We apply the technique of Hamiltonian reduction for the construction of three-dimensional $\mathcal{N}=4$ supersymmetric mechanics specified by the presence of a Dirac monopole. For this purpose we take the conventional $\mathcal{N}=4$ supersymmetric mechanics on the four-dimensional conformally-flat spaces and perform its Hamiltonian reduction to three-dimensional system. We formulate the final system in the canonical coordinates, and present, in these terms, the explicit expressions of the Hamiltonian and supercharges. We show that, besides a magnetic monopole field, the resulting system is specified by the presence of a spin-orbit coupling term. A comparision with previous work is also carried out.

We make a detailed study of the moduli space of winding number two ($k=2$) axially symmetric vortices (or equivalently, of coaxial composite of two fundamental vortices), occurring in $U(2)$ gauge theory with two flavors in the Higgs phase, recently discussed by Hashimoto and Tong and by Auzzi, Shifman, and Yung. We find that it is a weighted projective space $W\mathbf{C}{P}_{(2,1,1)}^2\simeq \mathbf{C}{P}^2/{\mathbf{Z}}_2$. This manifold contains an $A_1$-type (${\mathbf{Z}}_2$) orbifold singularity even though the full moduli space including the relative position moduli is smooth. The $SU(2)$ transformation properties of such vortices are studied. Our results are then generalized to $U(N)$ gauge theory with $N$ flavors, where the internal moduli space of $k=2$ axially symmetric vortices is found to be a weighted Grassmannian manifold. It contains singularities along a submanifold.

String models can produce successful inflationary scenarios in the context of brane collisions, and in many of these models cosmic strings may also be produced. In scenarios such as Kachru-Kallosh-Linde-Maldacena-McAllister-Trivedi (KKLMMT) scenario the string contribution is naturally predicted to be well below the inflationary signal for cosmic microwave background (CMB) temperature anisotropies, in agreement with the existing limits. We find that for $B$ type polarization of CMB the situation is reversed and the dominant signal comes from vector modes generated by cosmic strings, which exceeds the gravity wave signal from both inflation and strings. The signal can be detected for a broad range of parameter space; future polarization experiments may be able to detect the string signal down to the string tension $G\mu ={10}^{-9}$, although foregrounds and lensing are likely to worsen these limits. We argue that the optimal scale to search for the string signature is at $\ell \sim 1000$, but in models with high optical depth the signal from reionization peak at large scales is also significant. The shape of the power spectrum allows one to distinguish the string signature from the gravity waves from inflation, but only with a sufficiently high angular resolution experiment.

Light-quark hadronic physics admits two useful systematic expansions, the chiral and $1/N_c$ expansions. Their respective limits do not commute, making such cases where both expansions may be considered to be especially interesting. We first study $\pi N$ scattering lengths, showing that (as expected for such soft-pion quantities) the chiral expansion converges more rapidly than the $1/N_c$ expansion, although the latter nevertheless continues to hold. We also study the Adler-Weisberger and Goldberger-Miyazawa-Oehme sum rules of $\pi N$ scattering, finding that both fail if the large $N_c$ limit is taken prior to the chiral limit.

It is known that Vilenkin’s phenomenological equation of state for static straight cosmic strings is inconsistent with Brans-Dicke theory. We will prove that, in the presence of a cosmological constant, this equation of state is consistent with Brans-Dicke theory. The general solution of the full nonlinear field equations, representing the interior of a cosmic string with a cosmological constant, is also presented.

We derive a new kind of recursion relation to obtain the one-particle-irreducible Feynman diagrams for the effective action. By using this method, we have obtained the graphical representation of the four-loop effective action in the case of the general bosonic field theory which has vertices higher than the four-point vertex.

We present a general description of the propagation properties of quantum gravity modified electrodynamics characterized by constitutive relations up to second order in the correction parameter. The effective description corresponds to an electrodynamics in a dispersive and absorptive nonlocal medium, where the Green functions and the refraction indices can be explicitly calculated. The reality of the electromagnetic field together with the requirement of causal propagation in a given reference frame leads to restrictions in the form of such refraction indices. In particular, absorption must be present in all cases and, contrary to the usual assumption, it is the dominant aspect in those effective models which exhibit linear effects in the correction parameter not related to birefringence. In such a situation absorption is linear while propagation is quadratical in the correction parameter.

