I present a unified calculation of soft-gluon corrections to hard-scattering cross sections through next-to-next-to-next-to-leading order (NNNLO). Master formulas are derived, from a threshold resummation formalism, that can be applied to total and differential cross sections for hard-scattering processes in hadron colliders. I also present numerical results for charged Higgs production at the LHC where these corrections are large, and for top quark production at the Tevatron where these corrections greatly reduce the scale dependence of the cross section.

A theory of gravity with a generic action functional and minimally coupled to $N$ matter fields has a nontrivial fixed point in the leading large $N$ approximation. At this fixed point, the cosmological constant and Newton’s constant are nonzero and UV relevant; the curvature squared terms are asymptotically free with marginal behavior; all higher order terms are irrelevant and can be set to zero by a suitable choice of cutoff function.

Neutrinoless double beta decay data, together with information on the absolute neutrino masses obtained from the future KATRIN experiment and/or astrophysical measurements, provide a chance to find $CP$ violation in the lepton sector with Majorana neutrinos. We derive and discuss necessary conditions which make discovery of such $CP$ violation possible for the future neutrino oscillation and mass measurements data.

In the finite-temperature Yang-Mills theory we calculate the functional determinant for fermions in the fundamental representation of the $SU(N)$ gauge group in the background of an instanton with nontrivial holonomy at spatial infinity. This object, called the Kraan-van Baal-Lee-Lu caloron, can be viewed as composed of $N$ Bogomolny-Prasad-Sommerfeld monopoles (or dyons). We compute analytically two leading terms of the fermionic determinant at large separations between dyons.

Waves on “commutative” spacetimes like ${\mathbb{R}}^d$ are elements of the commutative algebra $C^0({\mathbb{R}}^d)$ of functions on ${\mathbb{R}}^d$. When $C^0({\mathbb{R}}^d)$ is deformed to a noncommutative algebra ${\mathcal{A}}_{\theta }({\mathbb{R}}^d)$ with deformation parameter $\theta$ (${\mathcal{A}}_0({\mathbb{R}}^d)=C^0({\mathbb{R}}^d)$), waves being its elements, are no longer complex-valued functions on ${\mathbb{R}}^d$. Rules for their interpretation, such as measurement of their intensity, and energy, thus need to be stated. We address this task here. We then apply the rules to interference and diffraction for $d\le 4$ and with time-space noncommutativity. Novel phenomena are encountered. Thus when the time of observation $T$ is so brief that $T\le 2\theta w$, where $w$ is the frequency of incident waves, no interference can be observed. For larger times, the interference pattern is deformed and depends on $\frac{\theta w}{T}$. It approaches the commutative pattern only when $\frac{\theta w}{T}\to 0$. As an application, we discuss interference of starlight due to cosmic strings.

This is the fifth paper in the series devoted to explicit formulation of the rules needed to manage an effective field theory of strong interactions in $S$-matrix sector. We discuss the principles of constructing the meaningful perturbation series and formulate two basic ones: uniformity and summability. Relying on these principles, one obtains the bootstrap conditions which restrict the allowed values of the physical (observable) parameters appearing in the extended perturbation scheme built for a given localizable effective theory. The renormalization prescriptions needed to fix the finite parts of counterterms in such a scheme can be divided into two subsets: minimal, needed to fix the $S$-matrix, and nonminimal, for eventual calculation of Green functions; in this paper we consider only the minimal one. In particular, it is shown that, in theories with the asymptotic behavior governed by known Regge intercepts, the system of independent renormalization conditions only contains those fixing the counterterm vertices with $n\le 3$ lines, while other prescriptions are determined by self-consistency requirements. Moreover, the prescriptions for $n\le 3$ cannot be taken arbitrarily: an infinite number of bootstrap conditions should be respected. The concept of localizability, introduced and explained in this article, is closely connected with the notion of resonance in the framework of perturbative quantum field theory. We discuss this point and, finally, compare the cornerstones of our approach with the philosophy known as “analytic $S$-matrix.”

Using black hole perturbation theory, we calculate the gravitational waves produced by test particles moving on bound geodesic orbits about rotating black holes. The orbits we consider are generic—simultaneously eccentric and inclined. The waves can be described as having radial, polar, and azimuthal “voices,” each of which can be made to dominate by varying eccentricity and inclination. Although each voice is generally apparent in the waveform, the radial voice is prone to overpowering the others. We also compute the radiative fluxes of energy and axial angular momentum at infinity and through the event horizon. These fluxes, coupled to a prescription for the radiative evolution of the Carter constant, will be used in future work to adiabatically evolve through a sequence of generic orbits. This will enable the calculation of inspiral waveforms that, while lacking certain important features, will approximate those expected from astrophysical extreme mass ratio captures sufficiently well to aid development of measurement algorithms on a relatively short time scale.

