The Pauli–Villars regularization scheme is applied to a calculation of the dressed-electron state and its anomalous magnetic moment in light-front-quantized QED in Feynman gauge. The regularization is provided by heavy, negative-metric fields added to the Lagrangian. The light-front QED Hamiltonian then leads to a well-defined eigenvalue problem for the dressed-electron state expressed as a Fock-state expansion. The Fock-state wave functions satisfy coupled integral equations that come from this eigenproblem. A finite system of equations is obtained by truncation to no more than two photons and no positrons; this extends earlier work that was limited to dressing by a single photon. Numerical techniques are applied to solve the coupled system and compute the anomalous moment, for which we obtain agreement with experiment, within numerical errors, but observe a small systematic discrepancy that should be due to the absence of electron-positron loops and of three-photon self-energy effects. We also discuss the prospects for application of the method to quantum chromodynamics.

Using EW-MSSM field theory, so the electroweak phase transition (EWPT) is first order, we derive the equations of motion (e.o.m.) for the gauge fields. With an isospin ansatz we derive e.o.m. for the electrically charged $W$ fields uncoupled from all other fields. These and the lepton currents serve as the current for the Maxwell-like e.o.m. for the electromagnetic field. The electromagnetic field arising during EWPT bubble nucleation without leptons is found. We then calculate the electron current contribution, which is seen to be quite large. This provides the basis for determining the magnetic field created by EWPT bubble collisions, which could seed galactic and extragalactic magnetic fields.

We show how the fields and particles of the standard model can be naturally realized in noncommutative gauge theory. Starting with a Yang-Mills matrix model in more than four dimensions, an $SU(n)$ gauge theory on a Moyal-Weyl space arises with all matter and fields in the adjoint of the gauge group. We show how this gauge symmetry can be broken spontaneously down to $SU(3{)}_c\times SU(2{)}_L\times U(1{)}_Q$ [resp. $SU(3{)}_c\times U(1{)}_Q$], which couples appropriately to all fields in the standard model. An additional $U(1{)}_B$ gauge group arises which is anomalous at low energies, while the trace-$U(1)$ sector is understood in terms of emergent gravity. A number of additional fields arise, which we assume to be massive, in a pattern that is reminiscent of supersymmetry. The symmetry breaking might arise via spontaneously generated fuzzy spheres, in which case the mechanism is similar to brane constructions in string theory.

The phase space of a Hamiltonian system is symplectic. However, the post-Newtonian Hamiltonian formulation of spinning compact binaries in existing publications does not have this property, when position, momentum, and spin variables $[\mathit{X},\mathit{P},{\mathit{S}}_1,{\mathit{S}}_2]$ compose its phase space. This may give a convenient application of perturbation theory to the derivation of the post-Newtonian formulation, but also makes classic theories of a symplectic Hamiltonian system a serious obstacle in application, especially in diagnosing integrability and nonintegrability from a dynamical system theory perspective. To completely understand the dynamical characteristic of the integrability or nonintegrability for the binary system, we construct a set of conjugate spin variables and reexpress the spin Hamiltonian part so as to make the complete Hamiltonian formulation symplectic. As a result, it is directly shown with the least number of independent isolating integrals that a conservative Hamiltonian compact binary system with both one spin and the pure orbital part to any post-Newtonian order is typically integrable and not chaotic. And a conservative binary system consisting of two spins restricted to the leading order spin-orbit interaction and the pure orbital part at all post-Newtonian orders is also integrable, independently on the mass ratio. For all other various spinning cases, the onset of chaos is possible.

By implementing the new IR-improved Dokshitzer-Gribov-Lipatov-Altarelli-Parisi-Callan-Symanzik (DGLAP-CS) kernels recently developed by one of us in the HERWIG6.5 environment we generate a new Monte Carlo (MC), HERWIRI1.0(31), for hadron-hadron scattering at high energies. We use MC data to illustrate the comparison between the parton shower generated by the standard DGLAP-CS kernels and that generated by the new IR-improved DGLAP-CS kernels. The interface to MC@NLO, MC@NLO/HERWIRI, is illustrated. Comparisons with FNAL data and some discussion of possible implications for LHC phenomenology are also presented.

We investigate the heavy-quark mass effects on the parton distribution functions in the unpolarized virtual photon up to the next-to-leading order in QCD. Our formalism is based on the QCD-improved parton model described by the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equation as well as on the operator product expansion supplemented by the mass-independent renormalization group method. We evaluate the various components of the parton distributions inside the virtual photon with the massive quark effects, which are included through the initial condition for the heavy-quark distributions, or equivalently from the matrix element of the heavy-quark operators. We discuss some features of our results for the heavy-quark effects and their factorization-scheme dependence.

