We consider the evolution of the orbit of a spinning compact object in a quasicircular, planar orbit around a Schwarzschild black hole in the extreme mass ratio limit. We compare the contributions to the orbital evolution of both spin-orbit coupling and the local self-force. Making assumptions about the behavior of the forces, we suggest that the decay of the orbit is dominated by the radiation reaction, and that the conservative effect is typically dominated by the spin force. We propose that a reasonable approximation for the gravitational waveform can be obtained by ignoring the local self-force, for adjusted values of the parameters of the system. We argue that this approximation will only introduce small errors in the astronomical determination of these parameters.

Since a positive future detection of nonlinearity in the cosmic microwave background anisotropy pattern might allow us to descriminate among different mechanisms giving rise to cosmological adiabatic perturbations, we study the evolution of the second-order cosmological curvature perturbation on superhorizon scales in the curvaton scenario. We provide the exact expression for the non-Gaussianity in the primordial perturbations including gravitational second-order corrections which are particularly relevant in the case in which the curvaton dominates the energy density before it decays. As a by-product, we show that in the standard scenario where cosmological curvature perturbations are induced by the inflaton field, the second-order curvature perturbation is conserved even during the reheating stage after inflation.

In a previous work, we proposed a new test of general relativity (GR) based on a general deflection formula which applies to all values of asymptotic speed $V_{\infty }(0\mathrm{}<~V_{\infty }<~1).$ The formula simplifies to Einstein’s light deflection result when $V_{\infty }=1.\mathrm{}$ At low velocity, the general deflection equation reduces to the classical Newtonian contribution along with additional terms which contain the GR effect. A spacecraft, such as the proposed interstellar mission which involves a close pass of the Sun, can be used to exaggerate the GR effect so that it can be accurately measured. In this paper we provide a detailed derivation of the general deflection equation, expressed in terms of the parametrized post-Newtonian constants $\beta$ and $\gamma .$ The resulting formula demonstrates that by measuring spacecraft trajectories we can determine $\beta$ and $\gamma$ independently. We show via a detailed covariance analysis that $\beta$ and $\gamma$ may be determined to a precision of $\sim 4\times {10}^{-5}$ and $\sim 8\times {10}^{-6},$ respectively, using foreseeable improvements in spacecraft tracking.

We discuss the onset of the nonlinear regime in the context of unified dark matter models involving a generalized Chaplygin gas. We show that the transition from dark-matter-like to dark-energy-like behavior will never be smooth. In some regions of space the transition will never take place while in others it may happen sooner or later than naively expected. As a result the linear theory used in previous studies may break down late in the matter dominated era even on large cosmological scales. We study the importance of this effect showing that its magnitude depends on the exact form of the equation of state in the low density regime. We expect that our results will be relevant for other unified dark matter scenarios, particularly those where the quartessence candidate is a perfect fluid.

The impact of higher-order final-state photonic corrections on the precise determination of the W-boson mass at the Fermilab Tevatron and CERN LHC colliders is evaluated. In the presence of realistic selection criteria, the shift in the W mass from a fit to the transverse mass distribution is found to be about 10 MeV in the $\overrightarrow{W}\mu \nu$ channel and a few MeV in the $\overrightarrow{W}e\nu$ channel. The calculation, which is implemented in a Monte Carlo event generator for data analysis, can contribute to reduce the uncertainty associated with the W mass measurement at future hadron collider experiments.

In this paper we present a little Higgs model that has custodial $\mathrm{SU}\left(2\right)\mathrm{}$ as an approximate symmetry. This theory is a simple modification of the “minimal moose” model with $\mathrm{SO}\left(5\right)\mathrm{}$ global symmetries protecting the Higgs boson mass. This allows for a simple limit where TeV physics makes small contributions to precision electroweak observables. The spectrum of particles and their couplings to standard model fields are studied in detail. At low energies this model has two Higgs doublets and it favors a light Higgs boson from precision electroweak bounds, though for different reasons than in the standard model. The limit on the breaking scale, f, is roughly 700 GeV, with a top partner of 2 TeV, $W^{\prime }$ and $B^{\prime }$ of 2.5 TeV, and heavy Higgs partners of 2 TeV. These particles are easily accessible at hadron colliders.

