Two-body Dirac equations (TBDE) of Dirac’s relativistic constraint dynamics have been successfully applied to obtain a covariant nonperturbative description of QED and QCD bound states. Coulomb-type potentials in these applications lead naively in other approaches to singular relativistic corrections at short distances that require the introduction of either perturbative treatments or smoothing parameters. We examine the corresponding singular structures in the effective potentials of the relativistic Schrödinger equation obtained from the Pauli reduction of the TBDE. We find that the relativistic Schrödinger equation leads in fact to well-behaved wave function solutions when the full potential and couplings of the system are taken into account. The most unusual case is the coupled triplet system with $S=1$ and $L=\{(J-1),(J+1)\}$. Without the inclusion of the tensor coupling, the effective $S$-state potential would become attractively singular. We show how including the tensor coupling is essential in order that the wave functions be well-behaved at short distances. For example, the $S$-state wave function becomes simply proportional to the $D$-state wave function and dips sharply to zero at the origin, unlike the usual $S$-state wave functions. Furthermore, this behavior is similar in both QED and QCD, independent of the asymptotic freedom behavior of the assumed QCD vector potential. Light- and heavy-quark meson states can be described well by using a simplified linear-plus-Coulomb-type QCD potential apportioned appropriately between world scalar and vector potentials. We use this potential to exhibit explicitly the origin of the large $\pi \mathrm{\text{−}}\rho$ splitting and effective chiral symmetry breaking. The TBDE formalism developed here may be used to study quarkonia in quark-gluon plasma environments.

I investigate the effects of the gluon self-energy in the color-flavor-locked phase of color superconductivity on the value of the gap. The light plasmon modes, which appear for energies smaller than twice the gap energy, provide the largest contribution. They modify the subsubleading term in the solution of the gap equation.

According to an idea that effective Yukawa coupling constants $Y_f^{\mathrm{eff}}$ are given vacuum expectation values $⟨Y_f⟩$ of fields (“Yukawaons”) $Y_f$ as $Y_f^{\mathrm{eff}}=y_f⟨Y_f⟩/\Lambda$, a possible superpotential form in the charged lepton sector under a U(3) [or O(3)] flavor symmetry is investigated. It is found that a specific form of the superpotential can lead to an empirical charged lepton mass relation without any adjustable parameters.

Katz and Vafa [Nucl. Phys. B497, 146 (1997)] showed how charged matter can arise geometrically by the deformation of ADE-type orbifold singularities in type IIa, M-theory, and F-theory compactifications. In this paper we use those same basic ingredients, used there to geometrically engineer specific matter representations, here to deform the compactification manifold itself in a way which naturally compliments many features of unified model building. We realize this idea explicitly by deforming a manifold engineered to give rise to an $S{U}_5$ grand unified model into a one giving rise to the standard model. In this framework, the relative local positions of the singularities giving rise to standard model fields are specified in terms of the values of a small number of complex structure moduli which deform the original manifold, greatly reducing the arbitrariness of their relative positions.

We derive electrically charged black hole solutions of the Einstein-Gauss-Bonnet equations with a nonlinear electrodynamics source in $n(\ge 5)$ dimensions. The spacetimes are given as a warped product ${\mathcal{M}}^2\times {\mathcal{K}}^{n-2}$, where ${\mathcal{K}}^{n-2}$ is a $(n-2)$-dimensional constant curvature space. We establish a generalized Birkhoff’s theorem by showing that it is the unique electrically charged solution with this isometry and for which the orbit of the warp factor on ${\mathcal{K}}^{n-2}$ is non-null. An extension of the analysis for full Lovelock gravity is also achieved with a particular attention to the Chern-Simons case.

A nonuniversal scalar mass supergravity type of model is explored where the first two generations of scalars and the third generation of sleptons may be very massive. The lighter or vanishing third generation of squarks as well as Higgs scalars at the unification scale cause the radiative electroweak symmetry breaking constraint to be less prohibitive. Thus, both flavor-changing neutral-current/$CP$-violation problems as well as the naturalness problem are within control. We identify a large slepton mass effect in the renormalization group equations of $m_{H_D}^2$ (for the down type of Higgs) that may turn the latter negative at the electroweak scale even for a small $\tan \beta$. A hyperbolic branch/focus pointlike effect is found for $m_A^2$ that may result in very light Higgs spectra. The lightest stable particle is dominantly a $b$-ino that pair annihilates via Higgs exchange, giving rise to a Wilkinson Microwave Anisotropy Probe satisfied relic density region for all $\tan \beta$. Detection prospects of such lightest stable particles in the upcoming dark matter experiments both of direct and indirect types (photon flux) are interesting. The Higgs bosons and the third generation of squarks are light in this scenario and these may be easily probed besides charginos and neutralinos in the early runs of the Large Hadron Collider.

