We develop, test, and compare new numerical and geometrical methods for improving the accuracy of extracting waveforms using characteristic evolution. The new numerical method involves use of circular boundaries to the stereographic grid patches which cover the spherical cross sections of the outgoing null cones. We show how an angular version of numerical dissipation can be introduced into the characteristic code to damp the high frequency error arising form the irregular way the circular patch boundary cuts through the grid. The new geometric method involves use of the Weyl tensor component ${\Psi }_4$ to extract the waveform as opposed to the original approach via the Bondi news function. We develop the necessary analytic and computational formula to compute the $O(1/r)$ radiative part of ${\Psi }_4$ in terms of a conformally compactified treatment of null infinity. These methods are compared and calibrated in test problems based upon linearized waves.

We derive the covariant formalism associated with the relativistic Sunyaev-Zel’dovich effect due to a nonthermal population of high energy electrons in clusters of galaxies. More precisely, we show that the formalism proposed by Wright in 1979, based on an empirical approach to compute the inverse Compton scattering of a population of relativistic electrons on CMB photons, can actually be reinterpreted as a Boltzmann-like equation, in the single scattering approximation.

A phenomenological analysis of the scalar meson $f_0(980)$ is performed that relies on the quasi-two-body decays $D$ and $D_s\to f_0(980)P$, with $P=\pi$, $K$. The two-body branching ratios are deduced from experimental data on $D$ or $D_s\to \pi \pi \pi$, $\overline{K}K\pi$ and from the $f_0(980)\to {\pi }^{+}{\pi }^{-}$ and $f_0(980)\to K^{+}{K}^{-}$ branching fractions. Within a covariant quark model, the scalar form factors for the transitions $D$ and $D_s\to f_0(980)$ are computed. The weak $D$ decay amplitudes, in which these form factors enter, are obtained in the naive factorization approach assuming a $q\overline{q}$ state for the scalar and pseudoscalar mesons. They allow to extract information on the $f_0(980)$ wave function in terms of $u\overline{u}$, $d\overline{d}$, and $s\overline{s}$ pairs as well as on the mixing angle between the strange and nonstrange components. The weak transition form factors are modeled by the one-loop triangular diagram using two different relativistic approaches: covariant light-front dynamics and dispersion relations. We use the information found on the $f_0(980)$ structure to evaluate the scalar and vector form factors in the transitions $D$ and $D_s\to f_0(980)$, as well as to make predictions for $B$ and $B_s\to f_0(980)$, for the entire kinematically allowed momentum range of $q^2$.

We further develop the constrained mass variable techniques to determine the mass scale of invisible particles pair-produced at hadron colliders. We introduce the constrained mass variable $M_{3C}$ which provides an event-by-event lower bound and upper bound to the mass scale given the two mass differences between the lightest three new particle states. This variable is most appropriate for short symmetric cascade decays involving two-body decays and on-shell intermediate states which end in standard-model particles and two dark-matter particles. An important feature of the constrained mass variables is that they do not rely simply on the position of the end point but use the additional information contained in events which lie far from the end point. To demonstrate our method we study the supersymmetric model SPS 1a. We select cuts to study events with two ${\tilde{\chi }}_2^o$ each of which decays to ${\tilde{\chi }}_1^o$, and two opposite-sign same-flavor charged leptons through an intermediate on-shell slepton. We find that with $300{\mathrm{fb}}^{-1}$ of integrated luminosity the invisible-particle mass can be measured to $M_{{\tilde{\chi }}_1^o}=96.4\pm 2.4\mathrm{GeV}$. Combining fits to the shape of the $M_{3C}$ constrained mass variable distribution with the $\max m_{ll}$ edge fixes the mass differences to $\pm 0.2\mathrm{GeV}$.

This paper is devoted to the study of the leading twist distribution amplitudes of $P$-wave nonrelativistic mesons. It is shown that at the leading order approximation in relative velocity of quark-antiquark pair inside the mesons these distribution amplitudes can be expressed through one universal function. As an example, the distribution amplitudes of $P$-wave charmonia mesons are considered. Within QCD sum rules the model for the universal function of $P$-wave charmonia mesons is built. In addition, relations are found between the moments of the universal function and the nonrelativistic QCD matrix elements that control relativistic corrections to any amplitude involving $P$-wave charmonia. Our calculation shows that characteristic size of these corrections is of order of $\sim 30\%$.

The simplest type III seesaw model as originally proposed introduces one lepton triplet. It thus contains four active neutrinos, two massive and two massless at tree level. We determine the radiative masses that the latter receive first at two loops. The masses are generally so tiny that they are definitely excluded by the oscillation data, if the heavy leptons are not very heavy, say, within the reach of the CERN LHC. To accommodate the data on masses, the seesaw scale must be as large as the scale of grand unification. This indicates that the most economical type III model would entail no new physics at low energies beyond the tiny neutrino masses.

