We obtain spin-dependent singlet, nonsinglet, and gluon structure functions by solving Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations in leading order and next-to-leading order at low $x$. The Taylor series expansion method is used to solve the evolution equations. We also calculated $t$ evolution of longitudinally polarized proton and neutron structure functions $g_1^p$ and $g_1^n$, respectively, and the results are compared with SLAC E143 data.

I show that the Wilson loop operator for the $SU(N)$ Yang-Mills gauge connection is exactly rewritten in terms of conserved gauge-invariant magnetic and electric currents through a non-Abelian Stokes theorem of the Diakonov-Petrov type. Here the magnetic current originates from the magnetic monopole derived in the gauge-invariant way from the pure Yang-Mills theory even in the absence of the Higgs scalar field, in sharp contrast to the ’t Hooft–Polyakov magnetic monopole in the Georgi-Glashow gauge-Higgs model. The resulting representation indicates that the Wilson loop operator in fundamental representations can be a probe for a single magnetic monopole irrespective of $N$ in $SU(N)$ Yang-Mills theory, against the conventional wisdom. Moreover, I show that the quantization condition for the magnetic charge follows from the fact that the non-Abelian Stokes theorem does not depend on the surface chosen for writing the surface integral. The obtained geometrical and topological representations of the Wilson loop operator have important implications to understanding quark confinement according to the dual superconductor picture.

Within the framework of the covariant formulation of light-front dynamics, we develop a general nonperturbative renormalization scheme based on the Fock decomposition of the state vector and its truncation. The counterterms and bare parameters needed to renormalize the theory depend on the Fock sectors. We present a general strategy in order to calculate these quantities, as well as state vectors of physical systems, in a truncated Fock space. The explicit dependence of our formalism on the orientation of the light-front plane is essential in order to analyze the structure of the counterterms. We apply our formalism to the two-body (one fermion and one boson) truncation in the Yukawa model and in QED, and to the three-body truncation in a scalar model. In QED, we recover analytically, without any perturbative expansion, the renormalization of the electric charge, according to the requirements of the Ward identity.

The energy conditions play an important role in the understanding of several properties of the Universe, including the current accelerating expansion phase and the possible existence of the so-called phantom fields. We show that the integrated bounds provided by the energy conditions on cosmological observables such as the distance modulus $\mu (z)$ and the lookback time $t_L(z)$ are not sufficient (or necessary) to ensure the local fulfillment of the energy conditions, making explicit the limitation of these bounds in the confrontation with observational data. We recast the energy conditions as bounds on the deceleration and normalized Hubble parameters, obtaining new bounds which are necessary and sufficient for the local fulfillment of the energy conditions. A statistical confrontation, with $1\sigma -3\sigma$ confidence levels, between our bounds and supernovae data from the gold and combined samples is made for the recent past. Our analyses indicate, with $3\sigma$ confidence levels, the fulfillment of both the weak energy condition ($\mathbf{W}\mathbf{E}\mathbf{C}$) and dominant energy condition ($\mathbf{D}\mathbf{E}\mathbf{C}$) for $z\le 1$ and $z\lesssim 0.8$, respectively. In addition, they suggest a possible recent violation of the null energy condition ($\mathbf{N}\mathbf{E}\mathbf{C}$) with $3\sigma$, i.e. a very recent phase of superacceleration. Our analyses also show the possibility of violation of the strong energy condition ($\mathbf{S}\mathbf{E}\mathbf{C}$) with $3\sigma$ in the recent past ($z\le 1$), but interestingly the $q(z)$-best-fit curve crosses the $\mathbf{S}\mathbf{E}\mathbf{C}$—fulfillment divider at $z\simeq 0.67$, which is a value very close to the beginning of the epoch of cosmic acceleration predicted by the standard concordance flat $\Lambda \mathrm{CDM}$ scenario.

In the left-right twin Higgs model, one of the neutral Higgses is a natural candidate for WIMP dark matter. We analyzed the dark matter relic density in this framework and identified regions of parameter space that provide the right amount of dark matter. We also studied the dark matter in the more general inert Higgs doublet model in which the mass splittings between the dark matter and other particles do not follow the relations in the left-right twin Higgs model.

We compute an effective action for a composite Higgs boson formed by new fermions belonging to a general technicolor non-Abelian gauge theory, using a quite general expression for the fermionic self-energy that depends on a certain parameter ($\alpha$), that defines the technicolor theory from the extreme walking behavior up to the one with a standard operator product expansion behavior. We discuss the values of the trilinear and quadrilinear scalar couplings. Our calculation spans all the possible physical possibilities for mass and couplings of the composite system. In the case of extreme walking technicolor theories we verify that it is possible to have a composite Higgs boson with a mass as light as the present experimental limit, contrary to the usual expectation of a heavy mass for the composite Higgs boson. In this case we obtain an upper limit for the Higgs boson mass, ($M_H\le \mathcal{O}(700)\mathrm{GeV}$ for $SU(2{)}_{\mathrm{TC}}$), and the experimental data on the Higgs boson mass constrain $SU(N{)}_{\mathrm{TC}}$ technicolor gauge groups to be smaller than $SU(10{)}_{\mathrm{TC}}$.

