A study of event-shape observables in proton-antiproton collisions at $\sqrt{s}=1.96\mathrm{TeV}$ is presented. The data for this analysis were recorded by the CDF II Detector at the Tevatron Collider. The variables studied are the transverse thrust and thrust minor, both defined in the plane perpendicular to the beam direction. The observables are measured using energies from unclustered calorimeter cells. In addition to studies of the differential distributions, we present the dependence of event-shape mean values on the leading-jet transverse energy. Data are compared with pythia Tune A and to resummed parton-level predictions that were matched to fixed-order results at next-to-leading-order (NLO) accuracy ($\mathrm{NLO}+\mathrm{NLL}$). Predictions from pythia Tune A agree fairly well with the data. However, the underlying event contributes significantly to these observables, making it difficult to make direct comparisons to the $\mathrm{NLO}+\mathrm{NLL}$ predictions, which do not account for the underlying event. To overcome this difficulty, we introduce a new observable, a weighted difference of the mean values of the thrust and thrust minor, which is less sensitive to the underlying event, allowing for a comparison with $\mathrm{NLO}+\mathrm{NLL}$. Both pythia Tune A and the $\mathrm{NLO}+\mathrm{NLL}$ calculations agree well within the $20\%$ theoretical uncertainty with the data for this observable, indicating that perturbative QCD successfully describes shapes of the hadronic final states.

We develop a practical method to analyze the mixing structure of hadrons consisting of two components of quark composite and hadronic composite. As an example, we investigate the properties of the axial vector meson $a_1(1260)$ and discuss its mixing properties quantitatively. We also make reference to the large $N_c$ procedure and its limitation for the classification of such a mixed state.

Black hole perturbation theory is typically studied on time surfaces that extend between the bifurcation sphere and spatial infinity. From a physical point of view, however, it may be favorable to employ time surfaces that extend between the future event horizon and future null infinity. This framework resolves problems regarding the representation of quasinormal mode eigenfunctions and the construction of short-ranged potentials for the perturbation equations in frequency domain.

We address the question of whether the large-$N$ expansion in pure $\mathrm{SU}(N)$ gauge theories requires that $k$-string tensions must have a power series expansion in $1/N^2$, as in the sine law, or whether $1/N$ contributions are also allowable, as in Casimir scaling. We find that $k$-string tensions may, in fact, have $1/N$ corrections, and consistency with the large-$N$ expansion in the open string sector depends crucially on an exact cancellation, which we will prove, among terms involving odd powers of $1/N$ in particular combinations of Wilson loops. It is shown how these cancellations are fulfilled, and consistency with the large-$N$ expansion achieved, in a concrete example, namely, strong coupling lattice gauge theory with the heat-kernel action. This is a model which has both a $1/N^2$ expansion and Casimir scaling of the $k$-string tensions. Analysis of the closed string channel in this model confirms our conclusions, and provides further insights into the large-$N$ dependence of energy eigenstates and eigenvalues.

We search for self-gravitating oscillating field lumps (pulsons) in the scalar model with logarithmic potential. With the use of a Krylov-Bogoliubov–type asymptotic expansion in the gravitational constant, the pulson solutions of the Einstein-Klein-Gordon system are obtained in the Schwarzschild coordinates. They are expressed in terms of solutions of the singular Hill’s equation. The masses of the obtained pulsons are calculated. The initial conditions are found under which the pulson solutions become periodic. These conditions are then used in direct numerical integration of the Einstein-Klein-Gordon system. It is shown that they do evolve into a very long-lived periodic pulson. Stability of the self-gravitating pulsons and their possible astrophysical applications are briefly discussed.

