The three-gluon glueball states are studied with the generalization of a semirelativistic potential model giving good results for two-gluon glueballs. The Hamiltonian depends only on 3 parameters fixed on two-gluon glueball spectra: the strong coupling constant, the string tension, and a gluon size which removes singularities in the potential. The Casimir scaling determines the structure of the confinement. Our results are in good agreement with other approaches and lattice calculation for the odderon trajectory but differ strongly from lattice in the $J^{+-}$ sector. We propose a possible explanation for this problem.

We discuss $Q$-balls in the complex signum-Gordon model in $d$-dimensional space for $d=1$, 2, 3. The $Q$-balls have strictly finite size. Their total energy is a powerlike function of the conserved $U(1)$ charge with the exponent equal to $(d+2)(d+3{)}^{-1}$. In the cases $d=1$ and $d=3$ explicit analytic solutions are presented.

Magnetic fields in Friedmann universes can experience superadiabatic growth without departing from conventional electromagnetism. The reason is the relativistic coupling between vector fields and spacetime geometry, which slows down the decay of large-scale magnetic fields in open universes, compared to that seen in perfectly flat models. The result is a large relative gain in magnetic strength that can lead to astrophysically interesting $B$ fields, even if our Universe is only marginally open today.

We calculate the polarization tensor of charged gluons in a Abelian homogeneous magnetic background field at a finite temperature in one-loop order in Lorentz background field gauge in full generality. Thereby, we first determine the ten independent tensor structures. For the calculation of the corresponding form factors, we use the Schwinger representation and represent form factors as double parametric integrals and a sum resulting from the Matsubara formalism used. The integrands are given explicitly in terms of hyperbolic trigonometric functions. Like in the case of neutral gluons, the polarization tensor is not transversal. Out of the tensor structures, seven are transversal and three are not. The nontransversal part follows explicitly from our calculations.

In this paper, we evaluate the self-energy of the vector mesons at one loop in our recently proposed subtraction scheme for the massive nonlinearly realized SU(2) Yang-Mills theory. We check the fulfillment of physical unitarity. The resulting self-mass can be compared with the value obtained in the massive Yang-Mills theory based on the Higgs mechanism, consisting in extra terms due to the presence of the Higgs boson (tadpoles included). Moreover, we evaluate all the one-loop counterterms necessary for the next order calculations. By construction, they satisfy all the equations of the model (Slavnov-Taylor, local functional equation, and Landau gauge equation). They are sufficient to make all the one-loop amplitudes finite through the hierarchy encoded in the local functional equation.

Gravitational waveforms from the inspiral and ring-down stages of the binary black-hole coalescences can be modeled accurately by approximation/perturbation techniques in general relativity. Recent progress in numerical relativity has enabled us to model also the nonperturbative merger phase of the binary black-hole coalescence problem. This enables us to coherently search for all three stages of the coalescence of nonspinning binary black holes using a single template bank. Taking our motivation from these results, we propose a family of template waveforms which can model the inspiral, merger, and ring-down stages of the coalescence of nonspinning binary black holes that follow quasicircular inspiral. This two-dimensional template family is explicitly parametrized by the physical parameters of the binary. We show that the template family is not only effectual in detecting the signals from black-hole coalescences, but also faithful in estimating the parameters of the binary. We compare the sensitivity of a search (in the context of different ground-based interferometers) using all three stages of the black-hole coalescence with other template-based searches which look for individual stages separately. We find that the proposed search is significantly more sensitive than other template-based searches for a substantial mass range, potentially bringing about remarkable improvement in the event rate of ground-based interferometers. As part of this work, we also prescribe a general procedure to construct interpolated template banks using nonspinning black-hole waveforms produced by numerical relativity.