We present exact solutions of the massless Klein-Gordon equation in a spacetime in which an infinite straight cosmic string resides. The first solution represents a plane wave entering perpendicular to the string direction. We also present and analyze a solution with a static pointlike source. In the short wavelength limit these solutions approach the results obtained by using the geometrical optics approximation: magnification occurs if the observer lies in front of the string within a strip of angular width $8\pi G\mu$, where $\mu$ is the string tension. We find that when the distance from the observer to the string is less than ${10}^{-3}(G\mu {)}^{-2}\lambda \sim 150\mathrm{Mpc}(\lambda /\mathrm{AU})(G\mu /{10}^{-8}{)}^{-2}$, where $\lambda$ is the wavelength, the magnification is significantly reduced compared with the estimate based on the geometrical optics due to the diffraction effect. For gravitational waves from neutron star (NS)-NS mergers the several lensing events per year may be detected by DECihertz interferometer gravitational wave observatory (DECIGO)/big bang observer (BBO).

Measurements of ellipticities of background galaxies are sensitive to the reduced shear, the cosmic shear divided by $(1-\kappa )$ where $\kappa$ is the projected density field. We compute the difference between shear and reduced shear both analytically and with simulations. The difference becomes more important on smaller scales, and will impact cosmological parameter estimation from upcoming experiments. A simple recipe is presented to carry out the required correction.

We study a particular supersymmetric realization of the Peccei-Quinn symmetry which provides a suitable candidate for the curvaton field. The class of models considered also solves the $\mu$ problem, while generating the Peccei-Quinn scale dynamically. The curvaton candidate is a pseudo-Nambu-Goldstone boson corresponding to an angular degree of freedom orthogonal to the axion field. Its order parameter increases substantially following a phase transition during inflation. This results in a drastic amplification of the curvaton perturbations. Consequently, the mechanism is able to accommodate low-scale inflation with Hubble parameter at the TeV scale. Hence, we investigate modular inflation using a string axion field as the inflaton with inflation scale determined by gravity mediated soft supersymmetry breaking. We find that modular inflation with the orthogonal axion as curvaton can indeed account for the observations for natural values of the parameters.

There is good evidence from $N$-body simulations that the velocity distribution in the outer parts of halos is radially anisotropic, with the kinetic energy in the radial direction roughly equal to the sum of that in the two tangential directions. We provide a simple algorithm to generate such cosmologically important distribution functions. Introducing $r_E(E)$, the radius of the largest orbit of a particle with energy $E$, we show how to write down almost trivially a distribution function of the form $f(E,L)=L^{-1}g(r_E)$ for any spherical model—including the “universal” halo density law (Navarro-Frenk-White profile). We in addition give the generic form of the distribution function for any model with a local density power-law index $\alpha$ and anisotropy parameter $\beta$ and provide limiting forms appropriate for the central parts and envelopes of dark matter halos. From those, we argue that, regardless of the anisotropy, the density falloff at large radii must evolve to $\rho \sim r^{-4}$ or steeper ultimately.

We investigate on the lattice the metastable confined phase above $T_c$ in $SU(N)$ gauge theories, for $N=8,10$, and $12$. In particular we focus on the decrease with the temperature of the mass of the lightest state that couples to Polyakov loops. We find that at $T=T_c$ the corresponding effective string tension ${\sigma }_{\mathrm{eff}}(T)$ is approximately half its value at $T=0$, and that as we increase $T$ beyond $T_c$, while remaining in the confined phase, ${\sigma }_{\mathrm{eff}}(T)$ continues to decrease. We extrapolate ${\sigma }_{\mathrm{eff}}(T)$ to even higher temperatures, and interpret the temperature where it vanishes as the Hagedorn temperature $T_H$. For $SU(12)$ we find that $T_H/T_c=1.116(9)$, when we use the exponent of the three-dimensional XY model for the extrapolation, which seems to be slightly preferred over a mean-field exponent by our data.

We extend our previous work [A. Higuchi and G. D. R. Martin, Found. Phys. 35, 1149 (2005)], which compared the predictions of quantum electrodynamics concerning radiation reaction with those of the Abraham-Lorentz-Dirac theory for a charged particle in linear motion. Specifically, we calculate the predictions for the change in position of a charged-scalar particle, moving in three-dimensional space, due to the effect of radiation reaction in the one-photon-emission process in quantum electrodynamics. The scalar particle is assumed to be accelerated for a finite period of time by a three-dimensional electromagnetic potential dependent only on one of the spacetime coordinates. We perform this calculation in the $\hslash \to 0$ limit and show that the change in position agrees with that obtained in classical electrodynamics with the Lorentz-Dirac force treated as a perturbation. We also show for a time-dependent but space-independent electromagnetic potential that the forward-scattering amplitude at order $e^2$ does not contribute to the position change in the $\hslash \to 0$ limit after the mass renormalization is taken into account.

We describe plane-fronted waves in the Yang-Mills type quadratic metric-affine theory of gravity. The torsion and the nonmetricity are both nontrivial, and they do not belong to the triplet ansatz.

We derive an expression for the luminosity distance in a perturbed Friedmann universe. We define the correlation function and the power spectrum of the luminosity distance fluctuations and express them in terms of the initial spectrum of the Bardeen potential. We present semianalytical results for the case of a pure CDM (cold dark matter) universe. We argue that the luminosity distance power spectrum represents a new observational tool which can be used to determine cosmological parameters. In addition, our results shed some light into the debate whether second order small scale fluctuations can mimic an accelerating universe.

