to be optimal for estimating parameters of complex exponentials. Furthermore, different fitting methods have different performance in the presence of noise. The main purpose of this paper is to introduce the gravitational wave community to modern variations of a linear parameter estimation technique first devised in 1795 by Prony: the Kumaresan-Tufts and matrix pencil methods. Using “test” damped sinusoidal signals in Gaussian white noise we illustrate the advantages of these methods, showing that they have variance and bias at least comparable to standard nonlinear least-squares techniques. Then we compare the performance of different methods on unequal-mass binary black hole merger waveforms. The methods we discuss should be useful both theoretically (to monitor errors and search for nonlinearities in numerical relativity simulations) and experimentally (for parameter estimation from ringdown signals after a gravitational wave detection).

In most theories of gravity involving torsion, the source for torsion is the intrinsic spin of matter. Since the spins of fermions are normally randomly oriented in macroscopic bodies, the amount of torsion generated by macroscopic bodies is normally negligible. However, in a recent paper, Mao et al. (arXiv:gr-qc/0608121) point out that there is a class of theories, including the Hayashi-Shirafuji (1979) theory, in which the angular momentum of macroscopic spinning bodies generates a significant amount of torsion. They further argue that, by the principle of action equals reaction, one would expect the angular momentum of test bodies to couple to a background torsion field, and therefore the precession of the Gravity Probe B gyroscopes should be affected in these theories by the torsion generated by the Earth. We show that in fact the principle of action equals reaction does not apply to these theories, essentially because the torsion is not an independent dynamical degree of freedom. We examine in detail a generalization of the Hayashi-Shirafuji theory suggested by Mao et al. called Einstein-Hayashi-Shirafuji theory. There are a variety of different versions of this theory, depending on the precise form of the coupling to matter chosen for the torsion. We show that, for any coupling to matter that is compatible with the spin transport equation postulated by Mao et al., the theory has either ghosts or an ill-posed initial-value formulation. These theoretical problems can be avoided by specializing the parameters of the theory and in addition choosing the standard minimal coupling to matter of the torsion tensor. This yields a consistent theory, but one in which the action equals reaction principle is violated, and in which the angular momentum of the gyroscopes does not couple to the Earth’s torsion field. Thus, the Einstein-Hayashi-Shirafuji theory does not predict a detectable torsion signal for Gravity Probe B. There may be other torsion theories which do.

The continuous infall of dark matter with low velocity dispersion from all directions in a galactic halo leads to the formation of caustics which are very small scale ($\sim \mathrm{parsec}$) high density structures. If the dark matter is made up of supersymmetric neutralinos, the annihilation of these particles produces a characteristic spectrum of gamma rays which, in principle, could be detected. The annihilation signal at different energy bands is computed and compared with the expected gamma ray background.

We report on a large-scale numerical study of networks of semilocal cosmic strings in flat space in the parameter regime in which they are perturbatively stable. We find a population of segments with an exponential length distribution and indications of a scaling network without significant loop formation. Very deep in the stability regime strings of superhorizon size grow rapidly and “percolate” through the box. We believe these should lead at late times to a population of infinite strings similar to topologically stable strings. However, the strings are very light; scalar gradients dominate the energy density, and the network has thus a global texturelike signature. As a result, the observational constraints, at least from the temperature power spectrum of the cosmic microwave background, on models predicting semilocal strings should be closer to those on global textures or monopoles, rather than on topologically stable gauged cosmic strings.

In minimal supergravity, the parameter space where the slepton is the lightest superpartner is usually neglected, because of strong constraints on charged dark matter. When the gravitino is the true lightest superpartner, this region avoids these constraints and offers spectacular collider signals. We investigate this scenario for the Large Hadron Collider and find that a large portion of the ignored minimal supergravity parameter space can lead to discovery within the first physics run, with $1–4{\mathrm{fb}}^{-1}$ of data. We find that there are regions where discovery is feasible with only 1 d of running.

We examine the possibility of measuring the three gauge couplings at high scales at the Large Hadron Collider (LHC), in order to see the first steps as they run toward grand unification at much higher energies. Using the minimal supersymmetric standard model (MSSM) with sparticle masses of several hundred GeV as an example of a theory in which the couplings do unify at very high energies, we find that the processes $pp\to {\ell }^{+}\nu$, $pp\to {\ell }^{+}{\ell }^{-}$, and $pp\to \gamma j$ can be useful to discriminate the SM from the MSSM with masses at the few hundred GeV scale and determine that the couplings are converging at better than the SM prediction toward the GUT scale. Such measurements indirectly probe the existence of lower mass states, charged under the SM gauge groups, but which may be difficult to produce directly or extract from backgrounds at the LHC.