As predicted by quantum chromodynamics (QCD), at around $T\sim 190\mathrm{MeV}$ in the early Universe, the QCD transition occurs during which the quarks are combined into the massive hadrons. This process reduces the effective relativistic degree of freedom and causes a change in the expansion behavior of the Universe. Similarly, the $e^{+}{e}^{-}$ annihilation occurred around $T\sim 0.5\mathrm{Mev}$ and has the same kind of effect. Besides, the dark energy also drives the present stage accelerating expansion. We study these combined effects on the relic gravitational waves (RGWs). In our treatment, the QCD transition and the $e^{+}{e}^{-}$ annihilation are each, respectively, represented by a short period of expansion inserted into the radiation era. Incorporating these effects, the equation of RGWs is analytically solved for a spatially flat universe, evolving from the inflation up to the current acceleration, and the spectrum of RGWs is obtained, covering the whole range of frequency $>{10}^{-19}\mathrm{Hz}$. It is found that the QCD transition causes a reduction of the amplitude of RGWs by $\sim 20\%$ in the range $>{10}^{-9}\mathrm{Hz}$, and the $e^{+}{e}^{-}$ annihilation causes a reduction of $\sim 10\%$ in the range $>{10}^{-12}\mathrm{Hz}$. In the presence of the dark energy, the combination of the QCD transition and the $e^{+}{e}^{-}$ annihilation causes a larger reduction of the amplitude by $\sim 30\%$ for the range $>{10}^{-9}\mathrm{Hz}$, which covers the bands of operation of LIGO and LISA. By analysis, it is shown that RGWs will be difficult to detect by the present LIGO, but can be tested by LISA for certain inflationary models.

In the mathematically rigorous analysis of semiclassical Einstein equations, the renormalization of the stress-energy tensor plays a crucial role. We address such a topic in the case of a scalar field with both arbitrary mass and coupling with gravity in the hypothesis that the underlying algebraic quantum state is of the Hadamard type. Particularly, if we focus on highly symmetric solutions of the semiclassical Einstein equations, the envisaged method displays a de Sitter-type behavior even without an a priori introduced cosmological constant. As a further novel result, we shall show that these solutions turn out to be stable.

In the scalar-tensor gravitational theories Newton’s constant $G_N$ evolves in the expanding universe. Likewise, it has been speculated that the acceleration scale ${\mathfrak{a}}_0$ in Milgrom’s modified Newtonian dynamics is tied to the scale of the cosmos, and must thus evolve. With the advent of relativistic implementations of the modified dynamics, one can address the issue of variability of the two gravitational “constants” with some confidence. Using TeVeS, the tensor-vector-scalar gravitational theory, as an implementation of Milgrom’s modified Newtonian dynamics, we calculate the dependence of $G_N$ and ${\mathfrak{a}}_0$ on the TeVeS parameters and the coeval cosmological value of its scalar field, ${\varphi }_c$. We find that $G_N$, when expressed in atomic units, is strictly nonevolving, a result fully consistent with recent empirical limits on the variation of $G_N$. By contrast, we find that ${\mathfrak{a}}_0$ depends on ${\varphi }_c$ and may thus vary with cosmological epoch. However, for the brand of TeVeS which seems most promising, ${\mathfrak{a}}_0$ variation occurs on a time scale much longer than Hubble’s, and should be imperceptible back to redshift unity or even beyond it. This is consistent with emergent data on the rotation curves of disk galaxies at significant redshifts.

Cold dark matter may be in a metastable state and decays to other particles with a very long lifetime. If the decaying products of the dark matter are weakly interacting, e.g., neutrinos, then it would have little impact on astrophysical processes and is therefore difficult to observe. However, such a decay would affect the expansion history of the Universe because of the change of the equation of state. We utilize a high-quality type Ia supernovae data set selected from several recent observations and the position of the first peak of the cosmic microwave background angular spectrum given by the Wilkinson Microwave Anisotropy Probe three-year data to constrain the dark matter decay-to-neutrino rate $\Gamma =\alpha {\Gamma }_{\chi }$, where $\alpha$ is the fraction of the rest mass which gets converted to neutrinos, and ${\Gamma }_{\chi }$ is the decay width. We find that ${\Gamma }^{-1}>0.7\times {10}^3\mathrm{Gyr}$ at 95.5% confidence level.