We investigate phase transitions in scalar field theories using the functional renormalization group (RG) equation. We analyze a system with $\mathrm{U}(2)\times \mathrm{U}(2)$ symmetry, in which there is a parameter ${\lambda }_2$ that controls the strength of the first-order phase transition driven by fluctuations. In the limit of ${\lambda }_2\to 0$, the $\mathrm{U}(2)\times \mathrm{U}(2)$ theory is reduced to an $\mathrm{O}(8)$ scalar theory that exhibits a second-order phase transition in three dimensions. We develop a new insight for the understanding of the fluctuation-induced first-order phase transition as a smooth continuation from the standard RG flow in the $\mathrm{O}(8)$ system. In our view from the RG flow diagram on coupling parameter space, the region that favors the first-order transition emerges from the unphysical region to the physical one as ${\lambda }_2$ increases from zero. We give this interpretation based on the Taylor expansion of the functional RG equations up to the fourth order in terms of the field, which encompasses the $\epsilon$-expansion results. We compare results from the expansion and from the full numerical calculation and find that the fourth-order expansion is only of qualitative use and that the sixth-order expansion improves the quantitative agreement.

We study the sensitivity of the Tevatron and the 7 TeV LHC to a leptoquark $S$ coupling to a top quark and a charged lepton $L$ ($=e$, $\mu$, or $\tau$). For the Tevatron, we focus on the case $m_S<m_t$, where the leptoquark pair production cross section is large, and the decay is three-body: $S\to Wb{L}^{\pm }$. We argue that existing Tevatron observations could exclude $m_S\lesssim 160\mathrm{GeV}$. For $m_S>m_t$, we show that the LHC experiments with low integrated luminosity could be sensitive to such leptoquarks decaying to $t{l}^{\pm }$ with $l=\mu$ or $\tau$.

We consider the central exclusive production of $q\overline{q}$ pairs and Higgs boson in proton-proton collisions at LHC. The amplitude for the process is derived within the $k_{\perp }$-factorization approach and considered in different kinematical asymptotics, in particular, in the important high quark transverse momenta and massless quark limits. Quark helicity and spin-projection amplitudes in two different frames are shown in extenso. Rapidity distributions, quark jet $p_{\perp }$ distributions, invariant $q\overline{q}$ mass distributions, angular azimuthal correlations between outgoing protons and jets are presented. Irreducible $b\overline{b}$ background to the central exclusive Higgs boson production is analyzed in detail, in particular, how to impose cuts to maximize signal-to-background ratio.

We consider quantum Einstein gravity in three dimensional de Sitter space. The Euclidean path integral is formulated as a sum over geometries, including both perturbative loop corrections and nonperturbative instanton corrections coming from geometries with nontrivial topology. These nontrivial geometries have a natural physical interpretation. Conventional wisdom states that the sphere is the unique Euclidean continuation of de Sitter space. However, when considering physics only in the causal patch of a single observer other Euclidean geometries, in this case lens spaces, contribute to physical observables. This induces quantum gravitational effects which lead to deviations from the standard thermal behavior obtained by analytic continuation from the three sphere. The sum over these geometries can be formulated as a sum over cosets of the modular group; this is the de Sitter analog of the celebrated “black hole Farey Tail.” We compute the vacuum partition function including the sum over these geometries. Perturbative quantum corrections are computed to all orders in perturbation theory using the relationship between Einstein gravity and Chern-Simons theory, which is checked explicitly at tree and one-loop level using heat kernel techniques. The vacuum partition function, including all instanton and perturbative corrections, is shown to diverge in a way which cannot be regulated using standard field theory techniques.

