The implementation of gauge theories on a four-dimensional anisotropic lattice with two distinct lattice spacings is discussed, with special attention to the case where two axes are finely and two axes are coarsely discretized. Feynman rules for the Wilson gauge action are derived and the renormalizability of the theory and the recovery of the continuum limit are analyzed. The calculation of the gluon propagator and the restoration of Lorentz invariance in on-shell states is presented to one-loop order in lattice perturbation theory for ${SU(N}_c)$ on both 2+2 and 3+1 lattices.

We study the influence of unitarity corrections on the Drell-Yan transverse momentum distribution within the color dipole approach. These unitarity corrections are implemented through the multiple scattering Glauber-Mueller approach, which is contrasted with a phenomenological saturation model. The process is analyzed for the center of mass energies of the BNL Relativistic Heavy Ion Collider (RHIC, $\sqrt{s}=500\mathrm{}\mathrm{GeV})$ and of the CERN Large Hadron Collider (LHC, $\sqrt{s}=14\mathrm{}\mathrm{TeV}).\mathrm{}$ In addition, the results are extrapolated down to current energies of proton-proton collisions, where nonasymptotic corrections to the dipole approach are needed. It is also shown that, in the absence of saturation, the dipole approach can be related to the QCD Compton process.

We examine the assumptions underlying the (model-dependent) predictions of $q^2{q}^2$ or tetraquark spectra. The models implemented so far have used only two-body interactions proportional to the color charges; that assumption is the source of many serious shortcomings. We extend the analysis to three- and four-body interactions based on color SU(3) algebra, while including all relevant information one has about three-quark forces from lattice QCD. Thus we find that (quasi)stable tetraquarks are not necessarily a consequence of color SU(3) dynamics, let alone of QCD. We make this statement and the conditions under which it holds more precise in the text. In the process we are led to a set of sufficient conditions for a mathematical description of the hadronic world as we know it, i.e., of baryons and $q\overline{q}$ mesons, without going into the question of tetraquark existence. These conditions are as follows. (1) Stability: All the (colorless and colored) states’ energies must be bounded from below. (2) Confinement: A color singlet $q\overline{q}$ potential energy must (infinitely) rise with the separation distance. (3) Color ordering: Colored states must be heavier than color-neutral ones. (4) Clustering: Any multiquark color-singlet state Hamiltonian must turn into a sum of three-quark (baryons) and quark-antiquark (mesons) cluster Hamiltonians, in the limit of asymptotically large separations. We discuss the consistency of these four requirements with color SU(3) symmetry and with each other.

In this work the charm and bottom quark masses are determined from QCD moment sum rules for the charmonium and upsilon systems. To illustrate the special character of these sum rules when applied to Coulomb systems, we first set up and study the behavior of the sum rules in quantum mechanics. In our analysis, we include both the results from nonrelativistic QCD and perturbation theory at next-next-to-leading order. The moments are evaluated at different values of $q^2$ which correspond to different relative influences among the theoretical contributions. In the numerical analysis, we obtain the masses by choosing central values for all input parameters. The error is estimated from a variation of these parameters. First, the analysis is performed in the pole mass scheme. Second, we employ the potential-subtracted mass in intermediate steps of the calculation to then infer the quark masses in the $\overline{\mathrm{MS}}$ scheme. Our final results for the pole and $\overline{\mathrm{MS}}$ masses are $M_c=1.75\mathrm{}\pm 0.15\mathrm{GeV},m_c{(m}_c)=1.19\mathrm{}\pm 0.11\mathrm{GeV},M_b=4.98\mathrm{}\pm 0.125\mathrm{GeV},$ and $m_b{(m}_b)=4.24\mathrm{}\pm 0.10\mathrm{GeV}.$

In this work we probe the Einstein-Born-Infeld (EBI) black hole in the isolated horizon framework. It turns out that the EBI black hole is consistent with the heuristic model for colored black holes proposed by Ashtekar et al. [Class. Quantum Grav. 18, 919 (2001)] when one considers the Born-Infeld (BI) parameter playing the role of the color parameter. This remarkable coincidence points to a wide range of validity of the Ashtekar model proved, in this case, for black holes that go from Schwarzschild to Reissner-Nordström black holes, passing through a continuous set of nonlinear electromagnetic black holes with fixed mass and charge but with distinct BI parameter.

We calculate the tree-level expressions for the electroweak precision observables in the $\mathrm{SU}\left(5\right)/SO\left(5\right)\mathrm{}$ littlest Higgs model. The source for these corrections are the exchange of heavy gauge bosons and a triplet Higgs vacuum expectation value (VEV). Weak isospin violating contributions are present because there is no custodial $\mathrm{SU}\left(2\right)\mathrm{}$ global symmetry. The bulk of these weak isospin violating corrections arise from heavy gauge boson exchange while a smaller contribution comes from the triplet Higgs VEV. A global fit is performed to the experimental data and we find that throughout the parameter space the symmetry breaking scale is bounded by $f>\mathrm{}4\mathrm{}\mathrm{TeV}$ at 95% C.L. Stronger bounds on f are found for generic choices of the high energy gauge couplings. We find that even in the best case scenario one would need fine-tuning of less than a percent to get a Higgs boson mass as light as 200 GeV.