In studies of the QCD deconfining phase transition or crossover by means of heavy ion experiments, one ought to be concerned about nonequilibrium effects due to heating and cooling of the system. Motivated by this, we look at hysteresis methods to study the dynamics of phase transitions. Our systems are temperature driven through the phase transition using updating procedures in the Glauber universality class. Hysteresis calculations are presented for a number of observables, including the (internal) energy, properties of Fortuin-Kasteleyn clusters and structure functions. We test the methods for 2D Potts models, which provide a rich collection of phase transitions with a number of rigorously known properties. Comparing with equilibrium configurations we find a scenario where the dynamics of the transition leads to a spinodal decomposition which dominates the statistical properties of the configurations. One may expect an enhancement of low energy gluon production due to spinodal decomposition of the Polyakov loops, if such a scenario is realized by nature.

The scalar isoscalar form factor $\sigma \mathrm{}\left(t\right)\mathrm{}$ of the nucleon is calculated in the limit of a large number of colors in the framework of the chiral quark-soliton model. The calculation is free of adjustable parameters and based on an approximation justified by the small packing fraction of instantons in the QCD vacuum model, from which the chiral quark-soliton model was derived. The result for $\sigma \mathrm{}\left(t\right)\mathrm{}$ reproduces all features of the form factor observed in previous exact numerical calculations in the chiral quark-soliton model and in chiral perturbation theory, and agrees well with the available phenomenological information. The Feynman-Hellmann theorem is used to study the pion mass dependence of the nucleon mass and a good agreement with lattice QCD results is observed. The use of the present method to extrapolate lattice data to the chiral limit is discussed.

We provide a complete and consistent framework to include subasymptotic perturbative as well as mass corrections to the leading twist $(\tau =2)$ evaluation of charged and neutral current weak structure functions and the perturbative neutrino cross sections. We reexamine previous calculations in a modern language and fill in the gaps that we find missing for a complete and ready-to-use “NLO $\xi$-scaling” formulary. In particular, as a new result we formulate the mixing of the partonic and hadronic structure function tensor basis in the operator approach to deep inelastic scattering. As an underlying framework we follow the operator product expansion in the manner of Georgi and Politzer that allows the inclusion of target mass corrections at arbitrary order in QCD and we provide explicit analytical and numerical results at NLO. We compare this approach with a simpler collinear parton model approach to $\xi$ scaling. Along with target mass corrections we include heavy quark mass effects as a calculable leading twist power suppressed correction. The complete corrections have been implemented into a Monte Carlo integration program to evaluate structure functions and/or integrated cross sections. As applications, we compare the operator approach with the collinear approximation numerically and we investigate the NLO and mass corrections to observables that are related to the extraction of the weak mixing angle from a Paschos-Wolfenstein-like relation in neutrino-iron scattering. We expect that the interpretation of neutrino scattering events in terms of oscillation physics and electroweak precision physics will benefit from our results.

The triviality and vacuum stability bounds on the Higgs-boson mass ${(m}_h)$ are reexamined in the presence of weakly coupled new interactions parametrized in a model-independent way by effective operators of dimension 6. The constraints from precision tests of the standard model are taken into account. It is shown that for the scale of new physics in the region $\Lambda \simeq 2–50\mathrm{TeV},$ the standard model triviality upper bound remains unmodified whereas it is natural to expect that the lower bound derived from the requirement of vacuum stability is substantially modified depending on the scale Λ and strength of the coefficients of the effective operators. A natural generalization of the standard triviality condition leads also to a substantial reduction of the allowed region in the $\left(\Lambda {,m}_h\right)$ space.