At a time when galaxy surveys and other observations are reaching unprecedented sky coverage and precision, it seems timely to investigate the effects of general relativistic nonlinear dynamics on the growth of structures and on observations. Analytic inhomogeneous cosmological models are an indispensable way of investigating and understanding these effects in a simplified context. In this paper, we develop exact inhomogeneous solutions of general relativity with pressureless matter (dust, describing cold dark matter) and cosmological constant $\Lambda$, which can be used to model an arbitrary initial matter distribution along one line of sight. In particular, we consider the second class Szekeres models with $\Lambda$, and split their dynamics into a flat $\Lambda \mathrm{CDM}$ background and exact nonlinear inhomogeneities, obtaining several new results. One single metric function $Z$ describes the deviation from the background. We show that $F$, the time dependent part of $Z$, satisfies the familiar linear differential equation for $\delta$, the first-order density perturbation of dust, with the usual growing and decaying modes. In the limit of small perturbations, $\delta \approx F$ as expected, and the growth of inhomogeneities links up exactly with standard perturbation theory. In particular, we exhibit an exact conserved curvature variable, necessary for the existence of the growing mode, which is the nonlinear extension of the first-order curvature perturbation. We provide analytic expressions for the exact nonlinear $\delta$ and the growth factor in our models. For the case of over-densities, we find that, depending on the initial conditions, the growing mode may or may not lead to a pancake singularity, analogous to a Zel’dovich pancake. This is in contrast with the $\Lambda =0$ pure Einstein-de Sitter background where, at any given point in comoving (Lagrangian) coordinates, pancakes will always occur. Analyzing the covariant variables associated with the space-time, we derive the associated dynamical system, which we are able to decouple and reduce to two differential equations, one for ${\Omega }_{\Lambda }$ representing the background dynamics, and one for $\delta$ describing the dynamics of the inhomogeneities. Our models are Petrov type D, which we show by explicitly deriving the only nonzero Weyl scalar ${\Psi }_2$, which does not depend on $\Lambda$. Since this is the only Weyl contribution to the geodesic deviation equation, $\Lambda$ can only contribute to lensing through its contribution to the background expansion.

In this paper we study the kinetic theory of many-particle astrophysical systems and we present a consistent version of the collisionless Boltzmann equation in the first post-Newtonian (1PN) approximation. We argue that the equation presented by Rezania and Sobouti, in Astron. Astrophys. 354, 1110 (2000) is not the correct expression to describe the evolution of a collisionless self-gravitating gas. One of the reasons that account for the previous statement is that the energy of a free-falling test particle, obeying the 1PN equations of motion for static gravitational fields, is not a static solution of the mentioned equation. The same statement holds for the angular momentum, in the case of spherical systems. We provide the necessary corrections and obtain an equation that is consistent with the corresponding equations of motion and the 1PN conserved quantities. We suggest some potential relevance for the study of high-density astrophysical systems and as an application we construct the corrected version of the post-Newtonian polytropes.

Different holographic dark-energy models are studied from a unifying point of view. We compare models for which the Hubble scale, the future event horizon or a quantity proportional to the Ricci scale are taken as the infrared cutoff length. We demonstrate that the mere definition of the holographic dark-energy density generally implies an interaction with the dark-matter component. We discuss the relation between the equation-of-state parameter and the energy density ratio of both components for each of the choices, as well as the possibility of noninteracting and scaling solutions. Parameter estimations for all three cutoff options are performed with the help of a Bayesian statistical analysis, using data from supernovae type Ia and the history of the Hubble parameter. The $\Lambda \mathrm{CDM}$ model is the clear winner of the analysis. According to the Bayesian information criterion (BIC), all holographic models should be considered as ruled out, since the difference $\Delta \mathrm{BIC}$ to the corresponding $\Lambda \mathrm{CDM}$ value is $>10$. According to the Akaike information criterion (AIC), however, we find $\Delta \mathrm{AIC}<2$ for models with Hubble-scale and Ricci-scale cutoffs, indicating, that they may still be competitive. As we show for the example of the Ricci-scale case, also the use of certain priors, reducing the number of free parameters to that of the $\Lambda \mathrm{CDM}$ model, may result in a competitive holographic model.

We give an estimate for the upper bounds on rates of lepton flavor violating (LFV) decays $M\to {\mu }^{\pm }{e}^{\mp }$ of vector mesons $M={\rho }^0$, $\omega$, $\varphi$, $J/\psi$, ${\rm Y}$ and the $Z^0$ boson in a model-independent way, analyzing the corresponding lowest dimension effective operators. These operators also contribute to nuclear $\mu -e$-conversion. Based on this observation and using the existing experimental limits on this LFV nuclear process, we show that the studied two-body LFV decays of vector bosons are strongly suppressed independent on the explicit realization of new physics. The upper limits on the rates of some of these decays are significantly more stringent than similar limits known in the literature. In view of these results, experimental observation of the two-body LFV decays of vector bosons looks presently unrealistic.

