We show how to relate the moments of the reconstructed hadronic invariant mass distribution to the moments of the physical spectrum in a model independent way. The only information needed on detector resolution functions is their first few moments. Theoretical predictions for the first three moments as functions of nonperturbative parameters are given for various lepton energy cuts.

The unintegrated quark and gluon distributions in the pion and nucleon are analyzed using the CCFM equations in the single-loop approximation. We utilize the transverse-coordinate (or impact-parameter) representation which diagonalizes the equations and study in detail the dependence on the transverse coordinate induced by the CCFM evolution. We find considerable broadening of the transverse-momentum distributions with an increasing magnitude of the hard scale Q. For instance, at the Bjorken $x=0.1\mathrm{}$ the root mean squared transverse momentum of the gluons is enhanced by about 1 GeV when evolved from the initial low scale to $Q^2=10\mathrm{}{\mathrm{GeV}}^2,$ and by about 2 GeV when evolved up to $Q^2=100\mathrm{}{\mathrm{GeV}}^2.$ The broadening effect is enhanced with decreasing Bjorken x, and is stronger for the gluons than for the quarks. Analytic solution for the average transverse momentum corresponding to the x moments of the distributions is obtained. The parton luminosities are also discussed.

The ratio of neutral Higgs field vacuum expectation values, $\tan \beta ,$ is one of the most important parameters to determine in type-II two Higgs doublet models, specifically the minimal supersymmetric standard model. Assuming the energies and integrated luminosity of a future high energy $e^{+}{e}^{-}$ linear collider of $\sqrt{s}=500,$ 800, 1000, and 1500 GeV and $\mathcal{L}=1\mathrm{}{\mathrm{ab}}^{-1}$ we show that associated ${\mathrm{tH}}^{\pm }$ production in $\gamma \gamma$ collisions can be used to make an accurate determination of $\tan \beta$ for low and high $\tan \beta$ by precision measurements of the $\gamma \overrightarrow{\gamma }{H}^{\pm }t+X$ cross section.

We study the detectability of departures from the inflationary consistency equation, $r\equiv T/S\simeq -{5n}_T,$ where T and S are the tensor and scalar contributions to the quadrupole variance, respectively. The consistency equation holds if inflation is driven by a slowly rolling scalar field. Quantum loop corrections lead to observable violations if they are nearly maximal and $r\gtrsim \mathrm{0.1.}$ Large departures $(|\Delta n_T|\gtrsim 0.1)$ can be seen if $r\gtrsim \mathrm{0.001.}$ High angular resolution can be important for detecting a nonzero ${r+5n}_T,$ even when not important for detecting a nonzero r.

The curvaton was introduced recently as a distinct inflationary mechanism for generating adiabatic density perturbations. Implicit in that scenario is that the curvaton offers a new mechanism for reheating after inflation, as it is a form of energy density not diluted by the inflationary expansion. We consider curvaton reheating in the context of a braneworld inflation model, steep inflation, which features a novel use of the braneworld to give a new mechanism for ending inflation. The original steep inflation model featured reheating by gravitational particle production, but the inefficiency of that process causes observational difficulties. We demonstrate here that the phenomenology of steep inflation is much improved by curvaton reheating.

The coming flood of cosmic microwave background (CMB) polarization experiments, spurred by the recent detection of CMB polarization by the DASI and WMAP instruments, will be confronted by many new analysis tasks specific to polarization. For the analysis of CMB polarization data sets, the devil is truly in the details. With this in mind, we present details of the data analysis for the POLAR experiment, which recently led to the tightest upper limits on the polarization of the cosmic microwave background radiation at large angular scales. We discuss the data selection process, map-making algorithms, offset removal, and likelihood analysis which were used to find upper limits on the polarization. Stated using the modern convention for reporting CMB Stokes parameters, these limits are 5.0 μK on both E- and B-type polarization at 95% confidence. Finally, we discuss simulations used to test our analysis techniques and to probe the fundamental limitations of the experiment.

The anomalous processes $\overrightarrow{\gamma }3\pi$ and $\gamma \overrightarrow{\pi }\pi \pi$ are investigated within the Dyson-Schwinger framework using the rainbow-ladder approximation. Calculations reveal that a complete set of ladder diagrams beyond the impulse approximation are necessary to reproduce the fundamental low-energy theorem for the anomalous form factor. Higher momentum calculations also agree with the limited form factor data and exhibit the same resonance behavior as the phenomenological vector meson dominance model.