In this paper, we investigate the behavior of noncommutative IR divergences and will also discuss their cancellation in the physical cross sections. The commutative IR (soft) divergences existing in the nonplanar diagrams will be examined in order to prove an all-order cancellation of these divergences using the Weinberg’s method. In noncommutative QED, collinear divergences due to triple photon splitting vertex, were encountered, which are shown to be canceled out by the noncommutative version of KLN theorem. This guarantees that there is no mixing between the Collinear, soft divergences and noncommutative IR divergences.

The transition magnetic moments of Majorana neutrinos ${\mu }_{{\nu }_{ij}}$ ($ij=e\mu$, $e\tau$, $\mu \tau$) are calculated in grand unified theory (GUT) constrained Minimal Supersymmetric Standard Model (MSSM) with explicit $R$-parity violation. It is assumed that neutrinos acquire masses via one-loop (quark-squark and lepton-slepton) radiative corrections. The mixing of squarks, sleptons, and quarks is considered explicitly. The connection between ${\mu }_{{\nu }_{ij}}$ and the entries of neutrino mass matrix is studied. The current upper limits on ${\mu }_{{\nu }_{ij}}$ are deduced from the elements of phenomenological neutrino mass matrix, which is reconstructed using the neutrino oscillation data and the lower bound on the neutrinoless double beta decay half-life. Further, the results for ${\mu }_{{\nu }_{e\mu }}$, ${\mu }_{{\nu }_{e\tau }}$ and ${\mu }_{{\nu }_{\mu \tau }}$ are presented for the cases of inverted and normal hierarchy of neutrino masses and different SUSY scenarios. The largest values are of the order of ${10}^{-17}$ in units of Bohr magneton.

We discuss the influence of fixed-target Drell-Yan data on the extraction of parton distribution functions at next-to-next-to-leading order (NNLO) in QCD. When used in a parton distribution fit, the Drell-Yan (DY) data constrain sea quark distributions at large values of Bjorken $x$. We find that not all available DY data are useful for improving the precision of parton distribution functions (PDFs) obtained from a fit to the deep inelastic scattering (DIS) data. In particular, some inconsistencies between DIS-based parton distribution functions and DY data for large values of dilepton rapidity are found. However, by selecting a sample of the DY data that is both representative and consistent with the DIS data, we are able to perform a combined PDF fit that significantly improves the precision of nonstrange quark distributions at large values of $x$. The NNLO QCD corrections to the DY process are crucial for improving the precision. They reduce the uncertainty of the theoretical prediction, making it comparable to the experimental uncertainty in DY cross-sections over a broad range of $x$.

The time dependent neutrino oscillation signals due to the passage of a shock wave through the supernovae are analyzed for the case of three active neutrinos and also for the case that there are two additional sterile neutrinos. It is shown that, even without flavor identification and energy measurement, detailed information about the masses and mixing angles of the neutrinos may be obtained with a detector with excellent time resolution such as IceCube. Such a signal would also give important information about the nature of the shock wave within the supernovae.

The quasielastic weak production of $\Lambda$ and $\Sigma$ hyperons from nucleons and nuclei induced by antineutrinos is studied in the energy region of some ongoing neutrino oscillation experiments in the intermediate energy region. The hyperon-nucleon transition form factors determined from neutrino-nucleon scattering and an analysis of high precision data on semileptonic decays of neutron and hyperons using SU(3) symmetry have been used. The nuclear effects due to Fermi motion and final state interaction effects due to hyperon-nucleon scattering have also been studied. The numerical results for differential and total cross sections have been presented.

We discuss inelastic collisions of two rotating disks by using the conservation laws for baryonic mass and angular momentum. In particular, we formulate conditions for the formation of a new disk after the collision and calculate the total energy loss to obtain upper limits for the emitted gravitational energy.

