A new method of calculation of amplitudes of different processes in quantum electrodynamics is proposed. The method does not use the Feynman technique of trace of product of matrices calculation. The method strongly simplifies calculation of cross sections for different processes. The effectiveness of the method is shown on the cross-section calculation of Coulomb scattering, Compton scattering, and electron-positron annihilation.

Flavor-violating interactions involving new heavy particles are among proposed explanations for the $t\overline{t}$ forward-backward asymmetry observed at the Tevatron. Many of these models generate a $t\overline{t}$-plus-jet signal at the LHC. In this paper, we identify several new charge-asymmetric variables in $t\overline{t}j$ events that can contribute to the discovery of such models at the LHC. We propose a data-driven method for the background, largely eliminating the need for a Monte Carlo prediction of $t\overline{t}$-plus-jets, and thus reducing systematic errors. With a fast detector simulation, we estimate the statistical sensitivity of our variables for one of these models, finding that charge-asymmetric variables could materially assist in the exclusion of the Standard Model (SM) across much of the mass and coupling range, given 5 inverse fb of data. Should any signal appear, our variables will be useful in distinguishing classes of models from one another.

The dimensional reduction of the bosonic sector of five-dimensional minimal supergravity to a Lorentzian four-dimensional spacetime leads to a theory with a massless axion and a dilaton coupled to gravity and two $U(1)$ gauge fields and the dimensionally reduced equations of motion have $SL(2,\mathbb{R})/SO(2)$-duality invariance. In our previous work, utilizing the duality invariance, we formulated solution-generation techniques within five-dimensional minimal supergravity. In this work, by choosing a timelike Killing vector, we consider dimensional reduction to a four-dimensional Euclidean space, in which the field equations have $SL(2,\mathbb{R})/SO(1,1)$ invariance. In the timelike case, we develop a new duality transformation technique, while in the spacelike case we have done that in the previous work. As an example, by applying it to the Rasheed solutions, we obtain rotating Kaluza-Klein black hole solutions in five-dimensional minimal supergravity. In general, in contrast to the spacelike case, the resulting dimensionally reduced solution includes the so-called NUT (Newman, Unti, and Tamburino) parameter, and therefore from a four-dimensional point of view, such a spacetime is not asymptotically flat. However, it is shown that in some special cases, it can describe ordinary Kaluza-Klein black holes.

The retarded Green function for fields propagating on a Schwarzschild black hole space-time possesses a branch cut on the complex-frequency plane. Classically, the branch cut is important, for example, in order to fully determine the response of the black hole to a linear field perturbation. The branch cut is also useful for the calculation of the self-force on a point particle moving in the Schwarzschild background. In this paper we use techniques of analytic continuation to the complex plane of the radial coordinate in order to calculate the branch cut contribution to the Green function in the limit of large imaginary frequency. It is expected that the contribution of this frequency regime to the perturbation response and to the self-force will be mostly for short time intervals. We also determine the highly damped quasinormal mode frequencies for electromagnetic perturbations in Schwarzschild for the first time (previously only the leading imaginary part was known). We find that these frequencies behave like ${\omega }_{\ell n}=-{\displaystyle \frac{in}{2}}-{\displaystyle \frac{i[\ell (\ell +1){]}^2}{2n}}+{\displaystyle \frac{{\pi }^{1/2}(1-i)[\ell (\ell +1){]}^3}{2^{3/2}{n}^{3/2}}}+O(n^{-2})$. The highly damped quasinormal modes are particularly interesting for theories of quantum gravity in that they are believed to probe the small scale structure of the space-time.

