In a recent paper, we presented an asymptotic formula for the fermion-induced effective energy in 3+1 dimensions in the presence of a cylindrically symmetric inhomogeneous strong magnetic field. However, there are some points which were not clearly explained. In fact, the arguments, which led us to the asymptotic formula, are based on a numerical study of the integral of Eq. (10), as we will see in the main part of this paper. The aim of this work is to present this study in detail.

We investigate the line element of spacetime around a linear cosmic string in the presence of a cosmological constant. We obtain a static form of the metric and argue that it should be discarded because of asymptotic considerations. Then a time dependent and consistent form of the metric is obtained and its properties are discussed. This may be considered an example of a preferred frame in physics.

The neutrino mean free paths in hot neutron-star matter are obtained in the presence of kaon condensates. The kaon-induced neutrino absorption process, which is allowed only in the presence of kaon condensates, is considered for both nondegenerate and degenerate neutrinos. The neutrino mean free path due to this process is compared with that for neutrino-nucleon scattering. While the mean free path for the kaon-induced neutrino absorption process is shown to be shorter than for the ordinary two-nucleon absorption process by several orders of magnitude when the temperature is not very high, the neutrino-nucleon scattering process still has a dominant contribution to the neutrino opacity. Thus, the kaon-induced neutrino absorption process has a minor effect on the thermal and dynamical evolution of protoneutron stars.

We study the possible effects of $\mathrm{CP}$ violation in the Higgs sector on $t\overline{t}$ production at a $\gamma \gamma$ collider. These studies are performed in a model-independent way in terms of six form factors $\{\mathfrak{R}{(S}_{\gamma }),\mathfrak{I}{(S}_{\gamma }),\mathfrak{R}{(P}_{\gamma }),\mathfrak{I}{(P}_{\gamma }{),S}_t{,P}_t\}$ which parametrize the $\mathrm{CP}$ mixing in the Higgs sector, and a strategy for their determination is developed. We observe that the angular distribution of the decay lepton from $t/\overline{t}$ produced in this process is independent of any $\mathrm{CP}$ violation in the $\mathrm{tbW}$ vertex and hence best suited for studying $\mathrm{CP}$ mixing in the Higgs sector. Analytical expressions are obtained for the angular distribution of leptons in the c.m. frame of the two colliding photons for a general polarization state of the incoming photons. We construct combined asymmetries in the initial state lepton (photon) polarization and the final state lepton charge. They involve $\mathrm{CP}$ even (x’s) and odd (y’s) combinations of the mixing parameters. We study limits up to which the values of x and y, with only two of them allowed to vary at a time, can be probed by measurements of these asymmetries, using circularly polarized photons. We use the numerical values of the asymmetries predicted by various models to discriminate among them. We show that this method can be sensitive to the loop-induced $\mathrm{CP}$ violation in the Higgs sector in the minimal supersymmetric standard model.

An integral representation is suggested for generalized parton distributions which automatically satisfies the polynomiality and positivity constraints. This representation has the form of an integral of perturbative triangle diagrams over the masses of three propagators with an appropriate weight depending on these masses. An arbitrary D term can be added.

We consider the impact of the recent KamLAND data on neutrino oscillations, the first terrestrial neutrino experiment that can probe the solar neutrino anomaly. By combining the first 145.1 days of KamLAND data with the full sample of the latest solar neutrino data we find an enhanced rejection against non-large-mixing-angle (LMA) oscillations, allowed only at more than $4\sigma$ with respect to the LMA solution. Furthermore, the new data have a strong impact in narrowing down the allowed range of $\Delta m^2$ inside the LMA region. In contrast, our global analysis indicates that the new data have little impact on the location of the best fit point. In particular, the solar neutrino mixing remains significantly nonmaximal $\left(3\mathrm{}\sigma \right).\mathrm{}$