We conjecture that, in certain cases, quantum dynamics is consistent in the presence of closed timelike curves. We consider time dependent orbifolds of three-dimensional Minkowski space describing, in the limit of large anti-de Sitter (AdS) radius, Bañados, Teitelboim, Zanelli (BTZ) black holes inside the horizon. Although perturbative unitarity fails, we show that, for discrete values of the gravitational coupling, particle propagation is consistent with unitarity. This quantization corresponds to the quantization of the black hole angular momentum, as expected from the dual conformal field theory (CFT) description. Note, however, that we recover this result by analyzing the physics inside the horizon and near the singularity. The space-time under consideration has no AdS boundary, and we are therefore not using any assumption regarding a possible dual formulation. We perform the computation at very low energies, where string effects are irrelevant and interactions are dominated by graviton exchange in the eikonal regime. We probe the noncausal structure of space-time to leading order, but work to all orders in the gravitational coupling.

We analyze the cosmic nongaussianity produced in inflation models with multiple uncoupled fields with monomial potentials, such as Nflation. Using the horizon-crossing approximation to compute the nongaussianity, we show that when each field has the same form of potential, the prediction is independent the number of fields, their initial conditions, and the spectrum of masses/couplings. It depends only on the number of $e$-foldings after the horizon crossing of observable perturbations. We also provide a further generalization to the case where the fields can have monomial potentials with different powers. Unless the horizon-crossing approximation is substantially violated, the predicted nongaussianity is too small to ever be observed.

The power spectrum of a homogeneous and isotropic stochastic variable, characterized by a finite correlation length, does not, in general, vanish on scales larger than the correlation scale. If the variable is a divergence-free vector field, we demonstrate that its power spectrum is blue on large scales. Accounting for this fact, we compute the gravitational waves induced by an incompressible turbulent fluid and by a causal magnetic field present in the early universe. The gravitational wave power spectra show common features: they are both blue on large scales, and they both peak at the correlation scale. However, the magnetic field can be treated as a coherent source and it is active for a long time. This results in a very effective conversion of magnetic energy in gravitational wave energy at horizon crossing. Turbulence instead acts as a source for gravitational waves over a time interval much shorter than a Hubble time, and the conversion into gravitational wave energy is much less effective. We also derive a strong constraint on the amplitude of a primordial magnetic field when the correlation length is much smaller than the horizon.

Using a post-Newtonian diagnostic tool developed by Mora and Will, we examine numerically generated quasiequilibrium initial data sets that have been used in recently successful numerical evolutions of binary black holes through plunge, merger and ringdown. We show that a small but significant orbital eccentricity is required to match post-Newtonian and quasiequilibrium calculations. If this proves to be a real eccentricity, it could affect the fine details of the subsequent numerical evolutions and the predicted gravitational waveforms.

We present the QCD corrections to the processes $p\overline{p}/pp\to e\mu +X$ at the Tevatron and the CERN large hadron collider (LHC). The numerical results show that variation of $K$ factor is in the range between 1.28 (1.32) and 1.79 (1.58) at the Tevatron (LHC). We find that the QCD correction part from the one-loop gluon-gluon fusion subprocess is remarkable at the LHC and should be taken into account.

A definite relative phase and amplitude exists between the doubly-Cabibbo-suppressed amplitude for $D^0\to K^0{M}^0$ and the Cabibbo-favored amplitude for $D^0\to {\overline{K}}^0{M}^0$, where $M^0=({\pi }^0,\eta ,{\eta }^{\prime })$: $A(D^0\to K^0{M}^0)=-{tan}^2{\theta }_{C}A(D^0\to {\overline{K}}^0{M}^0)$. Here ${\theta }_C$ is the Cabibbo angle. This relation, although previously recognized (for $M^0={\pi }^0$) as a consequence of the U-spin subgroup of SU(3), is argued to be less sensitive to corrections involving SU(3) breaking than related U-spin relations involving charged kaons or strange $D$ mesons. A corresponding relation between $D^{+}\to K^0{\pi }^{+}$ and $D^{+}\to {\overline{K}}^0{\pi }^{+}$ is not predicted by U-spin. As a consequence, one expects the asymmetry parameters $R(D^0,M^0)\equiv [\Gamma (D^0\to K_S{M}^0)-\Gamma (D^0\to K_L{M}^0)/[\Gamma (D^0\to K_S{M}^0)+\Gamma (D^0\to K_L{M}^0)]$ each to be equal to $2{tan}^2{\theta }_C=0.106$, in accord with a recent CLEO measurement $R(D^0)\equiv R(D^0,{\pi }^0)=0.122\pm 0.024\pm 0.030$. No prediction for the corresponding ratio $R(D^{+})$ is possible on the basis of U-spin.