We present a lattice calculation of the hadronic vacuum polarization and the lowest order hadronic contribution (HLO) to the muon anomalous magnetic moment, $a_{\mu }=(g-2)/2$, using $2+1$ flavors of improved staggered fermions. A precise fit to the low-$q^2$ region of the vacuum polarization is necessary to accurately extract the muon $g-2$. To obtain this fit, we use staggered chiral perturbation theory, including a model to incorporate the vector particles as resonances, and compare these to polynomial fits to the lattice data. We discuss the fit results and associated systematic uncertainties, paying particular attention to the relative contributions of the pions and vector mesons. Using a single lattice spacing ensemble generated by the MILC Collaboration ($a=0.086\mathrm{fm}$), light quark masses as small as roughly one-tenth the strange quark mass, and volumes as large as $(3.4\mathrm{fm}{)}^3$, we find $a_{\mu }^{\mathrm{HLO}}=(713\pm 15)\times {10}^{-10}$ and $(748\pm 21)\times {10}^{-10}$ where the error is statistical only and the two values correspond to linear and quadratic extrapolations in the light quark mass, respectively. Considering various systematic uncertainties not eliminated in this study (including a model of vector resonances used to fit the lattice data and the omission of disconnected quark contractions in the vector-vector correlation function), we view this as agreement with the current best calculations using the experimental cross section for $e^{+}{e}^{-}$ annihilation to hadrons, $(692.4\pm 5.9\pm 2.4)\times {10}^{-10}$, and including the experimental decay rate of the tau lepton to hadrons, $(711.0\pm 5.0\pm 0.8\pm 2.8)\times {10}^{-10}$. We discuss several ways to improve the current lattice calculation.

The physical process version and equilibrium state version of the first law of thermodynamics for a black object consisting of $n$-dimensional charged stationary axisymmetric black hole surrounded by $a$ black rings, the so-called black Saturn, was derived. The general setting for our derivations is $n$-dimensional dilaton gravity with $p+1$ strength form fields.

It has been proposed that cosmic acceleration or inflation can be driven by replacing the Einstein-Hilbert action of general relativity with a function $f(R)$ of the Ricci scalar $R$. Such $f(R)$ gravity theories have been shown to be equivalent to scalar-tensor theories of gravity that are incompatible with Solar System tests of general relativity, as long as the scalar field propagates over Solar System scales. Specifically, the parameterized post-Newtonian (PPN) parameter in the equivalent scalar-tensor theory is $\gamma =1/2$, which is far outside the range allowed by observations. In response to a flurry of papers that questioned the equivalence of $f(R)$ theory to scalar-tensor theories, it was recently shown explicitly, without resorting to the scalar-tensor equivalence, that the vacuum field equations for $1/R$ gravity around a spherically symmetric mass also yield $\gamma =1/2$. Here we generalize this analysis to $f(R)$ gravity and enumerate the conditions that, when satisfied by the function $f(R)$, lead to the prediction that $\gamma =1/2$.

We show that domain walls are probes that enable one to distinguish large-distance modified gravity from general relativity (GR) at short distances. For example, low-tension domain walls are stealth in modified gravity, while they do produce global gravitational effects in GR. We demonstrate this by finding exact solutions for various domain walls in the DGP model. A wall with tension lower than the fundamental Planck scale does not inflate and has no gravitational effects on a 4D observer, since its 4D tension is completely screened by gravity itself. We argue that this feature remains valid in a generic class of models of infrared modified gravity. As a byproduct, we obtain exact solutions for supermassive codimension-2 branes.

We investigate the effect of the bulk content in the general Gauss-Bonnet braneworld on the evolution of the Universe. We find that the Gauss-Bonnet term and the combination of the dark radiation and the matter content of the bulk play a crucial role in the Universe’s evolution. We show that our model can describe the superacceleration of our Universe with the equation of state of the effective dark energy in agreement with observations.

We study the asymptotic behavior of spherically symmetric solutions in the Skyrme model. We show that the relaxation to the degree-one soliton (called the Skyrmion) has a universal form of a superposition of two effects: exponentially damped oscillations (the quasinormal ringing) and a power-law decay (the tail). The quasinormal ringing, which dominates the dynamics for intermediate times, is a linear resonance effect. In contrast, the polynomial tail, which becomes uncovered at late times, is shown to be a nonlinear phenomenon.