We report on an all-sky search for periodic gravitational waves in the frequency band 50–800 Hz and with the frequency time derivative in the range of 0 through $-6\times {10}^{-9}\mathrm{Hz}/\mathrm{s}$. Such a signal could be produced by a nearby spinning and slightly nonaxisymmetric isolated neutron star in our Galaxy. After recent improvements in the search program that yielded a $10\times$ increase in computational efficiency, we have searched in two years of data collected during LIGO’s fifth science run and have obtained the most sensitive all-sky upper limits on gravitational-wave strain to date. Near 150 Hz our upper limit on worst-case linearly polarized strain amplitude $h_0$ is $1\times {10}^{-24}$, while at the high end of our frequency range we achieve a worst-case upper limit of $3.8\times {10}^{-24}$ for all polarizations and sky locations. These results constitute a factor of 2 improvement upon previously published data. A new detection pipeline utilizing a loosely coherent algorithm was able to follow up weaker outliers, increasing the volume of space where signals can be detected by a factor of 10, but has not revealed any gravitational-wave signals. The pipeline has been tested for robustness with respect to deviations from the model of an isolated neutron star, such as caused by a low-mass or long-period binary companion.

We show that the running of operators which mix under renormalization can be computed fully nonperturbatively as a product of continuum step-scaling matrices. These step-scaling matrices are obtained by taking the “ratio” of $Z$ matrices computed at different energies in an RI-MOM type scheme for which twisted boundary conditions are an essential ingredient. Our method allows us to relax the bounds of the Rome-Southampton window. We also explain why such a method is important in view of the light quark physics program of the RBC-UKQCD Collaborations. To illustrate our method, using $n_f=2+1$ domain-wall fermions, we compute the nonperturbative running matrix of four-quark operators needed in $K\to \pi \pi$ decay and neutral kaon mixing. Our results are then compared to perturbation theory.

We investigate the effect of intermediate charmed meson loops on the $M1$ radiative decays $J/\psi \to {\eta }_c\gamma$ and ${\psi }^{\prime }\to {\eta }_c^{(\prime )}\gamma$ as well as the isospin [$SU(3)$] violating hadronic decays ${\psi }^{\prime }\to J/\psi {\pi }^0(\eta )$ using heavy hadron chiral perturbation theory . The calculations include tree level as well as one loop diagrams and are compared to the latest data from CLEO and BES-III. Our fit constrains the couplings of $1S$ and $2S$ charmonium multiplets to charmed mesons, denoted $g_2$ and $g_2^{\prime }$, respectively. We find that there are two sets of solutions for $g_2$ and $g_2^{\prime }$. One set, which agrees with previous values of the product $g_2{g}_2^{\prime }$ extracted from analyses that consider only loop contributions to ${\psi }^{\prime }\to J/\psi {\pi }^0(\eta )$, can only fit data on radiative decays with fine-tuned cancellations between tree level diagrams and loops in that process. The other solution for $g_2$ and $g_2^{\prime }$ leads to couplings that are smaller by a factor of 2.3. In this case tree level and loop contributions are of comparable size and the numerical values of the tree level contributions to radiative decays are consistent with estimates based on the quark model as well as nonrelativistic QCD. This result shows that tree level heavy hadron chiral perturbation theory couplings are as important as the one loop graphs with charmed mesons in these charmonium decays. The couplings $g_2$ and $g_2^{\prime }$ are also important for the calculations of the decays of charmed meson bound states, such as the $X(3872)$, to conventional charmonia.

The usual mathematical formalism of quantum field theory is not rigorous because it contains divergences that can only be renormalized by nonrigorous mathematical methods. So we present a method of subtraction of divergences using the formalism of decoherence. This is achieved by replacing the standard renormalization method by a projector on a well defined Hilbert subspace. In this way a list of problems of the standard formalism disappears while the physical results of quantum field theory remain valid. From its own nature, this formalism can be also used in nonrenormalizable theories.

We study the wave equation of a massive vector boson in the background of a $D$-dimensional Schwarzschild black hole. The mass term introduces a coupling between two physical degrees of freedom of the field, and we solve the resulting system of ordinary differential equations numerically, without decoupling. We show how to define decoupled transmission factors from an $\mathbf{S}$ matrix and compute them for various modes, masses, and space-time dimensions. The mass term lifts the degeneracy between transverse modes, in $D=4$, and excites the longitudinal modes, in particular, the $s$ wave. Moreover, it increases the contribution of waves with larger $\ell$, which can be dominant at intermediate energies. The transmission factors are then used to obtain the Hawking fluxes in this channel. Our results alert for the importance of modeling the longitudinal modes correctly, instead of treating them as decoupled scalars as they are in current black hole event generators; thus, they can be used to improve such generators for phenomenological studies of TeV gravity scenarios.