In this paper, we present a Lagrangian framework for the description of structure formation in general relativity, restricting attention to irrotational dust matter. As an application we present a self-contained derivation of a general-relativistic analogue of Zel’dovich’s approximation for the description of structure formation in cosmology and compare it with previous suggestions in the literature. This approximation is then investigated: paraphrasing the derivation in the Newtonian framework we provide general-relativistic analogues of the basic system of equations for a single dynamical field variable and recall the first-order perturbation solution of these equations. We then define a general-relativistic analogue of Zel’dovich’s approximation and investigate its implications by functionally evaluating relevant variables, and we address the singularity problem. We so obtain a possibly powerful model that, although constructed through extrapolation of a perturbative solution, can be used to put into practice nonperturbatively, e.g., problems of structure formation, backreaction problems, nonlinear properties of gravitational radiation, and light propagation in realistic inhomogeneous universe models. With this model we also provide the key building blocks for initializing a fully relativistic numerical simulation.

We compute the contribution to the scalar metric perturbations from large-scale magnetic fields which are generated during inflation. We show that apart from the usual passive and compensated modes, the magnetic fields also contribute to the constant mode from inflation. This is different from the causal (post-inflationary) generation of magnetic fields where such a mode is absent and it might lead to significant, non-Gaussian CMB anisotropies.

In this paper we present the connection between scattering amplitudes in momentum space and wave functions in coordinate space, generalizing previous work done for $s$-waves to any partial wave. The relationship to the wave function of the residues of the scattering amplitudes at the pole of bound states or resonances is investigated in detail. A sum rule obtained for the couplings provides a generalization to coupled channels, any partial wave and bound or resonance states, of Weinberg’s compositeness condition, which was only valid for weakly bound states in one channel and $s$-wave. An example, requiring only experimental data, is shown for the $\rho$ meson indicating that it is not a composite particle of $\pi \pi$ and $K\overline{K}$ but something else.

The production of top-antitop pairs at the Fermilab Tevatron shows a forward-backward asymmetry in which the top quark tends to follow the proton direction, while the antitop tends to follow the antiproton direction. The effect grows with increasing effective mass $m_{t\overline{t}}$ of the top-antitop pair, and with increasing rapidity difference between the top and antitop. The observed effect is about 3 times as large as predicted by next-to-leading-order QCD, but with the same sign. An estimate of nonfactorizable effects based on a QCD string picture finds they are negligible, but that small distortions of the $m_t$ spectrum are possible. Tests for such effects, both at and above the level of this estimate, are suggested.

We explore the connection between the strength of the electroweak phase transition and the properties of the Higgs boson. Our interest is in regions of parameter space that can realize electroweak baryogenesis. We do so in a simplified framework in which a single Higgs field couples to new scalar fields charged under $SU(3{)}_c$ by way of the Higgs portal. Such new scalars can make the electroweak phase transition more strongly first-order, while contributing to the effective Higgs boson couplings to gluons and photons through loop effects. For Higgs boson masses in the range $115\mathrm{GeV}\lesssim m_h\lesssim 130\mathrm{GeV}$, whenever the phase transition becomes strong enough for successful electroweak baryogenesis, we find that Higgs boson properties are modified by an amount observable by the LHC. We also discuss the baryogenesis window of the minimal supersymmetric standard model (MSSM), which appears to be under tension. Furthermore, we argue that the discovery of a Higgs boson with standard model-like couplings to gluons and photons will rule out electroweak baryogenesis in the MSSM.

We consider a simplified version of supersymmetric smooth hybrid inflation which contains a single ultraviolet cutoff $m_P=2.4\times {10}^{18}\mathrm{GeV}$, instead of the two cutoffs $m_P$ and $M_{*}\sim \mathrm{\text{few}}\times {10}^{17}\mathrm{GeV}$ that are normally employed. With global supersymmetry the scalar spectral index $n_s\simeq 0.97$, which is in very good agreement with the WMAP observations. With a nonminimal Kähler potential, the supergravity version of the model is compatible with the current central values of $n_s$ and also yields potentially observable gravity waves (tensor to scalar ratio $r\lesssim 0.02$).