In the SNO data from its salt run, probably the most significant result is the consistency with the previous results without assuming the ${}^8\mathrm{B}$ energy spectrum. In addition, they have excluded the maximal mixing at a very high confidence level. This has important implications on the double beta decay experiments. For the inverted or degenerate mass spectrum, we find $|〈m_{\nu }{〉}_{\mathrm{ee}}|>0.013\mathrm{}\mathrm{eV}$ at 95% C.L., and the next generation experiments can discriminate Majorana and Dirac neutrinos if the inverted or degenerate mass spectrum will be confirmed by the improvements in cosmology, tritium data beta decay, or long-baseline oscillation experiments.

Within the framework of the covariant formulation of light-front dynamics, we develop a nonperturbative renormalization scheme in the fermion model supposing that the composite fermion is a superposition of the “bare” fermion and a fermion+boson state. We first assume the constituent boson to be spinless. Then we address the case of gauge bosons in the Feynman and in the light-cone gauges. For all these cases the fermion state vector and the necessary renormalization counterterms are calculated analytically. It turns out that, in light-front dynamics, to restore the rotational invariance, an extra counterterm is needed, having no analogue in the Feynman approach. For gauge bosons the results obtained in the two gauges are compared with each other. In general, the number of spin components of the two-body $(\mathrm{fermion}+\mathrm{boson})$ wave function depends on the gauge. But due to the two-body Fock space truncation, only one nonzero component survives for each gauge. And moreover, the whole solutions for the state vector, found for the Feynman and light-cone gauges, are the same (except for the normalization factor). The counterterms are, however, different.

We study the modifications to the real part of the thermal self-energy for chiral fermions in the presence of a constant external hypermagnetic field. We compute the dispersion relation for fermions occupying a given Landau level to first order in $g^{\prime 2},$ $g^2$ and $g_{\phi }^2$ and to all orders in $g^{\prime }B,$ where $g^{\prime }$ and g are the $\mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_Y$ and $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L$ couplings of the standard model, respectively, $g_{\phi }$ is the fermion Yukawa coupling, and B is the hypermagnetic field strength. We show that in the limit where the temperature is large compared to $\sqrt{g^{\prime }B},$ left- and right-handed modes acquire finite and different B-dependent masses due to the chiral nature of their coupling with the external field. Given the current bounds on the strength of primordial magnetic fields, we argue that the above is the relevant scenario to study the effects of magnetic fields on the propagation of fermions prior to and during the electroweak phase transition.

We study the $Z_N$ flux tubes and monopole confinement in deformed $\mathcal{N}{=2\mathrm{}}^{*}$ super Yang-Mills theories. In order to do that we consider an $\mathcal{N}=4\mathrm{}$ super Yang-Mills theory with an arbitrary gauge group G and with the addition of some $\mathcal{N}=2,$ $\mathcal{N}=1,$ and $\mathcal{N}=0\mathrm{}$ deformation terms. We analyze some possible vacuum solutions and phases of the theory, depending on the deformation terms which are added. In the Coulomb phase for the $\mathcal{N}{=2\mathrm{}}^{*}$ theory, G is broken to ${U\left(1\right)\mathrm{}}^r$ and the theory has monopole solutions. Then, by adding some deformation terms, the theory passes to the Higgs or color superconducting phase, in which G is broken to its center $C_G.$ In this phase we construct the $Z_N$ flux tubes ansatz and obtain the BPS string tension. We show that the monopole magnetic fluxes are linear integer combinations of the string fluxes and therefore the monopoles can become confined. Then, we obtain a bound for the threshold length of the string breaking. We also show the possible formation of a confining system with three different monopoles for the $\mathrm{SU}\left(3\right)\mathrm{}$ gauge group. Finally we show that the BPS string tensions of the theory satisfy the Casimir scaling law.

We demonstrate that an equidistant area spectrum for the link variables in loop quantum gravity can reproduce both the thermodynamics and the quasinormal mode properties of black holes.

