In supersymmetric unified theories the dark matter particle can decay, just like the proton, through grand unified interactions with a lifetime of order of $\sim {10}^{26}\sec$. Its decay products can be detected by several experiments—including Fermi, HESS, PAMELA, ATIC, and IceCube—opening our first direct window to physics at the TeV scale and simultaneously at the unification scale $\sim {10}^{16}\mathrm{GeV}$. We consider possibilities for explaining the electron/positron spectra observed by HESS, PAMELA, and ATIC, and the resulting predictions for the gamma-ray, electron/positron, and neutrino spectra as will be measured, for example, by Fermi and IceCube. The discovery of an isotropic, hard gamma ray spectral feature at Fermi would be strong evidence for dark matter and would disfavor astrophysical sources such as pulsars. Substructure in the cosmic ray spectra probes the spectroscopy of new TeV-mass particles. For example, a preponderance of electrons in the final state can result from the lightness of selectrons relative to squarks. Decaying dark matter acts as a sparticle injector with an energy reach potentially higher than the LHC. The resulting cosmic ray flux depends only on the values of the weak and unification scales.

In supersymmetric models extended with an anomalous $U(1{)}_H$ different $R$-parity violating couplings can yield an unstable neutralino. We show that in this context astrophysical and cosmological constraints on neutralino decaying dark matter forbid bilinear $R$-parity breaking neutralino decays and lead to a class of purely trilinear $R$-parity violating scenarios in which the neutralino is stable on cosmological scales. We have found that among the resulting models some of them become suitable to explain the observed anomalies in cosmic-ray electron/positron fluxes.

Screening effects from sea pairs on the quark-antiquark static potential are analyzed phenomenologically from the light-quark to the heavy-quark meson spectra. From the high excited light-quark meson spectrum, a universal form for the screened static potential is proposed. This potential is then successfully applied to heavy quarkonia. Our results suggest the assignment of $X(4260)$ to the $4s$ state of charmonium and the possible existence of a $5s$ bottomonium resonance around 10748 MeV.

We present the first direct determination of the running top-quark mass based on the total cross section of top-quark pair production as measured at the Tevatron. Our theory prediction for the cross section includes various next-to-next-to-leading order QCD contributions, in particular, all logarithmically enhanced terms near threshold, the Coulomb corrections at two loops and all explicitly scale-dependent terms at next-to-next-to-leading order accuracy. The result allows for an exact and independent variation of the renormalization and factorization scales. For Tevatron and LHC we study its dependence on all scales, on the parton luminosity and on the top-quark mass using both the conventional pole mass definition as well as the running mass in the $\overline{\mathrm{MS}}$ scheme. We extract for the top quark an $\overline{\mathrm{MS}}$ mass of $m(\mu =m)={160.0}_{-3.2}^{+3.3}\mathrm{GeV}$, which corresponds to a pole mass of $m_t={168.9}_{-3.4}^{+3.5}\mathrm{GeV}$.

The renormalization-group properties of transverse-momentum dependent parton distribution functions in the light-cone gauge with the Mandelstam-Leibbrandt prescription for the gluon propagator are addressed. An expression for the transverse component of the gauge field at light-cone infinity, which plays a crucial role in the description of the final-/initial-state interactions in the light-cone axial gauge, is obtained. The leading-order anomalous dimension is calculated in this gauge and the relation to the results obtained in other gauges is worked out. It is shown that, using the Mandelstam-Leibbrandt prescription, the ensuing anomalous dimension does not receive contributions from extra rapidity divergences related to a cusped junction point of the Wilson lines.

We present a model for the decay $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$. The weak interaction part of this reaction is described using the effective weak Hamiltonian in the factorization approach. Hadronic final state interactions are taken into account through the $K\pi$ scalar and vector form factors fulfilling analyticity, unitarity, and chiral symmetry constraints. The model has only two free parameters that are fixed from experimental branching ratios. We show that the modulus and phase of the $S$ wave thus obtained agree nicely with experiments up to 1.55 GeV. We perform Monte Carlo simulations to compare the predicted Dalitz plot with experimental analyses. Allowing for a global phase difference between the $S$ and $P$ waves of $-65°$, the Dalitz plot of the $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$ decay, the $K\pi$ invariant mass spectra and the total branching ratio due to $S$-wave interactions are well reproduced.

We discuss the simplest mechanisms for generating neutrino masses at tree level and one loop level. We find a significant number of new possibilities where one can generate neutrino masses at the one-loop level by adding only two new types of representations. These models have renormalizable interactions that automatically conserve baryon number. Adding to the minimal standard model a scalar color octet with $SU(3)\underset{}{\overset{}{⨂}}SU(2)\underset{}{\overset{}{⨂}}U(1)$ quantum numbers, $(8,2,1/2)$, and a fermionic color octet in the fundamental or adjoint representation of $SU(2)$, one can generate neutrino masses in agreement with experiment. Signals at the LHC and constraints from flavor violation are briefly discussed.