We present the extension to four dimensions of a Euclidean two-dimensional model that exhibits spontaneous generation of a metric. In this model gravitons emerge as Goldstone bosons of a global $SO(4)\times GL(4)$ symmetry broken down to $SO(4)$. The microscopic theory can be formulated without having to appeal to any particular space-time metric and only assumes the preexistence of a manifold endowed with an affine connection. In this sense the microscopic theory is quasitopological. There are indications that suggest that the model may be renormalizable, a fact that seems to be due to the impossibility of constructing counterterms without a preexisting metric. The vierbein appears as a condensate of the fundamental fermions defining a vacuum that, if the background affine connection is set to zero, is the Euclidean continuation of de Sitter space-time. If perturbatively small affine connections are introduced on this background, fluctuations of the metric (i.e., gravitons) appear and are described by an effective theory at long distances whose more relevant operators correspond to the Einstein-Hilbert action with a cosmological constant. This effective action is derived in the large $N$ limit, $N$ being the number of fermion species in the fundamental theory. The counterterms required by the microscopic theory are directly related to the cosmological constant and Newton constant and their couplings could eventually be adjusted to the physical values of $M_p$ and $\Lambda$. The relevance of higher-dimensional operators is also briefly discussed.

In order to get a better understanding of holographic properties of gravitational theories with a vanishing cosmological constant, we analyze in detail the relation between asymptotically anti-de Sitter and asymptotically flat spacetimes in three dimensions. This relation is somewhat subtle because the limit of vanishing cosmological constant cannot be naively taken in standard Fefferman-Graham coordinates. After reformulating the standard anti-de Sitter results in Robinson-Trautman coordinates, a suitably modified Penrose limit is shown to connect both asymptotic regimes.

Using the framework of quantum graphity, we construct an explicit model of a quantum foam, a quantum spacetime with spatial nonlocal links. The states depend on two parameters: the minimal size of the link and their density with respect to this length. Macroscopic Lorentz invariance requires that the quantum superposition of spacetimes is suppressed by the length of these nonlocal links. We parametrize this suppression by the distribution of nonlocal links lengths in the quantum foam. We discuss the general case and then analyze two specific natural distributions. Corrections to the Lorentz dispersion relations are calculated using techniques developed in previous work.

Within the gravitational asymptotic safety program, the renormalization group (RG) flow of the $R^2$ truncation in three and four spacetime dimensions is analyzed in detail. In particular, we construct RG trajectories which emanate from the non-Gaussian UV fixed point and possess long classical regimes where the effective average action is well approximated by the classical Einstein-Hilbert action. As an application we study the spectral dimension of the effective quantum Einstein gravity spacetimes resulting from these trajectories, establishing that the picture of a multifractal spacetime is robust under the extension of the truncated theory space. We demonstrate that regimes of constant spectral dimension can either be attributed to universal features of RG fixed points or singular loci in the $\beta$ functions.

We investigate the phenomenological consequences of a modification of the initial state of quantum fluctuations of a single inflationary field. While single-field inflation with the standard Bunch-Davies initial vacuum state does not generally produce a measurable three-point function (bispectrum) in the so-called squeezed triangle configuration (where one wave number, $k$, is much smaller than the other two, $k\ll k_1\approx k_2$), allowing for a nonstandard initial state produces an exception. Here, we calculate the signature of an initial state modification in single-field slow-roll inflation as it would appear in both the scale-dependent bias of the large-scale structure and $\mu$-type distortion in the black-body spectrum of the cosmic microwave background (CMB). We parametrize the initial state modifications and identify certain choices of parameters as natural, though we also note some fine-tuned choices that can yield a larger bispectrum. In both cases, we observe a distinctive $k^{-3}$ signature in large-scale structure (as opposed to the $k^{-2}$ of the so-called local-form bispectrum). As a nonzero bispectrum in the squeezed configuration correlates one long-wavelength mode with two short-wavelength modes, it induces a correlation between the CMB temperature anisotropy observed on large scales with the temperature-anisotropy-squared on very small scales; this correlation persists as the small-scale anisotropy-squared is processed into the $\mu$-type distortion of the black-body spectrum. While the correlation induced by the local-form bispectrum turns out to be too small to detect in near future, a modified initial vacuum state enhances the signal by a large factor owing to an extra factor of $k_1/k$ compared to the local form. For example, a proposed absolutely-calibrated experiment, PIXIE, is expected to detect this correlation with a signal-to-noise ratio greater than 10, for an occupation number of about 0.5 in the observable modes. Relatively-calibrated experiments such as Planck and LiteBIRD should also be able to measure this effect, provided that the relative calibration between different frequencies meets the required precision. Our study suggests that the CMB anisotropy, the distortion of the CMB black-body spectrum, and the large-scale structure of the Universe offer new ways to probe the initial state of quantum fluctuations.