We report on a first theoretical study for neutrino-induced diffractive production of heavy pseudoscalar mesons ${\eta }_c$ and ${\eta }_b$ off a nucleon. Based on the factorization formalism for exclusive processes, we evaluate the forward diffractive production cross section in perturbative QCD in terms of the light-cone $Q\overline{Q}$ wave functions (WFs) of ${\eta }_{c,b}$ mesons and the gluon distribution of the nucleon. The light-cone WFs of the ${\eta }_c\left({\eta }_b\right)$ meson are constructed to satisfy the spin symmetry relations with those of the $J/\psi \left({\rm Y}\right)$ meson. The diffractive ${\eta }_c$ production is governed by the axial-vector coupling of the longitudinally polarized Z boson to a $Q\overline{Q}$ pair, and the resulting ${\eta }_c$ production rate is larger than that for the $J/\psi$ by one order of magnitude. We also discuss the production of bottomonium ${\eta }_b,$ which shows up for a higher beam energy.

We study the existence of classical soliton solutions with intrinsic angular momentum in Yang-Mills-Higgs theory with a compact gauge group $\mathcal{G}$ in (3+1)-dimensional Minkowski space. We show that for symmetric gauge fields the Noether charges corresponding to rigid spatial symmetries, as the angular momentum, can be expressed in terms of surface integrals. Using this result, we demonstrate in the case of $\mathcal{G}=SU\left(2\right)\mathrm{}$ the nonexistence of stationary and axially symmetric spinning excitations for all known topological solitons in the one-soliton sector, that is, for ’t Hooft–Polyakov monopoles, Julia-Zee dyons, sphalerons, and also vortices.

In this paper, the Becchi-Rouet-Stora-Tyutin (BRST) symmetry transformation is presented for the noncommutative $\mathrm{U}\mathrm{}\left(N\right)\mathrm{}$ gauge theory. The nilpotency of the charge associated with this symmetry is then proved. As a consequence of the spacelike noncommutativity parameter, the Hilbert space of physical states is determined by the cohomology space of the BRST operator as in the commutative case. Further, the unitarity of the S-matrix elements projected onto the subspace of the physical states is deduced.

We study the problem of integrating an invisible axion into the Randall-Sundrum scenario as an example of how to generate new energy scales between the extremes of the Planck mass and the electroweak scale. In this scenario, the axion corresponds to the phase of a complex bulk scalar field. We show how to generate an intermediate energy scale by including a third brane in the scenario. We discuss the stabilization of this brane in detail to demonstrate that no additional fine tunings arise.

We discuss the nuclear effects in the Paschos-Wolfenstein relationship in the context of the extraction of the weak mixing angle. We point out that the neutron excess correction to the Paschos-Wolfenstein relationship for a neutron-rich target is negative and large on the scale of the experimental errors of a recent NuTeV measurement. We find a larger neutron excess correction to the Paschos-Wolfenstein relationship for the total cross sections than that discussed by the NuTeV Collaboration. The phenomenological applications of this observation are discussed in the context of the NuTeV deviation. The uncertainties in the neutron excess correction are estimated. The effects due to the Fermi motion, nuclear binding, and nuclear shadowing are also discussed in the context of the total cross sections.

I consider gravity induced over a smooth (finite thickness) soliton. A graviton kinetic term is coupled to a bulk scalar that develops a solitonic vacuum expectation value. Couplings of Kaluza-Klein modes to soliton-localized matter are suppressed, giving rise to a crossover distance $r_c{=M}_P^2{/M}_{*}^3$ between the 4D and 5D behavior. This system can be viewed as a finite thickness brane regularization of the model of Dvali, Gabadadze, and Porrati.

We show that different thick domain wall spacetimes, for which the scalar field configuration and the potential are the same, can be found as solutions to the coupled Einstein-scalar field equations, depending on whether or not reflection symmetry on the wall is imposed. Spacetimes with reflection symmetry may be dynamic or static, while the asymmetric ones are static. Asymmetric walls are asymptotically flat on one side and reduce to the Taub spacetime on the other. Examples of asymmetric thick walls in D-dimensional spacetimes are given, and previous analysis on the distributional thin-wall limit of the dynamic symmetric thick walls are extended to the asymmetric case. A new family of reflection symmetric, static thick domain wall spacetimes, including previously known Bogomol’nyi-Prasad-Sommerfield walls, is presented.