We first apply the transformation of mixing azimuthal and internal coordinate or mixing time and internal coordinate to the 11D M-theory with a stack N M2-branes to find the spacetime of a stack of N D2-branes with magnetic or electric flux in 10 D IIA string theory, after the Kaluza-Klein reduction. We then perform the T-duality to the spacetime to find the background of a stack of N D3-branes with magnetic or electric flux. In the near-horizon limit the background becomes the magnetic or electric field deformed $\mathrm{Ad}{\mathrm{S}}_5\times S^5$. We adopt an ansatz to find the classical string solution which is rotating in the deformed $S^5$ with three angular momenta in the three rotation planes. The relations between the classical string energy and its angular momenta are found and results show that the external magnetic and electric fluxes will increase the string energy. Therefore, from the AdS/CFT point of view, the corrections of the anomalous dimensions of operators in the dual SYM theory will be positive. We also investigate the small fluctuations in these solutions and discuss the effects of magnetic and electric fields on the stability of these classical rotating string solutions. Finally, we find the possible solutions of string pulsating on the deformed spacetimes and show that the corrections to the anomalous dimensions of operators in the dual SYM theory are non-negative.

Recently we studied inflation models in which the inflaton potential is characterized by an underlying approximate global symmetry. In the first work we pointed out that in such a model curvature perturbations are generated after the end of the slow-roll phase of inflation. In this work we develop further the observational implications of the model and compute the degree of non-Gaussianity predicted in the scenario. We find that the corresponding nonlinearity parameter, $f_{NL}$, can be as large as ${10}^2$.

High-energy photons from pair annihilation of dark matter particles contribute to the cosmic gamma-ray background (CGB) observed in a wide energy range. Since dark matter particles are weakly interacting, annihilation can happen only in high density regions such as dark matter halos. The precise shape of the energy spectrum of CGB depends on the nature of dark matter particles—their mass and annihilation cross section, as well as the cosmological evolution of dark matter halos. In order to discriminate between the signals from dark matter annihilation and other astrophysical sources, however, the information from the energy spectrum of CGB may not be sufficient. We show that dark matter annihilation not only contributes to the mean CGB intensity, but also produces a characteristic anisotropy, which provides a powerful tool for testing the origins of the observed CGB. We develop the formalism based on a halo model approach to analytically calculate the three-dimensional power spectrum of dark matter clumping, which determines the power spectrum of annihilation signals. We show that the expected sensitivity of future gamma-ray detectors such as the Gamma Ray Large Area Space Telescope (GLAST) should allow us to measure the angular power spectrum of CGB anisotropy, if dark matter particles are supersymmetric neutralinos and they account for most of the observed mean intensity of CGB in GeV region. On the other hand, if dark matter has a relatively small mass, on the order of 20 MeV, and accounts for most of the CGB in MeV region, then the future Advanced Compton Telescope (ACT) should be able to measure the angular power spectrum in MeV region. As the intensity of photons from annihilation is proportional to the density squared, we show that the predicted shape of the angular power spectrum of gamma rays from dark matter annihilation is different from that due to other astrophysical sources such as blazars and supernovae, whose intensity is linearly proportional to density. Therefore, the angular power spectrum of the CGB provides a “smoking-gun” signature of gamma rays from dark matter annihilation. While the mean CGB intensity expected from dark matter halos with smooth density profiles is smaller than observed, the dark matter substructure within halos may provide the origin of additional boost factors for the annihilation signal. Our formalism can be used for any other radiation processes that involve collision of particles.

The non-Abelian Einstein-Born-Infeld-dilaton theory, which rules the dynamics of tensor-scalar gravitation coupled to a $su(2)$-valued gauge field ruled by Born-Infeld Lagrangian, is studied in a cosmological framework. The microscopic energy exchange between the gauge field and the dilaton which results from a nonuniversality of the coupling to gravity modifies the usual behavior of tensor-scalar theories coupled to matter fluids. General cosmological evolutions are derived for different couplings to gravitation and a comparison to universal coupling is highlighted. Evidences of cosmic acceleration are presented when the evolution is interpreted in the Jordan physical frame of a matter respecting the weak equivalence principle. The importance for the mechanism of cosmic acceleration of the dynamics of the Born-Infeld gauge field, the attraction role of the matter fluid, and the nonuniversality of the gravitational couplings are briefly outlined.

The presently accelerating universe may keep accelerating forever, eventually run into the event horizon problem, and thus be in conflict with the superstring idea. On the other hand, the current accelerating phase as well as the fate of the universe may be swayed by a negative cosmological constant, which dictates a big crunch. Based on the current observational data, in this paper we investigate how large the magnitude of a negative cosmological constant is allowed to be. In addition, for distinguishing the sign of the cosmological constant via observations, we point out that a measure of the evolution of the dark energy equation-of-state may be a good discriminator. Hopefully future observations will provide much more detailed information about dark energy and thereby indicate the sign of the cosmological constant as well as the fate of the presently accelerating universe.