Lattice fermions in five Euclidean dimensions and the corresponding effective theory in four dimensions are defined. The main properties of these theories include the suppression of high momentum modes of the lattice Dirac operator and their ability to continuously interpolate between quenched and dynamical fermions. In particular, the standard formulation of lattice QCD can be viewed as a limiting case of the theory.

We present a next-to-leading order QCD calculation of the cross section for isolated large-$p_T$ prompt photon production in collisions of transversely polarized protons. We devise a simple method of dealing with the phase space integrals in dimensional regularization in the presence of the $\cos \left(2\mathrm{}\Phi \right)$ azimuthal-angular dependence occurring for transverse polarization. Our results allow us to calculate the double-spin asymmetry $A_{\mathrm{TT}}^{\gamma }$ for this process at next-to-leading order accuracy, which may be used at BNL RHIC to measure the transversity parton distributions of the proton.

In this paper we present the calculation of a scalar pentagon integral with two consecutive massive external legs having an equal mass propagator embedded between them. We also deal with the two situations where the farthest external leg is either massive or not. The relevance of the calculation comes from its application in many perturbative QCD calculations as well as in QCD corrections for weak processes.

The first observation of ${\chi }_{\mathrm{cJ}}\mathrm{}(J=0,1,2\mathrm{})\mathrm{}$ decays to $\Lambda \overline{\Lambda }$ is reported using $\psi \mathrm{}\left(2S\right)\mathrm{}$ data collected with the Beijing Spectrometer detector at the Beijing Electron Positron Collider. The branching ratios are determined to be $\mathcal{B}({\chi }_{c0\mathrm{}}\to \Lambda \overline{\Lambda }{)=(4.7\mathrm{}}_{-1.2}^{+1.3\mathrm{}}\pm 1.0)\times {10}^{-4},$ $\mathcal{B}({\chi }_{c1\mathrm{}}\to \Lambda \overline{\Lambda }{)=(2.6\mathrm{}}_{-0.9}^{+1.0\mathrm{}}\pm 0.6)\times {10}^{-4}$ and $\mathcal{B}({\chi }_{c2\mathrm{}}\to \Lambda \overline{\Lambda }{)=(3.3\mathrm{}}_{-1.3}^{+1.5\mathrm{}}\pm 0.7)\times {10}^{-4}.$ The results are compared with model predictions.

High-energy scattering in nonconformal gauge theories is investigated using the AdS/conformal field theory (CFT) dual string-gravity theory. It is argued that strong-gravity processes, such as black hole formation, play an important role in the dual dynamics. Further information about this dynamics is found by performing a linearized analysis of gravity for a mass near an infrared brane; this gives the far field approximation to black hole or other strong-gravity effects, and in particular allows us to estimate their shape. From this shape, one can infer a total scattering cross section that grows with center of mass energy as ${\ln }^{2}E,$ saturating the Froissart bound.

The comparison of symmetries in the interior and the exterior of a domain wall is relevant when discussing the correspondence between domain walls and branes, and also when studying the interaction of walls and magnetic monopoles. I discuss the symmetries in the context of an $\mathrm{SU}\left(N\right)\mathrm{}\times Z_2$ model (for odd N) with a single adjoint scalar field. Situations in which the wall interior has less symmetry than the vacuum are easy to construct while the reverse situation requires significant engineering of the scalar potential.

We consider the CIV-DV prepotential $\mathcal{F}$ for $\mathcal{N}=1\mathrm{}\mathrm{SU}\left(n\right)\mathrm{}$ SYM theory at the extremum of the effective superpotential and prove the relation $2\mathcal{F}-S^i\partial \mathcal{F}/\partial S_i=-u_{2}2{\Lambda }^{2n}{/(n}^2-1).$

The possibility of obtaining singularity free cosmological solutions in four dimensional effective actions motivated by string theory is investigated. In these effective actions, in addition to the Einstein-Hilbert term, the dilatonic and the axionic fields are also considered as well as terms coming from the Ramond-Ramond sector. A radiation fluid is coupled to the field equations, which appears as a consequence of the Maxwellian terms in the Ramond-Ramond sector. Singularity free bouncing solutions in which the dilaton is finite and strictly positive are obtained for models with flat or negative curvature spatial sections when the dilatonic coupling constant is such that $\omega <-3/2,$ which may appear in the so called F theory in 12 dimensions. These bouncing phases are smoothly connected to the radiation dominated expansion phase of the standard cosmological model, and the asymptotic pasts correspond to very large flat spacetimes.