We investigate the dynamics of a bulk scalar field with various decay channels in the Randall-Sundrum infinite braneworld scenario. A bulk scalar field in this scenario has a quasilocalized mode which dominates the late-time behavior near the brane. As for this mode, an interesting point is the presence of dissipation caused by the escape of the energy in the direction away from the brane, even if the bulk scalar field does not have the interaction with the other bulk fields in the bulk and fields on the brane. We can interpret that this lost energy is transferred to the dark radiation. We show that such an effective 4-dimensional description for a bulk scalar field is valid including the various processes of energy dissipation.

An inflationary brane model driven by a bulk inflaton with exponential potential is proposed. We find a family of exact solutions that describe power-law inflation on the brane. These solutions enable us to derive exact solutions for metric perturbations analytically. By calculating scalar and tensor perturbations, we obtain a spectrum of primordial fluctuations at the end of the inflation. The amplitudes of scalar and tensor perturbations are enhanced in the same way if the energy scale of the inflation is sufficiently higher than the tension of the brane. Then the relative amplitude of scalar and tensor perturbations is not suppressed even for high-energy inflation. This is a distinguishable feature from the inflation model driven by inflaton on the brane where tensor perturbations are suppressed for high-energy inflation. We also point out that massive Kaluza-Klein modes are not negligible at high frequencies on 3-space of our brane.

We introduce and study a non-Gaussian paraxial cavity mode that has a special beam intensity by properly designing the end mirrors of a resonator. The final aim is to reduce the thermoelastic noise generated by the interaction between the field and the mirror by optimizing the shape of both. We present numerical results for the special design of a resonator as long as the Fabry-Pérot arms of the gravitational wave detector Laser Interferometric Gravitational Wave Observatory (LIGO). We discuss the alignment stability of such a cavity and we present the most important investigations we have done for implementing the reshaped mirrors we propose in the next LIGO configuration. We implement different numerical tools in order to understand the impact of both a small misalignment in the Fabry-Pérot cavity and imperfections in the radial profile of the mirrors on the power built up inside the resonators and on the signal at the dark port of the beam splitter. The results of all the simulation runs are compared with an analytical model that takes into account mismatch problems and losses.

The light gluino (12–16 GeV) and light sbottom (2–6 GeV) scenario has been used to explain the apparent overproduction of b quarks at the Fermilab Tevatron. This scenario also predicts the decay $\overrightarrow{Z}b\overline{b}\tilde{g}\tilde{g}$ where the gluinos subsequently decay into b quarks and sbottoms. We show that this can contribute to ${\Gamma }_{4b}=\Gamma \left(\overrightarrow{Z}b\overline{b}b\overline{b}\right)$ since most of the sbottoms and b quarks arising from gluino decay have a small angular separation. We find that while no excess in ${\Gamma }_{4b}$ is observable due to large uncertainties in experimental measurements, the ratio $\Gamma \left(\overrightarrow{Z}b\overline{b}\tilde{g}\tilde{g}\right)/\Gamma \left(\overrightarrow{Z}b\overline{b}b\overline{b}\right)$ can be large due to sensitivity to b-quark mass, the sbottom mixing angle and the gluino mass. We calculate it to be in the range 0.05–0.41 inclusive of the entire parameter space.

We discuss the effects of a t-channel excited electron neutrino on the reaction $e^{+}{e}^{-}\to W^{+}{W}^{-}.$ Data collected by the OPAL Collaboration at CERN LEP energies up to $189\mathrm{GeV}$ are used to establish $95\%$ confidence level bounds on the mass and couplings of this excited neutrino. Rejection limits are also obtained for a future $500\mathrm{GeV}$ Next Linear Collider machine, assuming no excited neutrino will be detected at such an energy regime.

The nonvalence spin-flavor structure of the proton extracted from semi-inclusive measurements of polarized deep inelastic scattering depends strongly on the transverse momentum of the detected hadrons which are used to determine the individual polarized sea distributions. This physics may explain the recent HERMES observation of a positively polarized strange sea through semi-inclusive scattering, in contrast with the negative strange sea polarization deduced from inclusive polarized deep inelastic scattering.