The contributions of the cosmological constant to the deflection angle and the time delays are derived from the integration of the gravitational potential as well as from Fermat’s principle. The findings are in agreement with recent results using exact solutions to Einstein’s equations and reproduce precisely the new $\Lambda$ term in the bending angle and the lens equation. The consequences on time-delay expressions are explored. While it is known that $\Lambda$ contributes to the gravitational time delay, it is shown here that a new $\Lambda$ term appears in the geometrical time delay as well. Although these newly derived terms are perhaps small for current observations, they do not cancel out as previously claimed. Moreover, as shown before, at galaxy cluster scale, the $\Lambda$ contribution can be larger than the second-order term in the Einstein deflection angle for several cluster lens systems.

We discuss a little Higgs scenario that introduces below the TeV scale just the two minimal ingredients of these models, a vectorlike $T$ quark and a singlet component (implying anomalous couplings) in the Higgs field, together with a pseudoscalar singlet $\eta$. In the model, which is a variation of Schmaltz’s simplest little Higgs model, all the extra vector bosons are much heavier than the $T$ quark. In the Yukawa sector the global symmetry is approximate, implying a single large coupling per flavor, whereas in the scalar sector it is only broken at the loop level. We obtain the one-loop effective potential and show that it provides acceptable masses for the Higgs $h$ and for the singlet $\eta$ with no need for an extra $\mu$ term. We find that $m_{\eta }$ can be larger than $m_h/2$, which would forbid the (otherwise dominant) decay mode $h\to \eta \eta$.

The suppression of flavor and $CP$ violation in supersymmetric theories may be due to the mechanism responsible for the structure of the Yukawa couplings. We study model independently the compatibility between low-energy flavor and $CP$ constraints and observability of superparticles at the LHC, assuming a generic correlation between the Yukawa couplings and the supersymmetry breaking parameters. We find that the superpotential operators that generate scalar trilinear interactions are generically problematic. We discuss several ways in which this tension is naturally avoided. In particular, we focus on several frameworks in which the dangerous operators are naturally absent. These frameworks can be combined with many theories of flavor, including those with (flat or warped) extra dimensions, strong dynamics, or flavor symmetries. We show that the resulting theories can avoid all the low-energy constraints while keeping the superparticles light. The intergenerational mass splittings among the sfermions can reflect the structure of the underlying flavor theory, and can be large enough to be measurable at the LHC. Detailed observations of the superparticle spectrum may thus provide new handles on the origin of the flavor structure of the standard model.

We perform an extraction of ${\alpha }_s$ based on sum rules involving isovector hadronic $\tau$ decay data. The particular sum rules employed are constructed specifically to suppress contributions associated with poorly known higher dimension condensates, and hence reduce theoretical systematic uncertainties associated with the treatment of such contributions which are shown to be present in earlier related analyses. Running our results from the $n_f=3$ to $n_f=5$ regime we find ${\alpha }_s(M_Z^2)=0.1187\pm 0.0016$, in excellent agreement with the recently updated global fit to electroweak data at the Z scale and other high-scale direct determinations.

The decays of the $X(3872)$ to $P$-wave quarkonia are calculated under the assumption that it is a shallow bound state of neutral charmed mesons. The $X(3872)$ is described using an effective theory of nonrelativistic $D$ mesons and pions (X-EFT). We calculate $X(3872)$ decays by first matching heavy hadron chiral perturbation theory ($\mathrm{HH}\chi \mathrm{PT}$) amplitudes for $D^0{\overline{D}}^{*0}\to {\chi }_{cJ}({\pi }^0,\pi \pi )$ onto local operators in X-EFT, and then using these operators to calculate the $X(3872)$ decays. This procedure reproduces the factorization theorems for $X(3872)$ decays to conventional quarkonia previously derived using the operator product expansion. For single pion decays, we find nontrivial dependence on the pion energy from $\mathrm{HH}\chi \mathrm{PT}$ diagrams with virtual $D$ mesons. This nontrivial energy dependence can potentially modify heavy-quark symmetry predictions for the relative sizes of decay rates. At leading order, decays to final states with two pions are dominated by the final state ${\chi }_{c1}{\pi }^0{\pi }^0$, with a branching fraction just below that for the decay to ${\chi }_{c1}{\pi }^0$. Decays to all other final states with two pions are highly suppressed.