It has been known for a long time that Einstein’s field equations when projected onto a black hole horizon look very similar to a Navier-Stokes equation in suitable variables. More recently, it was shown that the projection of Einstein’s equation onto any null surface in any spacetime reduces exactly to the Navier-Stokes form when viewed in the freely falling frame. We develop an action principle, the extremization of which leads to the above result, in an arbitrary spacetime. The degrees of freedom varied in the action principle are the null vectors in the spacetime and not the metric tensor. The same action principle was introduced earlier in the context of the emergent gravity paradigm wherein it was shown that the corresponding Lagrangian can be interpreted as the entropy density of spacetime. The current analysis strengthens this interpretation and reinforces the idea that field equations in gravity can be thought of as emergent. We also find that the degrees of freedom on the null surface are equivalent to a fluid with equation of state $PA=TS$. We demonstrate that the same relation arises in the context of a spherical shell collapsing to form a horizon.

We examine numerically the post-merger regime of two nonspining holes in non-head-on collisions in the realm of nonaxisymmetric Robinson-Trautman spacetimes. Characteristic initial data for the system are constructed and evolved via the Robinson-Trautman equation. The numerical integration is performed using a Galerkin spectral method which is sufficiently stable to reach the final configuration of the remnant black hole, when the gravitational wave emission ceases. The initial data contains three independent parameters, the ratio mass $\alpha$ of the individual colliding black holes, their initial premerger infalling velocity and the incidence angle of collision ${\rho }_0$. The remnant black hole is characterized by its final boost parameter, rest mass and scattering angle. The motion of the remnant black hole is restricted to the plane determined by the directions of the two initial colliding black holes, characterizing a planar collision. The net momentum fluxes carried out by gravitational waves are confined to this plane. We evaluate the efficiency of mass-energy extraction, the total energy and momentum carried out by gravitational waves and the momentum distribution of the remnant black hole for a large domain of initial data parameters. Our analysis is based on the Bondi-Sachs four-momentum conservation laws. The process of mass-energy extraction is shown to be less efficient as the initial data departs from the head-on configuration. Head-on collisions (${\rho }_0=0^o$) and orthogonal collisions (${\rho }_0=90°$) constitute, respectively, upper and lower bounds to the power emission and to the efficiency of mass-energy extraction. On the contrary, head-on collisions and orthogonal collisions constitute, respectively, lower and upper bounds for the momentum of the remnant. Distinct regimes of gravitational wave emission (bursts or quiescent emission) are characterized by the analysis of the time behavior of the gravitational wave power as a function of $\alpha$. In particular, the net gravitational wave flux is nonzero for equal-mass colliding black holes in non-head-on collisions. The momentum extraction and the patterns of the momentum fluxes, as a function of the incidence angle, are examined. The relation between the incidence angle and the scattering angle closely approximates a relation for the inelastic collision of classical particles in Newtonian dynamics.

A master equation for the evolution of a two-dimensional universe is derived based on the simplicial quantum gravity regarding the evolution as the Markov process of a space-time lattice. Three typical phases, expanding, elongating, and collapsing phase, which have been found in the numerical simulation, are studied together with their boundaries, analytically. Asymptotic solutions of the evolution equation for statistical quantities, such as the averaged area, the boundary length, correlations of their fluctuations, are obtained for each phase and boundary. After introducing a physical time, the cosmological significance of each phase is discussed.

Several recent studies have shown how to properly calculate the observed clustering of galaxies in a relativistic context, and uncovered corrections to the Newtonian calculation that become significant on scales near the horizon. Here, we retrace these calculations and show that, on scales approaching the horizon, the observed galaxy power spectrum depends strongly on which gauge is assumed to relate the intrinsic fluctuations in galaxy density to matter perturbations through a linear bias relation. Starting from simple physical assumptions, we derive a gauge-invariant expression relating galaxy density perturbations to matter density perturbations on large scales, and show that it reduces to a linear bias relation in a synchronous-comoving gauge, corroborating an assumption made in several recent papers. We evaluate the resulting observed galaxy power spectrum, and show that it leads to corrections similar to an effective non-Gaussian bias corresponding to a local $f_{\mathrm{NL},\mathrm{eff}}\lesssim 0.5$. This number can serve as a guideline as to which surveys need to take into account relativistic effects. We also discuss the scale-dependent bias induced by primordial non-Gaussianity in the relativistic context, which again is simplest in a synchronous-comoving gauge.