The shape of the beta-decay energy distribution is sensitive to the mass of the electron neutrino. Attempts to measure the endpoint shape of tritium decay have so far seen no distortion from the zero-mass form, thus placing an upper limit of $m_{\nu \beta }<2.3\mathrm{eV}$. Here, we show that a new type of electron energy spectroscopy could improve future measurements of this spectrum and therefore of the neutrino mass. We propose to detect the coherent cyclotron radiation emitted by an energetic electron in a magnetic field. For mildly relativistic electrons, like those in tritium decay, the relativistic shift of the cyclotron frequency allows us to extract the electron energy from the emitted radiation. We present calculations for the energy resolution, noise limits, high-rate measurement capability, and systematic errors expected in such an experiment.

We study cosmology of the Einstein-Yang-Mills theory in ten dimensions with a quartic term in the Yang-Mills field strength. We obtain analytically a class of cosmological solutions in which the extra dimensions are static and the scale factor of the four-dimensional Friedmann-Lemaitre-Robertson-Walker metric is an exponential function of time. This means that the model can explain inflation. Then we look for solutions that describe dynamical compactification of the extra dimensions. The effective cosmological constant ${\lambda }_1$ in the four-dimensional universe is determined from the gravitational coupling, ten-dimensional cosmological constant, gauge coupling, and higher derivative coupling. By numerical integration, the solution with ${\lambda }_1=0$ is found to behave as a matter-dominated universe which asymptotically approaches flat space-time, while the solution with a nonvanishing ${\lambda }_1$ approaches de Sitter space-time in the asymptotic future.

In this paper we will implement the inverse seesaw mechanism into the noncommutative framework on the basis of the $AC$ extension of the standard model. The main difference from the classical $AC$ model is the chiral nature of the $AC$ fermions with respect to a $U(1{)}_X$ extension of the standard model gauge group. It is this extension which allows us to couple the right-handed neutrinos via a gauge invariant mass term to left-handed $A$ particles. The natural scale of these gauge invariant masses is of the order of ${10}^{17}\mathrm{GeV}$ while the Dirac masses of the neutrino and the $AC$ particles are generated dynamically and are therefore much smaller ($\sim 1$ to $\sim {10}^6\mathrm{GeV}$). From this configuration, a working inverse seesaw mechanism for the neutrinos is obtained.

We investigate perturbations of the Schwarzschild geometry using a linearization of the Einstein vacuum equations within a Bondi-Sachs, or null cone, formalism. We develop a numerical method to calculate the quasinormal modes, and present results for the case $\ell =2$. The values obtained are different than those of a Schwarzschild black hole, and we interpret them as quasinormal modes of a Schwarzschild white hole.

We use the collision-free Boltzmann equation in Palatini $f(\mathcal{R})$ gravity to derive the virial theorem within the context of the Palatini approach. It is shown that the virial mass is proportional to certain geometrical terms appearing in the Einstein field equations which contributes to gravitational energy and that such geometric mass can be attributed to the virial mass discrepancy in a cluster of galaxies. We then derive the velocity dispersion relation for clusters, followed by the metric tensor components inside the cluster as well as the $f(\mathcal{R})$ Lagrangian in terms of the observational parameters. Since these quantities may also be obtained experimentally, the $f(\mathcal{R})$ virial theorem is a convenient tool to test the viability of $f(\mathcal{R})$ theories in different models. Finally, we discuss the limitations of our approach in light of the cosmological averaging used and questions that have been raised in the literature against such averaging procedures in the context of the present work.

Most numerical models of binary stars—in particular neutron stars in compact binaries—assume the companions to be either corotational or irrotational. Either one of these assumptions leads to a significant simplification in the hydrodynamic equations of stationary equilibrium. In this paper we develop a new formalism for the construction of binary stars with circulation intermediate between corotational and irrotational. Generalizing the equations for irrotational flow we cast the Euler equation, which is an algebraic equation in the case of corotational or irrotational fluid flow, as an elliptic equation for a new auxiliary quantity. We also suggest a parametrized decomposition of the fluid flow that allows for a variation of the stellar circulation.

Recent results from the PAMELA experiment indicate an excess in the positron spectrum above 10 GeV, but antiproton data are consistent with the expected astrophysical backgrounds. We propose a scenario that reproduces these features. Dark matter annihilates through channels involving a new heavy vectorlike lepton which then decays by mixing with standard model leptons. If charged, this heavy lepton might be produced at the LHC, and could lead to multilepton final states or to long-lived charged tracks. Large neutrino detectors such as ANTARES or IceCube might be sensitive to a monochromatic neutrino line. This scenario may be simply embedded in various models, including an extension to the next-to-minimal supersymmetric standard model.