Using existing experimental information from $K$, $B$, and $D$ decays as well as electroweak precision tests and oblique parameters, we provide constraints and correlations on the parameters of the $4\times 4$ mixing matrix for the standard model (SM) with four generations (SM4). We emphasize that some correlations amongst the parameters have important repercussions for key observables. We work with a particular representation of this matrix which is highly suited for extracting information from $B$ decays. In particular, in our parametrization for SM4, we extend the hierarchical structure seen in SM with three generations as an expansion in powers of $\lambda$, the sine of the Cabbibo angle. Implications of the resulting constraints for time-dependent and semileptonic $CP$ asymmetries for $D^0$, $B^0$, and for $B_s$ are also given. While we show that the semileptonic asymmetries may be significantly enhanced in SM4 over the SM, there are important constraints and correlations with other observables. In particular, we find that despite significant enhancement in the semileptonic asymmetry $a_{\mathrm{sl}}^s$ for $B_s$ over the SM, it is very difficult for SM4 to account for the central value of the recent D0 result, though given the large experimental error and other considerations, we do not regard this as a problem for SM4. Regarding the gold-plated measurement of $\sin 2\beta$ via $S_{\psi K_s}$, while SM4 can remove the tension that SM shows, as a consequence of one of the important correlations we find that the semileptonic asymmetry $a_{\mathrm{sl}}^d$ for $B_d$ gets appreciably restricted in SM4. In this context we suggest that existing data from $B$ factories taken on ${\rm Y}(4S)$ and ${\rm Y}(5S)$, and in the relevant continuum be used to constrain the semileptonic asymmetries for $B_d$, $B_s$ as well as their linear combination. Of course, the data from the Tevatron and LHCb experiments can provide nontrivial tests of SM4 as well.

We review a method, suggested many years ago, to numerically measure the relative amplitudes of the true Yang-Mills vacuum wavefunctional in a finite set of lattice-regulated field configurations. The technique is applied in $2+1$ dimensions to sets of Abelian plane wave configurations of varying amplitude and wavelength, and sets of non-Abelian constant configurations. The results are compared to the predictions of several proposed versions of the Yang-Mills vacuum wavefunctional that have appeared in the literature. These include (i) a suggestion in temporal gauge due to Greensite and Olejník; (ii) the “new variables” wavefunction put forward by Karabali, Kim, and Nair; (iii) a hybrid proposal combining features of the temporal gauge and new variables wavefunctionals; and (iv) Coulomb gauge wavefunctionals developed by Reinhardt and coworkers, and by Szczepaniak and coworkers. We find that wavefunctionals which simplify to a “dimensional-reduction” form at large scales, i.e., which have the form of a probability distribution for two-dimensional lattice gauge theory, when evaluated on long-wavelength configurations, have the optimal agreement with the data.

Parity-violating elastic electron-proton scattering measures $Q$ weak for the proton, $Q_W^p$. To extract $Q_W^p$ from data, all radiative corrections must be well-known. Recently, disagreement on the $\gamma Z$-box contribution to $Q_W^p$ has prompted the need for further analysis of this term. Here, we support one choice of a debated factor, go beyond the previously assumed equality of electromagnetic and $\gamma Z$ structure functions, and find an analytic result for one of the $\gamma Z$-box integrals. Our numerical evaluation of the $\gamma Z$ box is in agreement within errors with previous reports, albeit somewhat larger in central value, and is within the uncertainty requirements of current experiments.