We study the observational constraints for the axion models in string theory which can successfully act as quintessence. The evolution of the universe in this model is sensitive to the initial value of the axion field. This initial value of the axion field controls deviation of the cosmic evolution from the $\Lambda \mathrm{CDM}$ behavior. We use the recent Union2 Supernova Type Ia dataset as well as the data from BAO measurements, the WMAP measurement of the shift parameter and the $H(z)$ measurements. Using these data, we show that the reconstructed equation of state of the axion field has extremely small deviation from the cosmological constant $\omega =-1$ even at $2\sigma$ confidence level. Another interesting outcome of this analysis is that one can put bound on the supersymmetry (SUSY) breaking scale using cosmological measurements assuming the values of different string related parameters and vice versa.

The calculation of scattering amplitudes in Yang-Mills theory at loop level is important for the analysis of background processes at particle colliders as well as our understanding of perturbation theory at the quantum level. We present tools to derive relations for especially one-loop amplitudes, as well as several explicit examples for gauge theory coupled to a wide variety of matter. These tools originate in certain scaling behavior of permutation and cyclic sums of Yang-Mills tree amplitudes and loop integrands. In the latter case evidence exists for relations at all loop orders.

We study the $Z{a}_1$ decay mode of a heavy $CP$-even Higgs boson of the NMSSM, $h_2$, where $a_1$ is the lightest $CP$-odd Higgs state of this scenario, the former Higgs state produced in association with a bottom-antibottom pair, and find that, despite small event rates, a significant (in fact essentially background free) signal should be extractable at the LHC with very high luminosity, so long as a $Z\to jj$ (where $j$ represents a jet) and $a_1\to {\tau }^{+}{\tau }^{-}$ final state is exploited, in the presence of $b$ tagging.

The platinum channel (${\nu }_e$ or ${\overline{\nu }}_e$ appearance) has been proposed at neutrino factories as an additional channel that could help in lifting degeneracies and improving sensitivities to neutrino oscillation parameters, viz., ${\theta }_{13}$, ${\delta }_{CP}$, mass hierarchy, deviation of ${\theta }_{23}$ from maximality and its octant. This channel corresponds to ${\nu }_{\mu }\to {\nu }_e$ (${\overline{\nu }}_{\mu }\to {\overline{\nu }}_e$) oscillations of the initial neutrino flux, with the subsequent detection of electrons (positrons) from charged current interactions of the ${\nu }_e$ (${\overline{\nu }}_e$) in the detector. For small values of ${\theta }_{13}$, the dominant ${\nu }_{\mu }\to {\nu }_{\tau }$ (${\overline{\nu }}_{\mu }\to {\overline{\nu }}_{\tau }$) oscillation results in this signal being swamped by electrons arising from the leptonic decay of taus produced in charge-current interactions of ${\nu }_{\tau }$ (${\overline{\nu }}_{\tau }$) with the detector. We examine for the first time the role of this tau contamination to the electron events sample and find that it plays a significant role in the platinum channel compared to other channels, not only at high-energy neutrino factories but surprisingly even at low energy neutrino factories. Even when the platinum channel is considered in combination with other channels such as the golden (muon appearance) or muon disappearance channel, the tau contamination results in a loss in precision of the measured parameters.

The amplitude for Higgs decay to two photons is calculated in renormalizable and unitary gauges using dimensional regularization at intermediate steps. The result is finite, gauge independent, and in agreement with previously published results. The large Higgs mass limit is examined using the Goldstone-boson equivalence theorem as a check on the use of dimensional regularization and to explain the absence of decoupling.

We investigate the temporal Wilson loop using the Hamiltonian approach to Yang-Mills theory. In simple cases such as the Abelian theory or the non-Abelian theory in ($1+1$) dimensions, the known results can be reproduced using unitary transformations to take care of time evolution. We show how Coulomb gauge can be used for an alternative solution if the exact ground state wave functional is known. In the most interesting case of Yang-Mills theory in ($3+1$) dimensions, the vacuum wave functional is not known, but recent variational approaches in Coulomb gauge give a decent approximation. We use this formulation to compute the temporal Wilson loop and find that the Wilson and Coulomb string tension agree within our approximation scheme. Possible improvements of these findings are briefly discussed.

