The latest CTEQ6.6 parton distributions, obtained by global analysis of hard-scattering data in the framework of general-mass perturbative QCD, are employed to study theoretical predictions and their uncertainties for significant processes at the Fermilab Tevatron and CERN Large Hadron Collider. The previously observed increase in predicted cross sections for the standard-candle $W$ and $Z$ boson production processes in the general-mass scheme (compared to those in the zero-mass scheme) is further investigated and quantified. A novel method to constrain parton distribution function (PDF) uncertainties in LHC observables, by effectively exploiting PDF-induced correlations with benchmark standard model cross sections, is presented. Using this method, we show that the $t\overline{t}$ cross section can potentially serve as a standard-candle observable for the LHC processes dominated by initial-state gluon scattering. Among other benefits, precise measurements of $t\overline{t}$ cross sections would reduce PDF uncertainties in predictions for single top-quark and Higgs boson production in the standard model and minimal supersymmetric standard model.

We propose a novel neutrino mixing pattern in terms of only two small integers 1 and 2 together with their square roots and the imaginary number $i$. This ansatz is referred to as the “tetra-maximal” mixing because it can be expressed as a product of four rotation matrices, whose mixing angles are all $\pi /4$ in the complex plane. It predicts ${\theta }_{12}=\arctan (2-\sqrt{2})\approx 30.4°$, ${\theta }_{13}=\arcsin [(\sqrt{2}-1)/(2\sqrt{2})]\approx 8.4°$, ${\theta }_{23}=45°$ and $\delta =90°$ in the standard parametrization, and the Jarlskog invariant of leptonic $CP$ violation is found to be $\mathcal{J}=1/32$. These results are compatible with current data and can soon be tested in a variety of neutrino oscillation experiments. Implications of the tetra-maximal neutrino mixing on the decays of doubly-charged Higgs bosons $H^{\pm \pm }\to l_{\alpha }^{\pm }{l}_{\beta }^{\pm }$ (for $\alpha$, $\beta =e$, $\mu$, $\tau$) are also discussed in the triplet seesaw mechanism at the TeV scale, which will be explored at the upcoming LHC.

A modified version of the double potential formalism for the electrodynamics of dyons is constructed. Besides the two vector potentials, this manifestly duality invariant formulation involves four additional potentials, scalar potentials which appear as Lagrange multipliers for the electric and magnetic Gauss constraints and potentials for the longitudinal electric and magnetic fields. In this framework, a static dyon appears as a Coulomb-like solution without string singularities. Dirac strings are needed only for the Lorentz force law, not for Maxwell’s equations. The magnetic charge no longer appears as a topological conservation law but as a surface integral on a par with electric charge. The theory is generalized to curved space. As in flat space, the string singularities of dyonic black holes are resolved. As a consequence all singularities are protected by the horizon and the thermodynamics is shown to follow from standard arguments in the grand canonical ensemble.

We study null ray propagation in a spacetime of static Schwarzschild–Tangherlini black holes in an arbitrary number of dimensions. We focus on the bending angle and the retarded time delay for rays emitted in the vicinity of a black hole and propagating to the infinity. We obtain an analytic expression in terms of elementary functions which approximate the bending angle and time delay in these spacetimes with high accuracy. We analyze the relative error of the developed analytic approximations and show that it is quite small in the complete domain of the parameter space for the rays reaching the infinity and for a different number of the spacetime dimensions. Possible applications of the obtained results are briefly discussed.

A model of dark matter and dark energy based on the concept of gravitational polarization is investigated. We propose an action in standard general relativity for describing, at some effective or phenomenological level, the dynamics of a dipolar medium, i.e. one endowed with a dipole moment vector, and polarizable in a gravitational field. Using first-order cosmological perturbations, we show that the dipolar fluid is undistinguishable from standard dark energy (a cosmological constant $\Lambda$) plus standard dark matter (a pressureless perfect fluid), and therefore benefits from the successes of the $\Lambda$–cold-dark-matter scenario at cosmological scales. Invoking an argument of “weak clusterization” of the mass distribution of dipole moments, we find that the dipolar dark matter reproduces the phenomenology of the modified Newtonian dynamics at galactic scales. The dipolar medium action naturally contains a cosmological constant, and we show that if the model is to come from some fundamental underlying physics, the cosmological constant $\Lambda$ should be of the order of $a_0^2/c^4$, where $a_0$ denotes the modified Newtonian dynamics constant acceleration scale, in good agreement with observations.