The vector meson production in coherent hadron-hadron interactions at LHC energies is studied assuming that the color singlet $t$-channel exchange carries large momentum transfer. We consider the nonforward solution of the Balitsky, Fadin, Kuraev, and Lipatov equation at high energy and large momentum transfer and estimate the rapidity distribution and total cross section for the process $h_1{h}_2\to h_{1}J/\Psi X$, where $h_i$ can be a proton or a nucleus. We predict large rates, which implies that the experimental identification can be feasible at the LHC.

The mechanism of channel coupling via decay products is used to study energy shifts, level mixing as well as the possibility of new near-threshold resonances in $c\overline{c}$, $b\overline{b}$ systems. The Weinberg eigenvalue method is formulated in the multichannel problems, which allows one to describe coupled-channel resonances and wave functions in a unitary way, and to predict new states due to channel coupling. Realistic wave functions for all single-channel states and decay matrix elements computed earlier are exploited, and no new fitting parameters are involved. Examples of level shifts, widths, and mixings are presented; the dynamical origin of $X(3872)$ and the destiny of the single-channel $2{}^{3}P_1(c\overline{c})$ state are clarified. As a result a sharp and narrow peak in the state with quantum numbers $J^{PC}=1^{++}$ is found at 3.872 GeV, while the single-channel resonance originally around 3.940 GeV becomes increasingly broad and disappears with growing coupling to open channels.

We demonstrate that the current Tevatron dataset with $\int \mathcal{L}=5{\mathrm{fb}}^{-1}$ has strong sensitivity to the production of a fourth-generation Majorana neutrino ($N$) via an $s$-channel $Z$ boson $Z\to NN\to W\ell W\ell$, well beyond current experimental limits. A single Tevatron experiment could significantly extend current 95% C.L. mass lower limits, to $m_N>175\mathrm{GeV}/c^2$, or report $3\sigma$ evidence for the $N$ if $m_N<150\mathrm{GeV}/c^2$. With $5{\mathrm{fb}}^{-1}$, a single LHC experiment at $\sqrt{s}=10\mathrm{TeV}$ could expect to set a 95% C.L. mass lower limits of $m_N>300\mathrm{GeV}/c^2$, or report $3\sigma$ evidence for the $N$ if $m_N<225\mathrm{GeV}/c^2$.

We evaluate the impact of electroweak corrections of infrared origin on strongly interacting longitudinal gauge boson scattering, calculating all-order resummed expressions at the double log level. As a working example, we consider the standard model with a heavy Higgs. At energies typical of forthcoming experiments (LHC, International Linear Collider, Compact Linear Collider), the corrections are in the 10%–40% range, with the relative sign depending on the initial state considered and on whether or not additional gauge boson emission is included. We conclude that the effect of radiative electroweak corrections should be included in the analysis of longitudinal gauge boson scattering.

It is known, that a keV scale sterile neutrino is a good warm dark matter candidate. We study how this possibility could be realized in the context of gauge extensions of the standard model. The naïve expectation leads to large thermal overproduction of sterile neutrinos in this setup. However, we find that it is possible to use out-of-equilibrium decay of the other right-handed neutrinos of the model to dilute the present density of the keV sterile neutrinos and achieve the observed dark matter density. We present the universal requirements that should be satisfied by the gauge extensions of the standard model, containing right-handed neutrinos, to be viable models of warm dark matter, and provide a simple example in the context of the left-right symmetric model.

We consider the evolution of the ground state in the two Higgs doublet model during cooling down of the Universe after the big bang. Different regions in the space of free parameters of this model correspond to different sequences of thermal phase transitions. We discuss different paths of thermal evolution and corresponding evolution of physical properties of the system for different modern values of the parameters.

We study a gauge-invariant variational framework for the Yang-Mills vacuum wave functional. Our approach is built on gauge-averaged Gaussian trial functionals which substantially extend previously used trial bases in the infrared by implementing a general low-momentum expansion for the vacuum-field dispersion (which is taken to be analytic at zero momentum). When completed by the perturbative Yang-Mills dispersion at high momenta, this results in a significantly enlarged trial-functional space which incorporates both dynamical mass generation and asymptotic freedom. After casting the dynamics associated with these wave functionals into an effective action for collections of soft vacuum-field orbits, the leading infrared improvements manifest themselves as four-gradient interactions. Those turn out to significantly lower the minimal vacuum energy density, thus indicating a clear overall improvement of the vacuum description. The dimensional transmutation mechanism and the dynamically generated mass scale remain almost quantitatively robust, however, which ensures that our prediction for the gluon condensate is consistent with standard values. Further results include a finite group velocity for the soft gluonic modes due to the higher-gradient corrections and indications for a negative differential color resistance of the Yang-Mills vacuum.