We study the magnetic braking and viscous damping of differential rotation in incompressible, uniform density stars in general relativity. Differentially rotating stars can support significantly more mass in equilibrium than nonrotating or uniformly rotating stars, according to general relativity. The remnant of a binary neutron star merger or supernova core collapse may produce such a “hypermassive” neutron star. Although a hypermassive neutron star may be stable on a dynamical time scale, magnetic braking and viscous damping of differential rotation will ultimately alter the equilibrium structure, possibly leading to delayed catastrophic collapse. Here we treat the slow-rotation, weak-magnetic field limit in which $E_{\mathrm{rot}}\ll E_{\mathrm{mag}}\ll W,$ where $E_{\mathrm{rot}}$ is the rotational kinetic energy, $E_{\mathrm{mag}}$ is the magnetic energy, and W is the gravitational binding energy of the star. We assume the system to be axisymmetric and solve the magnetohydrodynamics (MHD) equations in both Newtonian gravitation and general relativity. For an initially uniform magnetic field parallel to the rotation axis in which we neglect viscosity, the Newtonian case can be solved analytically, but the other cases we consider require a numerical integration. Toroidal magnetic fields are generated whenever the angular velocity varies along the initial poloidal field lines. We find that the toroidal fields and angular velocities oscillate independently along each poloidal field line, which enables us to transform the original 2+1 equations into 1+1 form and solve them along each field line independently. The incoherent oscillations on different field lines stir up turbulent-like motion in tens of Alfvén time scales (“phase mixing”). In the presence of viscosity, the stars eventually are driven to uniform rotation, with the energy contained in the initial differential rotation going into heat. Our evolution calculations serve as qualitative guides and benchmarks for future, more realistic MHD simulations in full 3+1 general relativity.

We consider the gravitation-dilaton theory (not necessarily exactly solvable), whose potentials represent a generic linear combination of an exponential and linear functions of the dilaton. A black hole, arising in such theories, is supposed to be enclosed in a cavity, where it attains thermal equilibrium, whereas outside the cavity the field is in the Boulware state. We calculate quantum corrections to the Hawking temperature $T_H,$ with the contribution from the boundary taken into account. Vacuum polarization outside the shell tends to cool the system. We find that, for the shell to be in thermal equilibrium, it cannot be placed too close to the horizon. The quantum corrections to the mass due to vacuum polarization vanish in spite of nonzero quantum stresses. We discuss also the canonical boundary conditions and show that accounting for the finiteness of the system plays a crucial role in some theories (e.g., Callan-Giddings-Harvey-Strominger), where it enables us to define the stable canonical ensemble, whereas consideration in an infinite space would predict instability.

We construct two models of the formation of a galaxy with a central black hole, starting from a small initial fluctuation at recombination. This is an application of previously developed methods to find a Lemaître-Tolman model that evolves from a given initial density or velocity profile to a given final density profile. We show that the black hole itself could be either a collapsed object, or a nonvacuum generalization of a full Schwarzschild-Kruskal-Szekeres wormhole. Particular attention is paid to the black hole’s apparent and event horizons.

We investigate the structure of local anomalies of heterotic $E_8\times E_8^{\prime }$ theory on $T^6/Z_4.$ We show that the untwisted states lead to anomalies in 10, four, and in particular six dimensions. At each of the six dimensional fixed spaces of this orbifold the twisted states ensure, that the anomalies factorize separately. As some of these twisted states live on $T^2/Z_2,$ they give rise to four dimensional anomalies as well. At all four dimensional fixed points at worst a single Abelian anomaly can arise. Additionally we show that the anomalies in all these dimensions factorize in a universal way and can be canceled simultaneously.

The retarded electron propagator $S_R{(p}_0,\mathbf{p})$ at high momentum $p\gg T$ was shown by Blaizot and Iancu to be an entire function of complex $p_0.$ In this paper a specific form for $S_R{(p}_0,\mathbf{p})$ is obtained and checked by showing that its temporal Fourier transform $S_R(t,\mathbf{p})$ has the correct behavior at large t. Potential infrared and collinear divergences from the emission of soft photons do not occur.