The sound mode hydrodynamic dispersion relation is computed up to order $q^3$ for a class of gravitational duals which includes both Schwarzschild AdS and Dp-brane metrics. The implications for second order transport coefficients are examined within the context of Israel-Stewart theory. These sound mode results are compared with previously known results for the shear mode. This comparison allows one to determine the third order hydrodynamic contributions to the shear mode for the class of metrics considered here.

We compare waveforms and orbital dynamics from the first long-term, fully nonlinear, numerical simulations of a generic black-hole binary configuration with post-Newtonian (PN) predictions. The binary has mass ratio $q\sim 0.8$ with arbitrarily oriented spins of magnitude $S_1/m_1^2\sim 0.6$ and $S_2/m_2^2\sim 0.4$ and orbits 9 times prior to merger. The numerical simulation starts with an initial separation of $r\approx 11M$ and orbital parameters determined by 2.5 PN and 3.5 PN evolutions of a quasi-circular binary starting from $r=50M$. The resulting binaries have very little eccentricity according to the 2.5 PN and 3.5 PN systems, but show eccentricities of $e\sim 0.01–0.02$ and $e\sim 0.002–0.005$ in the respective numerical simulations, thus demonstrating that 3.5 PN significantly reduces the eccentricity of the binary compared to 2.5 PN. We perform three numerical evolutions from $r\approx 11M$ with maximum resolutions of $h=M/48$, $M/53.3$, $M/59.3$, to verify numerical convergence. We observe a reasonably good agreement between the PN and numerical waveforms, with an overlap of nearly 99% for the first six cycles of the ($\ell =2$, $m=\pm 2$) modes, 91% for the ($\ell =2$, $m=\pm 1$) modes, and nearly 91% for the ($\ell =3$, $m=\pm 3$) modes. The phase differences between numerical and post-Newtonian approximations appear to be independent of the $(\ell ,m)$ modes considered and relatively small for the first 3–4 orbits. An advantage of the 3.5 PN model over the 2.5 PN one seems to be observed, which indicates that still higher PN order (perhaps even 4.0 PN) may yield significantly better waveforms. In addition, we identify features in the waveforms likely related to precession and precession-induced eccentricity.

Based on a unified quantum field theory of spinors assumed to describe all matter fields and their interactions we construct the space-time structure of general relativity according to a general connection within the corresponding spinor space. The tetrad field and the corresponding metric field are composed from a space-time dependent basis of spinors within the internal space of the fundamental matter field. Similar to twistor theory the Minkowski signature of the space-time metric is related to this spinor nature of elementary matter, if we assume the spinor space to be endowed with a symplectic structure. The equivalence principle and the property of background independence arise from the fact that all elementary fields are composed from the fundamental spinor field. This means that the structure of space-time according to general relativity seems to be a consequence of a fundamental theory of matter fields and not a presupposition as in the usual setting of relativistic quantum field theories.

We present a candidate quantum field theory of gravity with dynamical critical exponent equal to $z=3$ in the UV. (As in condensed-matter systems, $z$ measures the degree of anisotropy between space and time.) This theory, which at short distances describes interacting nonrelativistic gravitons, is power-counting renormalizable in $3+1$ dimensions. When restricted to satisfy the condition of detailed balance, this theory is intimately related to topologically massive gravity in three dimensions, and the geometry of the Cotton tensor. At long distances, this theory flows naturally to the relativistic value $z=1$, and could therefore serve as a possible candidate for a UV completion of Einstein’s general relativity or an infrared modification thereof. The effective speed of light, the Newton constant and the cosmological constant all emerge from relevant deformations of the deeply nonrelativistic $z=3$ theory at short distances.

We study the phase space structure of the Jackiw-Teitelboim model in its connection variables formulation where the gauge group of the field theory is given by local $\mathrm{SL}(2,\mathbb{R})$ [or SU(2) for the Euclidean model], i.e. the de Sitter group in two dimensions. In order to make the connection with two-dimensional gravity explicit, a partial gauge fixing of the de Sitter symmetry can be introduced that reduces it to space-time diffeomorphisms. This can be done in different ways. Having no local physical degrees of freedom, the reduced phase space of the model is finite dimensional. The simplicity of this gauge field theory allows for studying different avenues for quantization, which may use various (partial) gauge fixings. We show that reduction and quantization are noncommuting operations: the representation of basic variables as operators in a Hilbert space depends on the order chosen for the latter. Moreover, a representation that is natural in one case may not even be available in the other leading to inequivalent quantum theories.

This paper presents a general averaging procedure for a set of observers which are tilted with respect to the cosmological matter fluid. After giving the full set of equations describing the local dynamics, we define the averaging procedure and apply it to the scalar parts of Einstein’s field equations. In addition to the standard backreaction, new terms appear that account for the effect of the peculiar velocity of the matter fluid as well as the possible effect of a shift in the coordinate system.