Stationary rotating strings can be viewed as geodesic motions in appropriate metrics in two-dimensional space. We obtain all solutions describing stationary rotating strings in flat spacetime as an application. These rotating strings have infinite length with various wiggly shapes. Averaged value of the string energy, the angular momentum, and the linear momentum along the string are discussed.

We examine medium-enhanced, neutrino scattering-induced decoherent production of dark matter candidate sterile neutrinos in the early universe. In cases with a significant net lepton number we find two resonances, where the effective in-medium mixing angles are large. We calculate the lepton number depletion-driven evolution of these resonances. We describe the dependence of this evolution on lepton numbers, sterile neutrino rest mass, and the active-sterile vacuum mixing angle. We find that this resonance evolution can result in relic sterile neutrino energy spectra with a generic form which is sharply peaked in energy. We compare our complete quantum kinetic equation treatment with the widely-used quantum Zeno ansatz.

We develop an analytic theory for the redshift space bispectrum of dark matter, haloes, and galaxies. This is done within the context of the halo model of structure formation, as this allows for the self-consistent inclusion of linear and nonlinear redshift-space distortions and also for the nonlinearity of the halo bias. The model is applicable over a wide range of scales: on the largest scales the predictions reduce to those of the standard perturbation theory (PT); on smaller scales they are determined primarily by the nonlinear virial velocities of galaxies within haloes, and this gives rise to the $U$-shaped anisotropy in the reduced bispectrum—a finger print of the Finger-Of-God distortions. We then confront the predictions with measurements of the redshift-space bispectrum of dark matter from an ensemble of numerical simulations. On very large scales, $k=0.05h{\mathrm{Mpc}}^{-1}$, we find reasonably good agreement between our halo model, PT and the data, to within the errors. On smaller scales, $k=0.1h{\mathrm{Mpc}}^{-1}$, the measured bispectra differ from the PT at the level of $\sim 10\%–20\%$, especially for colinear triangle configurations. The halo model predictions improve over PT, but are accurate to no better than 10%. On smaller scales $k=0.5–1.0h{\mathrm{Mpc}}^{-1}$, our model provides a significant improvement over PT, which breaks down. This implies that studies which use the lowest order PT to extract galaxy bias information are not robust on scales $k\gtrsim 0.1h{\mathrm{Mpc}}^{-1}$. The analytic and simulation results also indicate that there is no observable scale for which the configuration dependence of the reduced bispectrum is constant—hierarchical models for the higher-order correlation functions in redshift space are unlikely to be useful. It is hoped that our model will facilitate extraction of information from large-scale structure surveys of the Universe, because different galaxy populations are naturally included into our description.

Investigations of the dynamic modes of the Poincaré gauge theory of gravity found only two good propagating torsion modes; they are effectively a scalar and a pseudoscalar. Cosmology affords a natural situation where one might see observational effects of these modes. Here, we consider only the “scalar torsion” mode. This mode has certain distinctive and interesting qualities. In particular, this type of torsion does not interact directly with any known matter, and it allows a critical nonzero value for the affine scalar curvature. Via numerical evolution of the coupled nonlinear equations we show that this mode can contribute an oscillating aspect to the expansion rate of the Universe. From the examination of specific cases of the parameters and initial conditions we show that for suitable ranges of the parameters the dynamic “scalar torsion” model can display features similar to those of the presently observed accelerating universe.

We revisit a weak gravitational lensing problem by constructing a setup which describes the actual system as accurately as possible and solving the null geodesic equations. Details are given for the case of a universe driven only by a cosmological constant, $\Lambda$, which confirm the conventional results: The conventional lensing analysis is correct as it is, without any need for correction of $\mathcal{O}(\Lambda )$. We also treat the cases of the lensing in generic Friedmann-Robertson-Walker backgrounds.

Chiral corrections to the delta axial charge are determined using heavy baryon chiral perturbation theory. Knowledge of this axial coupling is necessary to assess virtual-delta contributions to nucleon and delta observables. We give isospin relations useful for a lattice determination of the axial coupling. Furthermore, we detail partially quenched chiral corrections, which are relevant to address partial quenching and/or mixed action errors in lattice calculations of the delta axial charge.