We analyze the potential of the Large Hadron Collider (LHC) to observe signatures of phenomenologically viable walking technicolor models. We study and compare the Drell-Yan and vector boson fusion mechanisms for the production of composite heavy vectors. We find that the heavy vectors are most easily produced and detected via the Drell-Yan processes. The composite Higgs phenomenology is also studied. If technicolor walks at the LHC, its footprints will be visible and our analysis will help in uncovering them.

We discuss production of nonphotonic electrons in proton-proton scattering at the relativistic heavy ion collider. The distributions in rapidity and transverse momentum of charm and bottom quarks/antiquarks are calculated in the $k_t$-factorization approach. We use Kwieciński unintegrated parton distributions and Ivanov-Nikolaev unintegrated gluon distribution. The hadronization of heavy quarks is done by means of Peterson and Braaten et al. fragmentation functions. The semileptonic decay functions are found by fitting recent semileptonic data obtained by the CLEO and BABAR collaborations. We get good description of the data at large transverse momenta of electrons and find a missing strength concentrated at small transverse momenta of electrons. Plausible missing mechanisms are discussed.

We examine the rare decays $B_s\to l^{+}{l}^{-}$ and $B\to K{l}^{+}{l}^{-}$ in the framework of the topcolor-assisted technicolor ($TC2$) model. The contributions of the new particles predicted by this model to these rare decay processes are evaluated. We find that the values of their branching ratios are larger than the standard model predictions by one order of magnitude in wide range of the parameter space. The longitudinal polarization asymmetry of leptons in $B_s\to l^{+}{l}^{-}$ can approach $\mathcal{O}({10}^{-2})$. The forward-backward asymmetry of leptons in $B\to K{l}^{+}{l}^{-}$ is not large enough to be measured in future experiments. We also give some discussions about the branching ratios and the asymmetry observables related to these rare decay processes in the littlest Higgs model with T-parity.

We consider a model based on $A_4⋉(Z_e\times Z_{\mu }\times Z_{\tau })$ flavor symmetry for tribimaximal lepton mixing with two scalar $A_4$ triplets whose vacuum expectation values have the same alignment. Neutrino masses are generated through effective dimension-five Weinberg operators. Charged lepton mass hierarchies are generated with an additional Froggatt-Nielsen $U(1{)}_F$ flavor symmetry under which right-handed leptons are charged.

The Cucchieri-Mendes bounds for the gluon propagator are discussed for the four dimensional pure-gauge SU(3) theory. Assuming a pure power law dependence on the inverse of the lattice volume, the lattice data gives a vanishing zero-momentum gluon propagator in the infinite-volume limit in agreement with the Gribov-Zwanziger horizon condition but contradicting the SU(2) analysis. The results are robust against variations of the lattice volumes and corrections to the power law. Our analysis considers also more general ansatze that, although not conclusive, open the possibility of having $D(0)\ne 0$ in the infinite-volume limit. A solution to this puzzle requires further investigations.

We consider the $N=4$ super Yang-Mills theory in flat $3+1$-dimensional space-time with a time dependent coupling constant which vanishes at $t=0$, like $g_{\mathrm{YM}}^2=t^p$. In an analogous quantum mechanics toy model we find that the response is singular. The energy diverges at $t=0$, for a generic state. In addition, if $p>1$ the phase of the wave function has a wildly oscillating behavior, which does not allow it to be continued past $t=0$. A similar effect would make the gauge theory singular as well, though nontrivial effects of renormalization could tame this singularity and allow a smooth continuation beyond $t=0$. The gravity dual in some cases is known to be a time dependent cosmology which exhibits a spacelike singularity at $t=0$. Our results, if applicable in the gauge theory for the case of the vanishing coupling, imply that the singularity is a genuine sickness and does not admit a meaningful continuation. When the coupling remains nonzero and becomes small at $t=0$, the curvature in the bulk becomes of order string scale. The gauge theory now admits a time evolution beyond this point. In this case, a finite amount of energy is produced which possibly thermalizes and leads to a black hole in the bulk.

Vortices of a new type, carrying non-Abelian flux moduli $C{P}^{n-1}\times C{P}^{r-1}$, are found in the context of softly broken $\mathcal{N}=2$ supersymmetric quantum chromodynamics. By tuning the bare quark masses appropriately, we identify the vacuum in which the underlying $SU(N)$ gauge group is partially broken to $SU(n)\times SU(r)\times U(1)/{\mathbb{Z}}_K$, where $K$ is the least common multiple of $(n,r)$, and with $N_f^{su(n)}=n$ and $N_f^{su(r)}=r$ flavors of light quark multiplets. At much lower energies, the gauge group is broken completely by the squark vacuum expectation values, and vortices develop which carry non-Abelian flux moduli $C{P}^{n-1}\times C{P}^{r-1}$. For $n>r$, at the length scale at which the $SU(n)$ fluctuations become strongly coupled and Abelianize, the vortex still carries weakly fluctuating $SU(r)$ flux moduli. We discuss the possibility that these vortices are related to the light non-Abelian monopoles found earlier in the fully quantum-mechanical treatment of $4D$ supersymmetric quantum chromodynamics.