The renormalized Feynman propagator for a scalar field in the background of a cosmic dispiration (a disclination plus a screw dislocation) is derived, opening a window to investigate vacuum polarization effects around a cosmic string with dislocation, as well as in the bulk of an elastic solid carrying a dispiration. The use of the propagator is illustrated by computing vacuum fluctuations. In particular it is shown that the dispiration polarizes the vacuum giving rise to an energy momentum tensor which, as seen from a local inertial frame, presents nonvanishing off-diagonal components. Such a new effect resembles that where an induced vacuum current arises around a needle solenoid carrying a magnetic flux (the Aharonov-Bohm effect), and may have physical consequences. Connections with a closely related background, namely the spacetime of a spinning cosmic string, are briefly addressed.

We propose an effective description of 0-brane black holes, in which the black hole is modeled as a gas of noninteracting quasiparticles in dual quantum mechanics. This simple model is shown to account for many of the static thermodynamic properties of the black hole. It also accounts for dynamical properties, such as the rate at which energy gets thermalized by the black hole. We use the model to show that the entropy of quantum mechanics is proportional to the black hole horizon area in Planck units.

k-essence models, relying on scalar fields with noncanonical kinetic terms, have been proposed as an alternative to quintessence in explaining the observed acceleration of the Universe. We consider the use of field redefinitions to cast k-essence in a more familiar form. While k-essence models cannot in general be rewritten in the form of quintessence models, we show that in certain dynamical regimes an equivalence can be made, which in particular can shed light on the tracking behavior of k-essence. In several cases, k-essence cannot be observationally distinguished from quintessence using the homogeneous evolution, though there may be small effects on the perturbation spectrum. We make a detailed analysis of two k-essence models from the literature and comment on the nature of the fine-tuning arising in the models.

We calculate dark matter scattering rates in the minimal supersymmetric extension of the standard model (MSSM), allowing the soft supersymmetry-breaking masses of the Higgs multiplets, $m_{1,2},$ to be nonuniversal (NUHM). Compared with the constrained MSSM (CMSSM) in which $m_{1,2}$ are required to be equal to the soft supersymmetry-breaking masses $m_0$ of the squark and slepton masses, we find that the elastic scattering cross sections may be up to two orders of magnitude larger than values in the CMSSM for similar lightest supersymmetric particle masses. We find the following preferred ranges for the spin-independent cross section, ${10}^{-6}\mathrm{pb}\gtrsim {\sigma }_{\mathrm{SI}}\gtrsim {10}^{-10}\mathrm{pb},$ and, for the spin-dependent cross section, ${10}^{-3}\mathrm{pb}\gtrsim {\sigma }_{\mathrm{SD}},$ with the lower bound on ${\sigma }_{\mathrm{SI}}$ dependent on using the putative constraint from the muon anomalous magnetic moment. We stress the importance of incorporating accelerator and dark matter constraints in restricting the NUHM parameter space, and also of requiring that no undesirable vacuum appear below the grand unified theory (GUT) scale. In particular, values of the spin-independent cross section another order of magnitude larger would appear to be allowed, for small $\tan \beta ,$ if the GUT vacuum stability requirement were relaxed, and much lower cross-section values would be permitted if the muon anomalous magnetic moment constraint were dropped.

We investigate the late-time behavior of a universe containing a supergravity gas and wrapped 2-branes in the context of M theory compactified on $T^{10}.$ The supergravity gas tends to drive uniform expansion, while the branes impede the expansion of the directions about which they are wrapped. Assuming spatial homogeneity, we study the dynamics both numerically and analytically. At late times the radii obey power laws which are determined by the brane wrapping numbers, leading to interesting hierarchies of scale between the wrapped and unwrapped dimensions. The biggest hierarchy that could evolve from an initial thermal fluctuation produces three large unwrapped dimensions. We also study configurations corresponding to string winding, in which the M2-branes are all wrapped around the (small) 11th dimension, and show that this recovers the scenario discussed by Brandenberger and Vafa.

We systematically discuss the consequences of genuine dimension-six Higgs operators. These operators are not subject to stringent constraints from electroweak precision data. However, they can modify the couplings of the Higgs boson to electroweak gauge bosons and, in particular, the Higgs self-interactions. We study the sensitivity to which those couplings can be probed at future $e^{+}{e}^{-}$ linear colliders in the sub-TeV and in the multi-TeV range. We find that for $\sqrt{s}=500\mathrm{}\mathrm{GeV}$ with a luminosity of $1{\mathrm{ab}}^{-1}$ the anomalous WWH and ZZH couplings may be probed to about the 0.01 level, and the anomalous HHH coupling to about the 0.1 level.