We examine recent extensions of the standard model with an up-type vectorlike isosinglet $T$ quark that mixes dominantly with the top quark. We take under scrutiny the nondecoupling effects which may reveal such a new heavy fermion through loop diagrams relevant for rare decays such as $K\to \pi \nu \overline{\nu }$, $B\to \pi (K)\nu \overline{\nu }$, and $B_{s,d}\to {\mu }^{+}{\mu }^{-}$. After demonstrating in detail the cancellation between the leading nondecoupling terms, we show that two residual forms $\sim s^2\ln m_T^2$ and $\sim s^4{m}_T^2$ act in a complementary way, so that the maximal allowed values of the decay rates are practically independent of $m_T$. While they correspond to $\sim 20\%$ or $\sim 30\%$ corrections to the SM rates for $K\to \pi \nu \overline{\nu }$ and $B\to \pi (K)\nu \overline{\nu }$, an increase by $\sim 50\%$ for $B_{s,d}\to {\mu }^{+}{\mu }^{-}$ decays offers a possibility to reveal an additional isosinglet state by measurements of these decays at the Large Hadron Collider.

We perform numerical simulations of lattice QCD with two flavors of dynamical overlap quarks, which have exact chiral symmetry on the lattice. While this fermion discretization is computationally demanding, we demonstrate the feasibility to simulate reasonably large and fine lattices by a careful choice of the lattice action and algorithmic improvements. Our production runs are carried out on a ${16}^3\times 32$ lattice at a single lattice spacing around 0.12 fm. We explore the sea quark mass region down to $m_s/6$, where $m_s$ is the physical strange quark mass, for a good control of the chiral extrapolation in future calculations of physical observables. We describe in detail our setup and algorithmic properties of the production simulations and present results for the static quark potential to fix the lattice scale and the locality of the overlap operator.

The ground-state energies of systems containing up to 12 ${\pi }^{+}$’s in a spatial volume $V\sim (2.5\mathrm{fm}{)}^3$ are computed in dynamical, mixed-action lattice QCD at a lattice spacing of $\sim 0.125\mathrm{fm}$ for four different values of the light-quark masses. Clean signals are seen for each ground-state, allowing for a precise extraction of both the ${\pi }^{+}{\pi }^{+}$ scattering length and ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ interaction from a correlated analysis of systems containing different numbers of ${\pi }^{+}$’s. This extraction of the ${\pi }^{+}{\pi }^{+}$ scattering length is consistent with that from the ${\pi }^{+}{\pi }^{+}$ system alone. The large number of systems studied here significantly strengthens the arguments presented in our earlier work and unambiguously demonstrates the presence of a low energy ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ interaction. The equation of state of a ${\pi }^{+}$ gas is investigated using our numerical results and the density dependence of the isospin chemical potential for these systems agrees well with the theoretical expectations of leading order chiral perturbation theory. The chemical potential is found to receive a substantial contribution from the ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ interaction at the lighter pion masses. An important technical aspect of this work is the demonstration of the necessity of performing propagator contractions in greater than double precision to extract the correct results.

The thermodynamics of massless ideal gas of overlap quarks has been investigated both analytically and numerically for both zero and nonzero baryon chemical potential. Any ${\mu }^2$ divergence is shown analytically to be absent for a class of actions with nonzero chemical potential. All such actions are shown to violate chiral invariance. While the parameter $M$ can be shown to be irrelevant in the continuum limit, as expected, it is shown numerically that the continuum limit can be reached with relatively coarser lattices for $1.5\le M\le 1.6$. Numerical limitations of the existing method of introduction of chemical potential are demonstrated. Finally we also show that the energy density for the massive overlap fermions has the correct continuum limit.

We present a numerical lattice quantum chromodynamics calculation of isovector form factors and the first few moments of the isovector structure functions of the nucleon. The calculation employs two degenerate dynamical flavors of domain-wall fermions, resulting in good control of chiral symmetry breaking. Nonperturbative renormalization of the relevant quark currents is performed where necessary. The DBW2 gauge action is used to further improve the chiral behavior while maintaining a reasonable physical lattice volume. The inverse lattice spacing, $a^{-1}$, is approximately 1.7 GeV. Degenerate up and down dynamical quark masses of approximately 1, $3/4$ and $1/2$ times the strange quark mass are used. The physical volume of the lattice is about $(1.9\mathrm{fm}{)}^3$. The ratio of the isovector vector to axial charges, $g_A/g_V$, tends to a lower value than the experimental value as the quark mass is reduced toward the physical point. Momentum-transfer dependences of the isovector vector, axial, induced-tensor and induced-pseudoscalar form factors are calculated. The Goldberger-Treiman relation holds at low momentum transfer and yields an estimation of the pion-nucleon coupling, $g_{\pi NN}=15.5(1.4)$, where the quoted error is only statistical. We find that the flavor nonsinglet quark momentum fraction $⟨x{⟩}_{u-d}$ and quark helicity fraction $⟨x{⟩}_{\Delta u-\Delta d}$ overshoot their experimental values after linear chiral extrapolation. We discuss possible systematic errors for this discrepancy. An estimate for transversity, $⟨1{⟩}_{\delta u-\delta d}=0.93(6)$ in $\overline{\mathrm{MS}}$ at 2 GeV, is obtained and a twist-3 polarized moment, $d_1$, appears small, suggesting that the Wandzura-Wilczek relation holds approximately. We discuss in detail the systematic errors in the calculation, with particular attention paid to finite volume, excited-state contamination, and chiral extrapolations.