We investigate a scenario where the recently discovered nonthermal hard x-ray emission from the Ophiuchus cluster originates from inverse Compton scattering of energetic electrons and positrons produced in weakly interacting dark matter pair annihilations. We show that this scenario can account for both the x ray and the radio emission, provided the average magnetic field is of the order of $0.1\mu \mathrm{G}$. We demonstrate that Gamma-Ray Large Area Telescope (GLAST) will conclusively test the dark matter annihilation hypothesis. Depending on the particle dark matter model, GLAST might even detect the monochromatic line produced by dark matter pair annihilation into two photons.

The case of a coupling between dark energy and matter [coupled quintessence (CQ)] or gravity [extended quintessence (EQ)] has recently attracted a deep interest and has been widely investigated both in the Einstein and in the Jordan frames (EF, JF), within scalar-tensor theories. Focusing on the simplest models proposed so far, in this paper we study the relation existing between the two scenarios, isolating the Weyl scaling which allows one to express them in the EF and JF. Moreover, we perform a comparative study of the behavior of linear perturbations in both scenarios, which turn out to behave in a markedly different way. In particular, while the clustering is enhanced in the considered CQ models with respect to the corresponding quintessence ones where the coupling is absent and to the ordinary cosmologies with a cosmological constant and cold dark matter ($\Lambda \mathrm{CDM}$), structures in EQ models may grow slower. This is likely to have direct consequences on the inner properties of nonlinear structures, like cluster concentration, as well as on the weak lensing shear on large scales. Finally, we specialize our study for interfacing linear dynamics and N-body simulations in these cosmologies, giving a recipe for the corrections to be included in N-body codes in order to take into account the modifications to the expansion rate, growth of structures, and strength of gravity.

We study the relativistic BCS-BEC crossover within a class of Nambu-Jona-Lasinio type models, including arbitrary Lorentz-scalar pairing channels. Using the mean-field approximation we investigate spectral properties of the collective bosonic excitations in the superfluid phase, with particular attention to the Nambu-Goldstone bosons of the broken symmetry. This is a first step towards a systematic improvement of the mean-field approximation by including the fluctuation effects. The general results are illustrated on pairing in dense two-flavor quark matter—the two-flavor color superconductor.

We consider models of maximal flavor violation, in which a new scalar mediates large $q_3\leftrightarrow q_1$ or $q_3\leftrightarrow q_2$ flavor-changing transitions ($q_i$ is an $i$’th generation quark), while $q_3\leftrightarrow q_3$ transitions are suppressed, e.g., ${\xi }_{31}$, ${\xi }_{13}\sim V_{tb}$ and ${\xi }_{33}\sim V_{td}$, where ${\xi }_{ij}$ are the new scalar couplings to quarks and $V$ is the Cabibbo-Kobayashi-Maskawa matrix. We show that, contrary to the conventional viewpoint, such models are not ruled out by the existing low-energy data on $K^0$, $B^0$ and $D^0$ oscillations and rare $K$ and $B$-decays. We also show that these models of maximal flavor violation can have surprising new signatures at the LHC and the Tevatron.

Quark and lepton flavor signals are studied in four supersymmetric models, namely, the minimal supergravity model, the minimal supersymmetric standard model with right-handed neutrinos, SU(5) supersymmetric grand unified theory with right-handed neutrinos, and the minimal supersymmetric standard model with U(2) flavor symmetry. We calculate $b\to s(d)$ transition observables in $B_d$ and $B_s$ decays, taking the constraint from the $B_s-{\overline{B}}_s$ mixing recently observed at the Tevatron into account. We also calculate lepton flavor violating processes $\mu \to e\gamma$, $\tau \to \mu \gamma$, and $\tau \to e\gamma$ for the models with right-handed neutrinos. We investigate possibilities to distinguish the flavor structure of the supersymmetry breaking sector with use of patterns of various flavor signals which are expected to be measured in experiments such as MEG, LHCb, and a future Super $B$ factory.