While the baryon asymmetry of the Universe is nowadays well measured by cosmological observations, the bounds on the lepton asymmetry in the form of neutrinos are still significantly weaker. We place limits on the relic neutrino asymmetries using some of the latest cosmological data, taking into account the effect of flavor oscillations. We present our results for two different values of the neutrino mixing angle ${\theta }_{13}$, and show that for large ${\theta }_{13}$ the limits on the total neutrino asymmetry become more stringent, diluting even large initial flavor asymmetries. In particular, we find that the present bounds are still dominated by the limits coming from big bang nucleosynthesis, while the limits on the total neutrino mass from cosmological data are essentially independent of ${\theta }_{13}$. Finally, we perform a forecast for Cosmic Origins Explorer, taken as an example of a future cosmic microwave background experiment, and find that it could improve the limits on the total lepton asymmetry approximately by up to a factor 6.6.

We revisit leptogenesis in the minimal nonsupersymmetric type I seesaw mechanism with two right-handed (RH) neutrinos, including flavor effects and allowing both RH neutrinos $N_1$ and $N_2$ to contribute, rather than just the lightest RH neutrino $N_1$ that has hitherto been considered. By performing scans over parameter space in terms of the single complex angle $z$ of the orthogonal matrix $R$, for a range of leptonic mixing parameters, we find that in regions around $z\sim \pm \pi /2$, for the case of a normal mass hierarchy, the $N_2$ contribution can dominate the contribution to leptogenesis, allowing the lightest RH neutrino mass to be decreased by about an order of magnitude in these regions, down to $M_1\sim 1.3\times {10}^{11}\mathrm{GeV}$ for vanishing initial $N_2$-abundance, with the numerical results supported by analytic estimates. We show that the regions around $z\sim \pm \pi /2$ correspond to light sequential dominance, so the new results in this paper may be relevant to unified model building.

We consider homogeneous Abelian vector fields in an expanding universe. We find a mechanical analogy in which the system behaves as a particle moving in three dimensions under the action of a central potential. In the case of bounded and rapid evolution compared to the rate of expansion, we show—by making use of the virial theorem—that for an arbitrary potential and polarization pattern, the average energy-momentum tensor is always diagonal and isotropic despite the intrinsic anisotropic evolution of the vector field. For simple power-law potentials of the form $V=\lambda (A^{\mu }{A}_{\mu }{)}^n$, the average equation of state is found to be $w=(n-1)/(n+1)$. This implies that vector coherent oscillations could act as natural dark matter or dark energy candidates. Finally, we show that under very general conditions, the average energy-momentum tensor of a rapidly evolving bounded vector field in any background geometry is always isotropic and has the perfect fluid form for any locally inertial observer.

A broad class of scenarios for new physics involving additional strongly interacting fields generically predicts signatures at hadron colliders which consist solely of large numbers of jets and substantial missing transverse energy. In this work, we investigate the prospects for discovery in such scenarios using a search strategy in which jet multiplicity and missing transverse energy are employed as the primary criteria for distinguishing signal from background. We examine the discovery reach this strategy affords in an example theory (a simplified supersymmetric model whose low-energy spectrum consists of a gluino, a light stop, and a light neutralino) and demonstrate that it frequently exceeds the reach obtained via other, alternative strategies.