The apparent accelerating expansion of the Universe, determined from observations of distant supernovae, and often taken to imply the existence of dark energy, may alternatively be explained by the effects of a giant underdense void if we relax the assumption of homogeneity on large scales. Recent studies have made use of the spherically symmetric, radially inhomogeneous Lemaître-Tolman-Bondi (LTB) models to derive strong constraints on this scenario, particularly from observations of the kinematic Sunyaev-Zel’dovich effect which is sensitive to large-scale inhomogeneity. However, most of these previous studies explicitly set the LTB “bang time” function to be constant, neglecting an important freedom of the general solutions. Here we examine these models in full generality by relaxing this assumption. We find that although the extra freedom allowed by varying the bang time is sufficient to account for some observables individually, it is not enough to simultaneously explain the supernovae observations, the small-angle CMB, the local Hubble rate, and the kinematic Sunyaev-Zel’dovich effect. This set of observables is strongly constraining, and effectively rules out simple LTB models as an explanation of dark energy.

It has been asserted in the literature that Mathisson’s helical motions are unphysical, with the argument that their radius can be arbitrarily large. We revisit Mathisson’s helical motions of a free spinning particle, and observe that such statement is unfounded. Their radius is finite and confined to the disk of centroids. We argue that the helical motions are perfectly valid and physically equivalent descriptions of the motion of a spinning body, the difference between them being the choice of the representative point of the particle, thus a gauge choice. We discuss the kinematical explanation of these motions, and we dynamically interpret them through the concept of hidden momentum. We also show that, contrary to previous claims, the frequency of the helical motions coincides, even in the relativistic limit, with the zitterbewegung frequency of the Dirac equation for the electron.

A sufficiently light scalar field slowly evolving in a potential can account for the dark energy that presently dominates the Universe. This quintessence field is expected to couple directly to matter components, unless some symmetry of a more fundamental theory protects or suppresses it. Such a coupling would leave distinctive signatures in the background expansion history of the Universe and on cosmic structure formation, particularly at galaxy cluster scales. Using semianalytic expressions for the cold dark matter (CDM) halo mass function, we make predictions for halo abundance in models where the quintessence scalar field is coupled to cold dark matter, for a variety of quintessence potentials. We evaluate the linearly extrapolated density contrast at the redshift of collapse using the spherical collapse model and we compare this result to the corresponding prediction obtained from the nonlinear perturbation equations in the Newtonian limit. For all the models considered in this work, if there is a continuous flow of energy from the quintessence scalar field to the CDM component, then the predicted number of CDM haloes can only lie below that of $\Lambda \mathrm{CDM}$, when each model shares the same cosmological parameters today. In the last stage of our analysis we perform a global MCMC fit to data to find the best fit values for the cosmological model parameters. We find that for some forms of the quintessence potential, coupled dark energy models can offer a viable alternative to $\Lambda \mathrm{CDM}$ in light of the recent detections of massive high-$z$ galaxy clusters, while other models of coupled quintessence predict a smaller number of massive clusters at high redshift compared to $\Lambda \mathrm{CDM}$.

We consider the optical properties of Lindquist-Wheeler (LW) models of the Universe. These models consist of lattices constructed from regularly arranged discrete masses. They are akin to the Wigner-Seitz construction of solid state physics, and result in a dynamical description of the large-scale Universe in which the global expansion is given by a Friedmann-like equation. We show that if these models are constructed in a particular way then the redshifts of distant objects, as well as the dynamics of the global space-time, can be made to be in good agreement with the homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) solutions of Einstein’s equations, at the level of $\lesssim 3\%$ out to $z\simeq 2$. Angular diameter and luminosity distances, on the other hand, differ from those found in the corresponding FLRW models, while being consistent with the “empty beam” approximation, together with the shearing effects due to the nearest masses. This can be compared with the large deviations found from the corresponding FLRW values obtained in a previous study that considered LW models constructed in a different way. We therefore advocate the improved LW models we consider here as useful constructions that appear to faithfully reproduce both the dynamical and observational properties of space-times containing discrete masses.