We analyze the moments of parton distribution functions in the pion calculated in lattice QCD, paying particular attention to their chiral extrapolation. Using the lowest three nontrivial moments calculated on the lattice, we assess the accuracy with which the x dependence of both the valence and sea quark distributions in the pion can be extracted. The resulting valence quark distributions at the physical pion mass are in fair agreement with existing Drell-Yan data, but the statistical errors are such that one cannot yet confirm (or rule out) the large-x behavior expected from hadron helicity conservation in perturbative QCD. However, one can expect that the next generation of calculations in lattice QCD will allow one to extract parton distributions with a level of accuracy comparable with current experiments.

We study two aspects of the color flavor locked phase of QCD in the Nambu–Jona-Lasinio approximation. The first one is the issue of the dependence on $\mu$ of the ultraviolet cutoff in the gap equation, which is solved by allowing for a running coupling constant. The second one is the dependence of the gap on the strange quark mass; using high density effective theory we perform an expansion in the parameter ${(m}_s/\mu {)}^2$ after checking that its numerical validity is already very good at first order.

We discuss a goodness-of-fit method which tests the compatibility between statistically independent data sets. The method gives sensible results even in cases where the ${\chi }^2$ minima of the individual data sets are very low or when several parameters are fitted to a large number of data points. In particular, it avoids the problem that a possible disagreement between data sets becomes diluted by data points which are insensitive to the crucial parameters. A formal derivation of the probability distribution function for the proposed test statistics is given, based on standard theorems of statistics. The application of the method is illustrated on data from neutrino oscillation experiments, and its complementarity to the standard goodness-of-fit is discussed.

We discuss an $O\left(N\right)\mathrm{}$ symmetric extension of the sine-Gordon (SG) equation which, using a path integral approach, allows for an expansion around the leading order in large N (Gaussian) approximation. The model is described by the Lagrangian $\mathcal{L}=\frac{1}{2}({\partial }_{\mu }\overrightarrow{\phi }{)}^2+N({\alpha }_0/{\beta }^2)\cos \beta \sqrt{\rho },$ with $\rho =\left(\overrightarrow{\phi }\cdot \overrightarrow{\phi }\right)/N.\mathrm{}$ At the leading order we show that the results of our approach agree with the ones of a large-$N$ variational computation. We discuss the striking differences arising for a nonpolynomial interaction between the large-$N$ form for $〈V\left[\phi \right]〉$ in the Gaussian approximation and the $N=1\mathrm{}$ case; when $V\left[\phi \right]$ is a polynomial no such drastic differences occur. We find that, for our large-$N$ extension of the sine-Gordon model, the unbroken ground state is unstable as one increases the coupling constant (as it is for the original SG equation) and we find in leading order that the unbroken symmetry vacuum is stable as long as ${\beta }^2<~24\pi .$

The possibility of noncommutative topological gravity arising in the same manner as Yang-Mills theory is explored. We use the Seiberg-Witten map to construct such a theory based on a $SL(2,\mathbf{C})$ complex connection, from which the Euler characteristic and the signature invariant are obtained. Finally, we speculate on the description of noncommutative gravitational instantons, as well as noncommutative local gravitational anomalies.

Recently we considered $N=2\mathrm{}$ super Yang-Mills theory with a $N=2\mathrm{}$ mass breaking term and showed the existence of Bogomol’nyi-Prasad-Sommerfield (BPS) $Z_k$ string solutions for arbitrary simple gauge groups which are spontaneously broken to non-Abelian residual gauge groups. We also calculated their string tensions exactly. In doing so, we have considered in particular the hypermultiplet in the same representation as that of a diquark condensate. In the present work, we analyze some of the different phases of the theory and find that the magnetic fluxes of the monopoles are multiples of the fundamental $Z_k$ string flux, allowing for monopole confinement in one of the phase transitions of the theory. We also calculate the threshold length for string breaking. Some of these confining theories can be obtained by adding a deformation term to the $N=2\mathrm{}$ or $N=4\mathrm{}$ superconformal theories.

We investigate the late-time behavior of particle creation from an extremal Reissner-Nordström (RN) black hole formed by gravitational collapse. We calculate explicitly the particle flux associated with a massless scalar field at late times after the collapse. Our result shows that the expected number of particles in any wave packet spontaneously created from the “in” vacuum state approaches zero faster than any inverse power of time. This result confirms the traditional belief that extremal black holes do not emit particles. We also calculate the expectation value of the stress energy tensor in a 1+1 RN black hole and show that it also drops to zero at late times. Some comments on previous work by other authors are provided.