We derive correlated bounds on ratios of deep inelastic structure functions from the dipole picture of photon-hadron scattering at high energies. In particular we consider ratios of the longitudinal structure function, the total structure function, and the charm part of the latter. We also consider ratios of total structure functions taken at the same energy but at three different photon virtualities. It is shown that by confronting these bounds with experimental data we can significantly constrain the range of validity of the dipole picture.

We generalize the description of the $d=4$ attractor mechanism based on an effective black hole potential to the presence of a gauging which does not modify the derivatives of the scalars and does not involve hypermultiplets. The obtained results do not rely necessarily on supersymmetry, and they can be extended to $d>4$, as well. Thence, we work out the example of the $stu$ model of $N=2$ supergravity in the presence of Fayet-Iliopoulos terms, for the supergravity analogues of the magnetic and $D0\mathrm{\text{−}}D6$ black hole charge configurations, and in three different symplectic frames: the $(SO(1,1){)}^2$, $SO(2,2)$ covariant and $SO(8)$-truncated ones. The attractive nature of the critical points, related to the semipositive definiteness of the Hessian matrix, is also studied.

We consider the vacuum energy of the electromagnetic field interacting with a spherical plasma shell together with a model for the classical motion of the shell. We calculate the heat kernel coefficients, especially that for the TM mode, and carry out the renormalization by redefining the parameters of the classical model. It turns out that this is possible and results in a model which, in the limit of the plasma shell becoming an ideal conductor, reproduces the vacuum energy found by Boyer in 1968.

Aspects of super-Planckian gravitational scattering and black hole formation are investigated, largely via a partial-wave representation. At large and decreasing impact parameters, amplitudes are expected to be governed by single-graviton exchange, and then by eikonalized graviton exchange, for which partial-wave amplitudes are derived. In the near-Schwarzschild regime, perturbation theory fails. However, general features of gravitational scattering associated with black hole formation suggest a particular form for amplitudes, which we express as a black hole ansatz. We explore features of this ansatz, including its locality properties. These amplitudes satisfy neither the Froissart bound nor, apparently, the more fundamental property of polynomial boundedness, through which locality is often encoded in an $S$-matrix framework. Nevertheless, these amplitudes do satisfy a macroscopic form of causality, expressed as a polynomial bound for the forward-scattering amplitude.

In order to deduce Einsteinian gravity from a topological action, we start from the metric-free Pontrjagin invariant in four dimensions. Using the Becchi-Rouet-Stora-Tyutin antifield formalism with a double duality gauge fixing, we obtain a consistent quantization in spaces of double dual curvature. They correspond to classical instanton type solutions of a curvature-squared model of gravity, in the affine form proposed already by Weyl and Yang. However, the exact vacuum solutions with double duality properties exhibit a “vacuum degeneracy.” By modifying the duality of the curvature via scale breaking terms, we demonstrate that only Einstein’s equations with an induced cosmological constant of partially topological origin emerge for the macroscopic “background.”

The squashed Kaluza-Klien (KK) black holes differ from the Schwarzschild black holes with asymptotic flatness or the black strings even at energies for which the KK modes are not excited yet, so that squashed KK black holes open a window in higher dimensions. Another important feature is that the squashed KK black holes are apparently stable and, thereby, let us avoid the Gregory-Laflamme instability. In the present paper, the evolution of scalar and gravitational perturbations in time and frequency domains is considered for these squashed KK black holes. The scalar field perturbations are analyzed for general rotating squashed KK black holes. Gravitational perturbations for the so-called zero mode are shown to be decayed for nonrotating black holes, in concordance with the stability of the squashed KK black holes. The correlation of quasinormal frequencies with the size of extra dimension is discussed.

What happened to the central cores of tidally destructed dark matter clumps in the Galactic halo? We calculate the probability of surviving of the remnants of dark matter clumps in the Galaxy by modelling the tidal destruction of the small-scale clumps. It is demonstrated that a substantial fraction of clump remnants may survive through the tidal destruction during the lifetime of the Galaxy if the radius of a core is rather small. The resulting mass spectrum of surviving clumps is extended down to the mass of the core of the cosmologically produced clumps with a minimal mass. Since the annihilation signal is dominated by the dense part of the core, destruction of the outer part of the clump affects the annihilation rate relatively weakly and the survived dense remnants of tidally destructed clumps provide a large contribution to the annihilation signal in the Galaxy. The uncertainties in the minimal clump mass resulting from the uncertainties in neutralino models are discussed.