Fast, reliable orbital evolutions of compact objects around massive black holes will be needed as input for gravitational wave search algorithms in the data stream generated by the planned Laser Interferometer Space Antenna (LISA). Currently, the state of the art is a time domain code by [Phys. Rev. D 81, 084021 (2010)] that computes the gravitational self-force on a point particle in an eccentric orbit around a Schwarzschild black hole. Existing time domain codes take up to a few days to compute just one point in parameter space. In a series of articles, we advocate the use of a frequency domain approach to the problem of gravitational self-force (GSF) with the ultimate goal of orbital evolution in mind. Here, we compute the GSF for a particle in a circular orbit in Schwarzschild spacetime. We solve the linearized Einstein equations for the metric perturbation in Lorenz gauge. Our frequency domain code reproduces the time-domain results for the GSF up to $\sim 1000$ times faster for small orbital radii. In forthcoming companion papers, we will generalize our frequency domain computations of the GSF to include bound (eccentric) orbits in Schwarzschild spacetimes, where we will employ the method of extended homogeneous solutions [Phys. Rev. D 78, 084021 (2008)]. We will eventually extend our methods to attempt a frequency domain computation of the GSF in Kerr spacetime.

Laboratory experiments measuring neutrino oscillations indicate small mass differences between different mass eigenstates of neutrinos. The absolute mass scale is however not determined, with at present the strongest upper limits coming from astronomical observations rather than terrestrial experiments. The presence of massive neutrinos suppresses the growth of perturbations below a characteristic mass scale, thereby leading to a decreased abundance of collapsed dark matter halos. Here we show that this effect can significantly alter the predicted luminosity function (LF) of high redshift galaxies. In particular we demonstrate that a stringent constraint on the neutrino mass can be obtained using the well measured galaxy LF and our semianalytic structure formation models. Combining the constraints from the Wilkinson Microwave Anisotropy Probe 7 yr (WMAP7) data with the LF data at $z\sim 4$, we get a limit on the sum of the masses of 3 degenerate neutrinos $\Sigma m_{\nu }<0.52\mathrm{eV}$ at the 95% C.L. The additional constraints using the prior on Hubble constant strengthens this limit to $\Sigma m_{\nu }<0.29\mathrm{eV}$ at the 95% C.L. This neutrino mass limit is a factor $\sim 4$ improvement compared to the constraint based on the WMAP7 data alone, and as stringent as known limits based on other astronomical observations. As different astronomical measurements may suffer from different set of biases, the method presented here provides a complementary probe of $\Sigma m_{\nu }$. We suggest that repeating this exercise on well measured luminosity functions over different redshift ranges can provide independent and tighter constraints on $\Sigma m_{\nu }$.

In this paper we present the constraints on cold dark matter (CDM) isocurvature contributions to the cosmological perturbations. By employing Markov chain Monte Carlo method, we perform a global analysis for cosmological parameters using the latest astronomical data, such as 7-year Wilkinson Microwave Anisotropy Probe (WMAP7) observations, matter power spectrum from the Sloan Digital Sky Survey, luminous red galaxies, and the Union2 type Ia supernovae sample. We find that the correlated mixture of adiabatic and isocurvature modes is slightly favored by the current observational data. We also obtain a tight limit on the fraction of the CDM isocurvature contributions, which should be less than 14.6% at 95% confidence level. With the presence of the isocurvature modes, the adiabatic spectral index becomes slightly bigger, $n_s^{\mathrm{adi}}=0.972\pm 0.014$ ($1\sigma$), and the tilt for isocurvature spectrum could be large, namely, the best fit value is $n_s^{\mathrm{iso}}=3.020$. Finally, we discuss the effect on WMAP normalization priors, shift parameter $R$, acoustic scale $l_A$, and $z_{*}$, from the CDM isocurvature perturbation. By fitting the mixed initial condition to the combined data, we find the mean values of $R$, $l_A$, and $z_{*}$ can be changed about $2.9\sigma$, $2.8\sigma$, and $1.5\sigma$ respectively, comparing with those obtained in the pure adiabatic condition.