We study the quasinormal modes of scalar perturbation in the background of five-dimensional charged Kaluza-Klein black holes with squashed horizons immersed in the Gödel universe. Besides the influence due to the compactness of the extra dimension, we disclose the cosmological rotational effect in the wave dynamics. The wave behavior affected by the Gödel parameter provides an interesting insight into the Gödel universe.

We compare the existing observational data on type Ia supernovae with the evolutions of the Universe predicted by a one-parameter family of tachyon models which we have introduced recently [Phys. Rev. D 69, 123512 (2004)]. Among the set of the trajectories of the model which are compatible with the data there is a consistent subset for which the Universe ends up in a new type of soft cosmological singularity dubbed big brake. This opens up yet another scenario for the future history of the Universe besides the one predicted by the standard $\Lambda \mathrm{CDM}$ model.

We show how to incorporate chiral-symmetry breaking in the soft-wall version of the anti-de Sitter/QCD model by using a modified dilaton profile and a quartic term in the bulk scalar potential. This allows one to separate the dependence on spontaneous and explicit chiral-symmetry breaking. Moreover, our 5D model automatically incorporates linear trajectories and non chiral-symmetry restoration for highly excited radial states. We compare our resulting mass spectra in the scalar, vector, and axial-vector sectors with the respective QCD resonances and find reasonable agreement using the known values for the pion mass and decay constant.

In extradimensional holographic approaches the flavor symmetry is gauged in the bulk, that is, treated as a local symmetry. Imposing such a local symmetry admits fewer terms coupling the (axial) vectors and (pseudo)scalars than if a global symmetry is imposed. The latter is the case in standard low-energy effective Lagrangians. Here we incorporate these additional, a priori only globally invariant terms into a holographic treatment by means of a Stückelberg completion. This work was motivated by our investigations concerning dynamical electroweak symmetry breaking by walking technicolor and we apply our findings to these theories.

We study various properties of a one-parameter mass term for the Skyrme model, originating from the works of Kopeliovich, Piette and Zakrzewski [V. B. Kopeliovich, B. Piette, and W. J. Zakrzewski, Phys. Rev. D 73, 014006 (2006).], through the use of axially symmetric solutions obtained numerically by simulated-annealing. These solutions allow us to observe asymptotic behaviors of the $B=2$ binding energies that differ to those previously obtained [B. Piette and W. J. Zakrzewski, Phys. Rev. D 77, 074009 (2008).]. We also decipher the characteristics of three distinct vibrational modes that appear as eigenstates of the vibrational Hamiltonian. This analysis further examine the assertion that the one-parameter mass term offers a better account of baryonic matter than the traditional mass term.

We compute the complete imaginary part of the nonrelativistic QCD (NRQCD) Lagrangian at order $1/M^4$ in the heavy-quark mass expansion, which includes center of mass operators, and at order ${\alpha }_s^2$ in the matching coefficients. We also compute the imaginary part of the NRQCD Lagrangian at order $1/M^6$ and at order ${\alpha }_s^2$ that contributes to the S-wave and P-wave inclusive decay widths of heavy quarkonium into light hadrons at order $v^7$ in the heavy-quark velocity expansion. If we count ${\alpha }_s(M)\sim v^2$, the calculation provides the complete next-to-leading order corrections to the P-wave hadronic widths, and in the original NRQCD power counting, the complete next-to-leading order corrections to the vector S-wave widths, and part of the next-to-next-to leading order corrections to the pseudoscalar S-wave widths. In the S-wave case, we confirm previous findings and add new terms in a more conservative power counting. In the P-wave case, our results are in disagreement with previous ones. Constraints induced by Poincaré invariance on the NRQCD four-fermion sector are studied for the first time and provide an additional check of the calculation. Perspectives for phenomenological applications are discussed.

It is shown that, at variance with previous analyses, the MIT bag model can explain the available data of the Sivers function and satisfies the Burkardt sum rule to a few percent accuracy. The agreement is similar to the one recently found in the constituent quark model. Therefore, these two model calculations of the Sivers function are in agreement with the present experimental and theoretical wisdom.

We consider the contributions to $g_{\mu }-2$ from fourth generation heavy neutral and charged leptons $N$ and $E$, respectively, at the one-loop level. Diagrammatically, there are two types of contributions: boson-boson-$N$ and $E-E$-boson in the loop diagram. In general, the effect from $N$ is suppressed by off-diagonal lepton mixing matrix elements. For $E$, we consider flavor changing neutral couplings arising from various new physics models, which are stringently constrained by $\mu \to e\gamma$. We assess how the existence of a fourth generation would affect these new physics models.