Wormholes and time machines are objects of great interest in general relativity. However, to support them it needs exotic matters which are impossible at the classical level. Semiclassical gravity introduces the quantum effects into the stress-energy tensor and constructs many self-consistent wormholes. But they are not traversable due to the averaged null energy condition. Loop quantum gravity (LQG) significantly modifies the Einstein equation in the deep quantum region. If we write the modified Einstein equation in the form of the standard one but with an effective stress-energy tensor, it is convenient to analyze the geometry in LQG through the energy condition. Loop quantum cosmology (LQC), an application of LQG, has an effective stress-energy tensor which violates some kinds of local energy conditions. So it is natural that the inflation emerges in LQC. In this paper, we investigate the averaged null energy condition in LQC in the framework of the effective Hamiltonian, and we find that the effective stress-energy tensor in LQC violates the averaged null energy condition in the massless scalar field coupled model.

Because the gravitational Hamiltonian is a pure boundary term on shell, asymptotic gravitational fields store information in a manner not possible in local field theories. This fact has consequences for both perturbative and nonperturbative quantum gravity. In perturbation theory about an asymptotically flat collapsing black hole, the algebra generated by asymptotic fields on future null infinity within any neighborhood of spacelike infinity contains a complete set of observables. Assuming that the same algebra remains complete at the nonperturbative quantum level, we argue that either (1) the $S$ matrix is unitary or (2) the dynamics in the region near timelike, null, and spacelike infinity is not described by perturbative quantum gravity about flat space. We also consider perturbation theory about a collapsing asymptotically anti-de Sitter (AdS) black hole, where we show that the algebra of boundary observables within any neighborhood of any boundary Cauchy surface is similarly complete. Whether or not this algebra continues to be complete nonperturbatively, the assumption that the Hamiltonian remains a boundary term implies that information available at the AdS boundary at any one time $t_1$ remains present at this boundary at any other time $t_2$.

We adopt methods from statistical field theory to stochastic inflation. For the example of a free test field in de Sitter and power-law inflation, the power spectrum of long-wavelength fluctuations is computed. We study its dependence on the shape of the filter that separates long- from short-wavelength modes. While for filters with infinite support the phenomenon of dimensional reductions is found on large superhorizon scales, filters with compact support return a scale-invariant power spectrum in the infrared. Features of the power spectrum, induced by the filter, decay within a few $e$-foldings. Thus the late-time power spectrum is independent of the filter details.

There is evidence for an excess in cosmic-ray electrons at about 500 GeV energy, that may be related to dark-matter annihilation. I have calculated the expected electron contributions from a pulsar and from Kaluza-Klein dark matter, based on a realistic treatment of the electron propagation in the Galaxy. Pulsars younger than about ${10}^5$ years naturally cause a narrow peak at a few hundred GeV in the locally observed electron spectrum, similar to that observed. On the other hand, if electron production by dark matter is predominantly occurring in high-mass clumps ($\gtrsim {10}^3{M}_{\odot }$), the sharp cutoff in the contribution from Kaluza-Klein particles is sometimes more pronounced, but often smoothed out and indistinguishable from a pulsar source, and therefore the spectral shape of the electron excess is insufficient to discriminate a dark-matter origin from more conventional astrophysical explanations.

We study open charm production at high energies in the framework of the quasi-multi-Regge-kinematics approach applying the quark-Reggeization hypothesis implemented with Reggeon-Reggeon-particle and Reggeon-particle-particle effective vertices. Adopting the Watt-Martin-Ryskin unintegrated quark and gluon distribution functions of the proton and photon, we thus nicely describe the proton structure function $F_{2,c}$ measured at DESY HERA as well as the transverse-momentum distributions of $D$ mesons created by photoproduction at HERA and by hadroproduction at the Fermilab Tevatron.

A Dalitz plot analysis of approximately 13 000 $D_s^{+}$ decays to ${\pi }^{+}{\pi }^{-}{\pi }^{+}$ has been performed. The analysis uses a $384{\mathrm{fb}}^{-1}$ data sample recorded by the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}$ storage ring running at center of mass energies near 10.6 GeV. Amplitudes and phases of the intermediate resonances which contribute to this final state are measured. A high precision measurement of the ratio of branching fractions is performed: $\mathcal{B}(D_s^{+}\to {\pi }^{+}{\pi }^{-}{\pi }^{+})/\mathcal{B}(D_s^{+}\to K^{+}{K}^{-}{\pi }^{+})=0.199\pm 0.004\pm 0.009$. Using a model-independent partial wave analysis, the amplitude and phase of the $\mathcal{S}$ wave have been measured.