We present a detailed study of the cosmological evolution in general vector-tensor theories of gravity without potential terms. We consider the evolution of the vector field throughout the expansion history of the Universe and carry out a classification of models according to the behavior of the vector field in each cosmological epoch. We also analyze the case in which the Universe is dominated by the vector field, performing a complete analysis of the system phase map and identifying those attracting solutions which give rise to accelerated expansion. Moreover, we consider the evolution in a universe filled with a pressureless fluid in addition to the vector field and study the existence of attractors in which we can have a transition from matter domination to vector domination with accelerated expansion so that the vector field may play the role of dark energy. We find that the existence of solutions with late-time accelerated expansion is a generic prediction of vector-tensor theories and that such solutions typically lead to the presence of future singularities. Finally, limits from local gravity tests are used to get constraints on the value of the vector field at small (Solar System) scales.

It has been shown that black holes would have formed in the early Universe if, on any given scale, the spectral amplitude of the cosmic microwave background exceeds ${\mathcal{P}}_{\zeta }\sim {10}^{-4}$. This value is within the bounds allowed by astrophysical phenomena for the small scale spectrum of the cosmic microwave background, corresponding to scales which exit the horizon at the end of slow-roll inflation. Previous work by Kohri et al. (2007) showed that for black holes to form from a single field model of inflation, the slope of the potential at the end of inflation must be flatter than it was at horizon exit. In this work we show that a phenomenological hilltop model of inflation, satisfying the Kohri et al. criteria, could lead to the production of black holes, if the power of the inflaton self-interaction is less than or equal to 3, with a reasonable number or $e$-folds. We extend our analysis to the running mass model, and confirm that this model results in the production of black holes, and by using the latest WMAP year 5 bounds on the running of the spectral index, and the black hole constraint we update the results of Leach et al. (2000) excluding more of parameter space.

We show that within the class of $f(R)$ gravity theories, Friedmann-Lemaître-Robertson-Walker power-law perfect fluid solutions only exist for $R^n$ gravity. This significantly restricts the set of exact cosmological solutions which have similar properties to what is found in standard general relativity.

The Dine-Seiberg-Thomas model (DSTM) is the simplest version of the new physics beyond the minimal supersymmetric standard model (MSSM), in the sense that its Higgs sector has just two dimension-five operators, which are obtained from the power series of the energy scale for the new physics in the effective action analysis. We study the possibility of spontaneous $CP$ violation in the Higgs sector of the DSTM, which consists of two Higgs doublets. We find that the $CP$ violation may be triggered spontaneously by a complex phase, obtained as the relative phase between the vacuum expectation values of the two Higgs doublets. At the tree level, for a reasonably established parameter region, the masses of the three neutral Higgs bosons and their corresponding coupling coefficients to a pair of $Z$ bosons in the DSTM are calculated such that the results are inconsistent with the experimental constraint by the LEP data. Thus, the LEP2 data exclude the possibility of spontaneous $CP$ violation in the DSTM at the tree level. On the other hand, we find that, for a wide area in the parameter region, the $CP$ symmetry may be broken spontaneously in the Higgs sector of the DSTM at the one-loop level, where top quark and scalar top quark loops are taken into account. The upper bound on the radiatively corrected mass of the lightest neutral Higgs boson of the DSTM is about 87 GeV, in the spontaneous $CP$ violation scenario. We confirm that the LEP data does not exclude this numerical result.

We propose a group theoretical method to study Isgur-Wise (IW) functions. A current matrix element splits into a heavy quark matrix element and an overlap of the initial and final clouds, related to the IW functions, that contain the long distance physics. The light cloud belongs to the Hilbert space of a unitary representation of the Lorentz group. Decomposing into irreducible representations one obtains the IW function as an integral formula, superposition of irreducible IW functions with positive measures, providing positivity bounds on its derivatives. Our method is equivalent to the sum rule approach, but sheds another light on the physics and summarizes and gives all its possible constraints. We expose the general formalism, thoroughly applying it to the case $j=0$ for the light cloud, relevant to the semileptonic decay ${\Lambda }_b\to {\Lambda }_c\ell {\overline{\nu }}_{\ell }$. In this case, the principal series of the representations contribute, and also the supplementary series. We recover the bound for the curvature of the $j=0$ IW function ${\xi }_{\Lambda }(w)$ that we did obtain from the sum rule method, and we get new bounds for higher derivatives. We demonstrate also that if the lower bound for the curvature is saturated, then ${\xi }_{\Lambda }(w)$ is completely determined, given by an explicit elementary function. We give criteria to decide if any Ansatz for the Isgur-Wise function is compatible or not with the sum rules. We apply the method to some simple model forms proposed in the literature. Dealing with a Hilbert space, the sum rules are convergent, but this feature does not survive hard gluon radiative corrections.

We study the photoabsorption reaction and real Compton scattering within the color dipole model. We rely on a photon wave function derived in the instanton-vacuum model and on the energy-dependent phenomenological elastic dipole amplitude. Data for the photoabsorption cross section at high energies agree with our parameter-free calculations. We also provide predictions for the differential real Compton scattering cross section. Although no data for small angle Compton scattering are available so far, this process can be measured in ultraperipheral hadronic and nuclear collisions at the LHC.