We study bounds on Higgs-boson masses from perturbative unitarity in the Georgi-Machacek model, whose Higgs sector is composed of a scalar isospin doublet and a real and a complex isospin triplet field. This model can be compatible with the electroweak precision data without fine-tuning because of the imposed global $SU(2{)}_R$ symmetry in the Higgs potential, by which the electroweak rho parameter is unity at the tree level. All possible two-body elastic-scattering channels are taken into account to evaluate the $S$-wave amplitude matrix, and then the condition of perturbative unitarity is imposed on the eigenvalues to obtain constraint on the Higgs parameters. Masses of all scalar bosons turn out to be bounded from above, some of which receive more strict upper bounds as compared to that in the standard model (712 GeV). In particular, the upper bound of the lightest scalar boson, whatever it would be, is about 270 GeV.

We derive lattice actions for Yang-Mills quantum mechanics for models with $\mathcal{Q}=4$, 8 and 16 supercharges which possess an exact supersymmetry at nonzero lattice spacing. These are obtained by dimensional reduction of twisted versions of the corresponding super Yang-Mills theories in $D=2$, 3 and 4 dimensions.

We consider the reconstruction technique in theories with a single or multiple (phantom and/or canonical) scalar fields. With the help of several examples, it is demonstrated explicitly that the universe expansion history, unifying early-time inflation and late-time acceleration, can be realized in scalar-tensor gravity. This is generalized to the theory of a scalar field coupled nonminimally to the curvature and to a Brans-Dicke-like theory. Different examples of unification of inflation with cosmic acceleration, in which de Sitter, phantom, and quintessence type fields play the fundamental role—in different combinations—are worked out. Specifically, the frame dependence and stability properties of de Sitter space scalar field theory are studied. Finally, for two-scalar theories, the late-time acceleration and early-time inflation epochs are successfully reconstructed, in realistic situations in which the more and more stringent observational bounds are satisfied, using the freedom of choice of the scalar field potential, and of the kinetic factor.

We study the effects of substructure in the Galactic halo on direct detection of dark matter, on searches for energetic neutrinos from weakly interacting massive particles (WIMP) annihilation in the Sun and Earth, and on the enhancement in the WIMP annihilation rate in the halo. Our central result is a probability distribution function (PDF) $P(\rho )$ for the local dark-matter density. This distribution must be taken into account when using null dark-matter searches to constrain the properties of dark-matter candidates. We take two approaches to calculating the PDF. The first is an analytic model that capitalizes on the scale-invariant nature of the structure-formation hierarchy in order to address early stages in the hierarchy (very small scales; high densities). Our second approach uses simulation-inspired results to describe the PDF that arises from lower-density larger-scale substructures which formed in more recent stages in the merger hierarchy. The distributions are skew positive, and they peak at densities lower than the mean density. The local dark-matter density may be as small as 1/10th the canonical value of $\simeq 0.4\mathrm{GeV}{\mathrm{cm}}^{-3}$, but it is probably no less than $0.2\mathrm{GeV}{\mathrm{cm}}^{-3}$.

We compute the two-loop heavy-quark jet function in the heavy-quark limit. This is one of the key ingredients in next-to-next-to-leading order and next-to-next-to-leading-log order computations of the invariant mass distribution of top-jets at a future $e^{+}{e}^{-}$ collider. The shape of the top-invariant mass distribution is affected by large logs which we compute at next-to-next-to-leading-log order. Exploiting the non-Abelian exponentiation theorem, a definition of the top jet mass is given which is transitive and whose renormalization group evolution is determined by the cusp-anomalous dimension to all orders in perturbation theory. Relations of the jet mass to the pole, $\overline{\mathrm{MS}}$, and 1S masses are presented at two-loop order.