We show that the color glass condensate dipole model of Iancu, Itakura, and Munier, improved to include the impact parameter dependence, gives a good fit to the total ${\gamma }^{*}p$ cross section measured at HERA if the anomalous dimension at the saturation scale, ${\gamma }_s$, is treated as a free parameter. We find that the optimum value of ${\gamma }_s=0.46$ is close to the value determined from numerical solution of the Balitsky-Kovchegov equation. The impact parameter dependent saturation scale is generally less than $0.5{\mathrm{GeV}}^2$ in the HERA kinematic regime for the most relevant impact parameters $b\sim 2–3{\mathrm{GeV}}^{-1}$. We compare predictions of the model to data on the longitudinal and heavy flavour structure functions, exclusive diffractive vector meson production, and deeply virtual Compton scattering at HERA. The model is found to be deficient for observables sensitive to moderately small dipole sizes, where an alternative model with explicit Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution performs better. The energy dependence of exclusive diffractive processes is shown to provide an important discriminator between different dipole model cross sections.

The final state of the decay $D^0\to {\pi }^{+}{\pi }^{-}{\pi }^0$ is analyzed in terms of isospin eigenstates. It is shown that the final state is dominated by the isospin-0 component. This suggests that isospin considerations may provide insight into this and perhaps other $D^0$-meson decays. We also discuss the isospin nature of the nonresonant contribution in the decay, which can be further understood by studying the decay $D^0\to {\pi }^0{\pi }^0{\pi }^0$.

We discuss two different configurations of $U_{\mathrm{PMNS}}=U_{\ell }^{†}{U}_{\nu }$ with maximal mixings in both $U_{\ell }$ and $U_{\nu }$. The nonmaximal mixing angles are assumed to be small, which means that they can be expanded in. Since we are particularly interested in the implications for $CP$ violation, we fully take into account complex phases. We demonstrate that one possibility leads to intrinsically large ${sin}^{2}2{\theta }_{13}$ and strong deviations from maximal mixings. The other possibility is generically close to tribimaximal mixing, and allows for large $CP$ violation. We demonstrate how the determination of the ${\theta }_{23}$ octant and the precision measurement of ${\delta }_{CP}$ could discriminate among different qualitative cases. In order to constrain the unphysical and observable phases even further, we relate our configurations to complex mass matrix textures. In particular, we focus on phase patterns which could be generated by powers of a single complex quantity $\eta \simeq {\theta }_C\exp (i\Phi )$, which can be motivated by Froggatt-Nielsen-like models. For example, it turns out that in all of the discussed cases, one of the Majorana phases is proportional to $\Phi$ to leading order. In the entire study, we encounter three different classes of sum rules, which we systematically classify.

The most general supersymmetric seesaw mechanism has too many parameters to be predictive and thus can not be excluded by any measurements of lepton flavor violating (LFV) processes. We focus on the simplest version of the type I seesaw mechanism assuming minimal supergravity boundary conditions. We compute branching ratios for the LFV scalar tau decays, ${\tilde{\tau }}_2\to (e,\mu )+{\chi }_1^0$, as well as loop-induced LFV decays at low energy, such as $l_i\to l_j+\gamma$ and $l_i\to 3l_j$, exploring their sensitivity to the unknown seesaw parameters. We find some simple, extreme scenarios for the unknown right-handed parameters, where ratios of LFV branching ratios correlate with neutrino oscillation parameters. If the overall mass scale of the left neutrinos and the value of the reactor angle were known, the study of LFV allows, in principle, to extract information about the so-far unknown right-handed neutrino parameters.