We compute the fourth order action in perturbation theory for scalar and second order tensor perturbations for a minimally coupled single field inflationary model, where the inflaton’s Lagrangian is a general function of the field’s value and its kinetic energy. We obtain the fourth order interaction Hamiltonian in two gauges, the comoving gauge and the uniform curvature gauge. Using the comoving gauge action we calculate the trispectrum at leading order in slow roll, finding agreement with a previously known result in the literature. We point out that, in general, to obtain the correct leading order trispectrum one cannot ignore second order tensor perturbations as previously done by others. The next-to-leading order corrections may become detectable depending on the shape, and we provide the necessary formalism to calculate them.

It is well known that finding and measuring the masses of particles in the minimal supersymmetric standard model (MSSM) at the Large Hadron Collider (LHC) may be possible using invariant mass distributions in exclusive channels containing $n_j$ jets and $n_l$ leptons. We perform this analysis for the $(n_j,n_l)=(0,4)$ decay of heavy Higgs bosons to neutralinos, $pp\to H/A\to {\tilde{\chi }}_i^0{\tilde{\chi }}_j^0$ ($i$, $j=2$, 3, 4), which then decay to four leptons and two lightest neutralinos ${\tilde{\chi }}_1^0$ via on-shell sleptons. When $i=j$ and the sleptons are degenerate, our Monte Carlo study shows that the LHC will be able to measure the Higgs and relevant neutralino and slepton masses to roughly 30%; however, if one of these is already known within 5%, the other three may be found to equal or better accuracy. This would provide the first accurate measurement of the $H/A$ mass via invariant mass distribution techniques.

We present a specific class of models for an infrared-finite analytic QCD coupling, such that at large spacelike energy scales the coupling differs from the perturbative one by less than any inverse power of the energy scale. This condition is motivated by the Institute for Theoretical and Experimental Physics operator product expansion philosophy. Allowed by the ambiguity in the analytization of the perturbative coupling, the proposed class of couplings has three parameters. In the intermediate energy region, the proposed coupling has low loop-level and renormalization scheme dependence. The present modification of perturbative QCD must be considered as a phenomenological attempt, with the aim of enlarging the applicability range of the theory of the strong interactions at low energies.

Lepton-flavor-violating $\tau$ decays are predicted in many extensions of the standard model at a rate observable at future collider experiments. In this article we focus on the decay $\tau \to \mu \mu \overline{\mu }$, which is a promising channel to observe lepton-flavor violation at the CERN Large Hadron Collider (LHC). We present analytic expressions for the differential decay width derived from a model-independent effective Lagrangian with general four-fermion operators, and estimate the experimental acceptance for detecting the decay $\tau \to \mu \mu \overline{\mu }$ at the LHC. Specific emphasis is given to decay angular distributions and how they can be used to discriminate new physics models. We provide specific predictions for various extensions of the standard model, including supersymmetric, little Higgs, and technicolor models.

We present a measurement of the correlated $b\overline{b}$ production cross section. The data used in this analysis were taken with the upgraded CDF detector (CDF II) at the Fermilab Tevatron collider, and correspond to an integrated luminosity of $742{\mathrm{pb}}^{-1}$. We utilize muon pairs with invariant mass $5\le m_{\mu \mu }\le 80\mathrm{GeV}/c^2$ produced by $b\overline{b}$ double semileptonic decays. For muons with $p_T\ge 3\mathrm{GeV}/c$ and $|\eta |\le 0.7$, that are produced by $b$ and $\overline{b}$ quarks with $p_T\ge 2\mathrm{GeV}/c$ and $|y|\le 1.3$, we measure ${\sigma }_{b\to \mu ,\overline{b}\to \mu }=1549\pm 133\mathrm{pb}$. We compare this result with theoretical predictions and previous measurements. We also report the measurement of ${\sigma }_{c\to \mu ,\overline{c}\to \mu }$, a by-product of the study of the background to $b\overline{b}$ production.

A weak quantum mechanical coupling is constructed permitting superluminal communication within a preferred region of a gravitating ${\mathrm{AdS}}_5$ spacetime. This is achieved by adding a spatially nonlocal perturbation of a special kind to the Hamiltonian of a four-dimensional conformal field theory with a weakly coupled ${\mathrm{AdS}}_5$ dual, such as maximally supersymmetric Yang-Mills theory. In particular, two issues are given careful treatment: (1) the UV-completeness of our deformed conformal field theory (CFT), guaranteeing the existence of a “deformed string theory” AdS dual and (2) the demonstration that superluminal effects can take place in AdS, both on its boundary as well as in the bulk. Exotic Lorentz-violating properties such as these may have implications for tests of general relativity, addressing the cosmological constant problem, or probing behind horizons. Our construction may give insight into the interpretation of wormhole solutions in Euclidean AdS gravity.