According to a recent proposal, the so-called Barbero-Immirzi parameter of loop quantum gravity can be fixed, using Bohr’s correspondence principle, from a knowledge of highly damped black hole oscillation frequencies. Such frequencies are rather difficult to compute, even for Schwarzschild black holes. However, it is now quite likely that they may provide a fundamental link between classical general relativity and quantum theories of gravity. Here we carry out the first numerical computation of very highly damped quasinormal modes (QNM’s) for charged and rotating black holes. In the Reissner-Nordström case QNM frequencies and damping times show an oscillatory behavior as a function of charge. The oscillations become faster as the mode order increases. At fixed mode order, QNM’s describe spirals in the complex plane as the charge is increased, tending towards a well defined limit as the hole becomes extremal. Kerr QNM’s have a similar oscillatory behavior when the angular index $m=0.\mathrm{}$ For $l=m=2\mathrm{}$ the real part of Kerr QNM frequencies tends to $2\Omega ,$ $\Omega$ being the angular velocity of the black hole horizon, while the asymptotic spacing of the imaginary parts is given by $2\pi T_H.$

A numerical analysis shows that the Einstein field equations allow static and spherically symmetric black hole solutions with scalar-field hair in asymptotically flat spacetimes. When regularity at the origin is imposed (i.e., in the absence of a horizon) globally regular scalar solitons are found. The asymptotically flat solutions are obtained provided that the scalar potential $V\left(\phi \right)$ of the theory is not positive semidefinite and such that its local minimum is also a zero of the potential, the scalar field settling asymptotically at that minimum. The configurations, although unstable under spherically symmetric linear perturbations, are regular and thus can serve as counterexamples to the no-scalar-hair conjecture.

We study primordial gravitational waves from inflation in the Randall-Sundrum braneworld model. The effect of a small change of the Hubble parameter during inflation is investigated using a toy model given by connecting two de Sitter branes. We analyze the power spectrum of the final zero-mode gravitons, which is generated from the vacuum fluctuations of both the initial Kaluza-Klein modes and the zero mode. The amplitude of fluctuations is confirmed to agree with the four-dimensional one at low energies, whereas it is enhanced due to the normalization factor of the zero mode at high energies. We show that the five-dimensional spectrum can be well approximated by applying a simple mapping to the four-dimensional fluctuation amplitude.

We present a thorough analysis of the quasinormal (QN) behavior associated with the decay of scalar, electromagnetic, and gravitational perturbations of Schwarzschild black holes in anti–de Sitter (AdS) spacetimes. As is known, the AdS QN spectrum crucially depends on the relative size of the black hole to the AdS radius. There are three different types of behavior depending on whether the black hole is large, intermediate, or small. The results of previous works, concerning lower overtones for large black holes, are completed here by obtaining higher overtones for all three black hole regimes. There are two major conclusions that one can draw from this work: First, asymptotically for high overtones, all the modes are evenly spaced, and this holds for all three types of regime, large, intermediate, and small black holes, independently of l, where l is the quantum number characterizing the angular distribution; second, the spacing between modes is apparently universal in that it does not depend on the field; i.e., scalar, electromagnetic, and gravitational QN modes all have the same spacing for high overtones. We are also able to prove why scalar and gravitational perturbations are isospectral, asymptotically for high overtones, by introducing appropriate superpartner potentials.

We perform a series of two-dimensional hydrodynamic simulations of the rotational collapse of a supernova core in axisymmetry. We employ a realistic equation of state (EOS) and take into account electron capture and neutrino transport by the so-called leakage scheme. It is an important step to apply the realistic EOS coupled with microphysics to 2D simulations for computing gravitational radiation in rotational core collapse. We use the quadrupole formula to calculate the amplitudes and the waveforms of the gravitational wave assuming Newtonian gravity. With these computations, we extend the conventional category of the gravitational waveforms. Our results show that the peak amplitudes of the gravitational wave are mostly within the sensitivity range of laser interferometers such as TAMA and the first LIGO for a source at a distance of 10 kpc. Furthermore, we find that the amplitudes of the second peaks are within the detection limit of the first LIGO for the source, and first point out the importance of the detection, since it will give us information as to the angular momentum distribution of evolved massive stars.

The time evolution of self-interacting spherically symmetric scalar fields in Minkowski spacetime is investigated based on the use of Green’s theorem. It is shown that a massive Klein-Gordon field can be characterized by the formation of certain expanding shell structures where all the shells are built up by very high frequency oscillations. This oscillation is found to be modulated by the product of a simple time decaying factor of the form $t^{-3/2}$ and of an essentially self-similar expansion. Apart from this self-similar expansion the developed shell structure is preserved by the evolution. In particular, the energy transported by each shell appears to be time independent.