Several models predict the existence of heavy colored resonances decaying to top quarks in the TeV energy range that might be discovered at the CERN LHC. In some of those models, moreover, a sizable charge asymmetry of top versus antitop quarks might be generated. The detection of these exotic resonances, however, requires selecting data samples where the top and the antitop quarks are highly boosted, which is experimentally very challenging. We asses that the measurement of the top quark charge asymmetry at the LHC is very sensitive to the existence of excited states of the gluon with axial-vector couplings to quarks. We use a toy model with general flavor independent couplings, and show that a signal can be detected with relatively not too energetic top and antitop quarks. We also compare the results with the asymmetry predicted by QCD, and show that its highest statistical significance is achieved with data samples of top-antitop quark pairs of low invariant masses.

We calculate the decay rate of bottomonium to two charm-quark jets ${\rm Y}\to c\overline{c}$ at the tree level and one-loop level including color-singlet and color-octet $b\overline{b}$ annihilations. We find that the short-distance coefficient of the color-octet piece is much larger than the color-singlet piece, and that the QCD correction will change the end point behavior of the charm quark jet. The color-singlet piece is strongly affected by the one-loop QCD correction. In contrast, the QCD correction to the color-octet piece is weak. Once the experiment can measure the branching ratio and energy distribution of the two charm-quark jets in the ${\rm Y}$ decay, the result can be used to test the color-octet mechanism or give a strong constraint on the color-octet matrix elements.

$Q$-lumps associated with the noncommutative $\mathbb{C}{P}^N$ model in $2+1$ dimensions are constructed. These are solitonic configurations which are time dependent and rotate with constant angular frequency. Energy of the $Q$-lumps is $E=2\pi k+\alpha |Q|$, and we find that in a regime in which the noncommutativity parameter $\theta$ is related to the moduli determining the size of the lumps, it can be viewed to depend on $\theta$ via the Noether charge $Q$. We present a collective coordinate-type analysis signalling that $\mathbb{C}{P}^1$ $Q$-lumps remain stable under small radiative perturbations.

We study the stability of noncommutative spaces in matrix models and discuss the continuum limit which leads to the noncommutative Yang-Mills theories. It turns out that most noncommutative spaces in bosonic models are unstable. This indicates perturbative instability of fuzzy ${\mathbb{R}}^D$ pointed out by Van Raamsdonk and Armoni et al. persists to nonperturbative level in these cases. In this sense, these bosonic noncommutative Yang-Mills theories are not well-defined, or at least their matrix model formulations studied in this paper do not work. We also show that noncommutative backgrounds are stable in a supersymmetric matrix model deformed by a cubic Myers term, though the deformation itself breaks supersymmetry.

We study the scattering of light (null geodesics) by two fixed extreme Reissner-Nordström black holes, in which the gravitational attraction of their masses is exactly balanced with the electrostatic repulsion of their charges, allowing a static spacetime. We identify the set of unstable periodic orbits that form part of the fractal repeller that completely describes the chaotic escape dynamics of photons. In the framework of periodic orbit theory, the analysis of the linear stability of the unstable periodic orbits is used to obtain the main quantities of chaos that characterize the escape dynamics of the photons scattered by the black holes. In particular, the escape rate that is compared with the result obtained from numerical simulations that consider statistical ensembles of photons. We also analyze the dynamics of photons in the proximity of a perturbed black hole and give an analytic estimate of the escape rate in this system.

We study the semiclassical properties of the Riemannian spin foam models with Immirzi parameter that are constructed via coherent states. We show that, in the semiclassical limit, the quantum spin foam amplitudes of an arbitrary triangulation are exponentially suppressed if the face spins do not correspond to a discrete geometry. When they do arise from a geometry, the amplitudes reduce to the exponential of $\mathrm{i}$ times the Regge action. Remarkably, the dependence on the Immirzi parameter disappears in this limit.

An approximate Foldy-Wouthuysen transformation for the Dirac Hamiltonian in arbitrary weak gravitational fields is constructed, resulting in a series with the expansion parameter $1/m{c}^2$.