We present supersymmetric Lorentz Chern-Simons terms coupled to anti–de Sitter supergravity in three dimensions with an arbitrary number (${\aleph }_0$) of supersymmetries. As an application to higher dimensions, we present analogous supersymmetric Lorentz Chern-Simons terms coupled to $N=1$ supergravity in 11 dimensions.

In two recent papers [4,5], it has been demonstrated that one can obtain quantum-corrected Boltzmann kinetic equations for leptogenesis using a top-down approach based on the Schwinger-Keldysh/Kadanoff-Baym formalism. These “Boltzmann-like” equations are similar to the ones obtained in the conventional bottom-up approach but differ in important details. In particular there is a discrepancy between the $CP$-violating parameter obtained in the first-principle derivation and in the framework of thermal field theory. Here we demonstrate that the two approaches can be reconciled if causal $n$-point functions are used in the thermal field theory approach. The new result for the medium correction to the $CP$-violating parameter is qualitatively different from the conventional one. The analogy to a toy model considered earlier enables us to write down consistent quantum-corrected Boltzmann equations, for thermal leptogenesis in the standard model extended by three right-handed neutrinos, which include quantum statistical terms and medium-corrected expressions for the $CP$-violating parameter.

In the baryogenesis via leptogenesis scenario the self-energy contribution to the $CP$-violating parameter plays a very important role. Here, we calculate it in a simple toy model of leptogenesis using the Schwinger-Keldysh/Kadanoff-Baym formalism as starting point. We show that the formalism is free of the double-counting problem typical for the canonical Boltzmann approach. Within the toy model, medium effects increase the $CP$-violating parameter. In contrast to results obtained earlier in the framework of thermal field theory, the medium corrections are linear in the particle number densities. In the resonant regime quantum corrections lead to modified expressions for the $CP$-violating parameter and for the decay width. Most notably, in the maximal resonant regime the Boltzmann picture breaks down and an analysis in the full Kadanoff-Baym formalism is required.

Many interesting models incorporate scalar fields with nonminimal couplings to the spacetime Ricci curvature scalar. As is well known, if only one scalar field is nonminimally coupled, then one may perform a conformal transformation to a new frame in which both the gravitational portion of the Lagrangian and the kinetic term for the (rescaled) field assume canonical form. We examine under what conditions the gravitational and kinetic terms in the Lagrangian may be brought into canonical form when more than one scalar field has nonminimal coupling. A particular class of two-field models admits such a transformation, but models with more than two nonminimally coupled fields, in general, do not.

A large class of the dynamical laws for causal sets described by a classical process of sequential growth yields a cyclic universe, whose cycles of expansion and contraction are punctuated by single “origin elements” of the causal set. We present evidence that the effective dynamics of the immediate future of one of these origin elements, within the context of the sequential growth dynamics, yields an initial period of de Sitter-like exponential expansion, and argue that the resulting picture has many attractive features as a model of the early universe, with the potential to solve some of the standard model puzzles without any fine-tuning.

Our Universe may be contained in one among a diverging number of bubbles that nucleate within an eternally inflating multiverse. A promising measure to regulate the diverging spacetime volume of such a multiverse is the scale-factor cutoff, one feature of which is bubbles are not rewarded for having a longer duration of slow-roll inflation. Thus, depending on the landscape distribution of the number of $e$-folds of inflation among bubbles like ours, we might hope to measure spatial curvature. We study a recently proposed cartoon model of inflation in the landscape and find a reasonable chance (about 10%) that the curvature in our Universe is well above the value expected from cosmic variance. Anthropic selection does not strongly select for curvature as small as is observed (relative somewhat larger values), meaning the observational bound on curvature can be used to rule out landscape models that typically give too little inflation.

A model of inflation is presented where the inflaton field is a complex scalar field coupled to a $U(1)$ gauge field. Because of the axial symmetry of the potential, the inflation is driven by the radial direction while the angular field is gauged by $U(1)$. Because of the coupling of the inflaton to the gauge field, a time-dependent mass term for the gauge field is generated dynamically and conformal invariance is broken. We study whether a significant amount of primordial magnetic fields can be generated during inflation by allowing a time-dependent $U(1)$ gauge kinetic coupling.