We analyze $f(R)$ modifications of Einstein’s gravity as dark energy models in the light of their connection with chameleon theories. Formulated as scalar-tensor theories, the $f(R)$ theories imply the existence of a strong coupling of the scalar field to matter. This would violate all experimental gravitational tests on deviations from Newton’s law. Fortunately, the existence of a matter dependent mass and a thin-shell effect allows one to alleviate these constraints. The thin-shell condition also implies strong restrictions on the cosmological dynamics of the $f(R)$ theories. As a consequence, we find that the equation of state of dark energy is constrained to be extremely close to $-1$ in the recent past. We also examine the potential effects of $f(R)$ theories in the context of the Eöt-wash experiments. We show that the requirement of a thin shell for the test bodies is not enough to guarantee a null result on deviations from Newton’s law. As long as dark energy accounts for a sizeable fraction of the total energy density of the Universe, the constraints that we deduce also forbid any measurable deviation of the dark energy equation of state from $-1$. All in all, we find that both cosmological and laboratory tests imply that $f(R)$ models are almost coincident with a $\Lambda \mathrm{CDM}$ model at the background level.

The phase parameters of matched-filtering searches for continuous gravitational-wave signals are sky position, frequency, and frequency time-derivatives. The space of these parameters features strong global correlations in the optimal detection statistic. For observation times smaller than 1 yr, the orbital motion of the Earth leads to a family of global-correlation equations which describes the “global maximum structure” of the detection statistic. The solution to each of these equations is a different hypersurface in parameter space. The expected detection statistic is maximal at the intersection of these hypersurfaces. The global maximum structure of the detection statistic from stationary instrumental-noise artifacts is also described by the global-correlation equations. This permits the construction of a veto method which excludes false candidate events.

We investigate neutrino emission from gamma-ray bursts (GRBs) under alternative scenarios for prompt emission (the photospheric and synchrotron self-Compton scenarios) rather than the classical optically thin synchrotron scenario. In the former scenario, we find that neutrinos from the $pp$ reaction can be very important at energies $\lesssim (10–100)\mathrm{TeV}$. They may be detected by IceCube/KM3Net and useful as a probe of baryon acceleration around/below the photosphere. In the latter scenario, we may expect $\sim \mathrm{EeV}$ $p\gamma$ neutrinos produced by soft photons. Predicted spectra are different from that in the classical scenario, and neutrinos would be useful as one of the clues to the nature of GRBs (the jet composition, emission radius, magnetic field, and so on).

Low-scale gaugino mediation predicts that gauginos are significantly heavier than scalar superpartners. In order of increasing mass the lightest superpartners are the gravitino, right-handed sleptons, and left-handed sleptons (no light neutralino). This implies that squark decay chains pass through one or more sleptons and typical final states from squark and gluino production at the LHC include multiple leptons. In addition, left-handed staus have large branching fractions into right-handed staus and the Higgs. As an example, we compute the spectrum of low-scale deconstructed gaugino mediation. In this model gauginos acquire masses at tree level at 5 TeV while scalar masses are generated radiatively from the gaugino masses.

We develop the formalism for the evaluation of density-density correlators in lattice QCD that includes techniques for the computation of the all-to-all propagators involved. A novel technique in this context is the implementation of the one-end trick in the meson sector. Density-density correlators provide a gauge invariant definition for the hadron wave function and yield information on hadron deformation. We evaluate density-density correlators using two degenerate flavors of dynamical Wilson fermions for the pion, the rho meson, the nucleon, and the $\Delta$. Using the one-end trick we obtain results that clearly show deformation of the rho meson.

In this paper, we study the effects of the unparticles on the parity violating asymmetry for the low energy electron-electron scattering, $e^{-}{e}^{-}\to e^{-}{e}^{-}$. Using the data from the E158 experiment at SLAC we extract the limits on the unparticle coupling ${\lambda }_{\mathrm{AV}}$, and on the energy scale $\Lambda$ at 95% C.L. for various values of the scaling dimension $d$.

We perform a systematic study of the masses of charmed and bottom baryons in the framework of the QCD sum rule approach. Contributions of the operators up to dimension six are included in operator product expansion. The resulting heavy baryon masses from the calculations are well consistent with the experimental values, and predictions to the spectroscopy of the unobserved bottom baryons are also presented.

The Hawking-Moss tunneling rate for a field described by the Dirac-Born-Infeld (DBI) action is calculated using a stochastic approach. We find that the effect of the nontrivial kinetic term is to enhance the tunneling rate, which can be exponentially significant. This result should be compared to the DBI enhancement found in the Coleman-de Luccia case.