Masses and widths of scalar-isoscalar multi-channel resonances from data analysis

Peculiarities of obtaining parameters for broad multi-channel resonances from data are discussed analyzing the experimental data on processes $\pi\pi\to\pi\pi,K\bar{K}$ in the $I^GJ^{PC}=0^+0^{++}$ channel in a model-independent approach based on analyticity and unitarity and using an uniformization procedure. We show that it is possible to obtain a good description of the $\pi\pi$ scattering data from the threshold to 1.89 GeV with parameters of resonances cited in the PDG tables as preferred. However, in this case, first, representation of the $\pi\pi$ background is unsatisfactory; second, the data on the coupled process $\pi\pi\to K\bar{K}$ are not well described even qualitatively above 1.15 GeV when using the resonance parameters from the only $\pi\pi$ scattering analysis. The combined analysis of these coupled processes is needed, which is carried out satisfactorily. Then both above-indicated flaws, related to the analysis of solely the $\pi\pi$-scattering, are cured. The most remarkable change of parameters with respect to the values of only $\pi\pi$ scattering analysis appears for the mass of the $f_0 (600)$ which is now in some accordance with the Weinberg prediction on the basis of mended symmetry and with an analysis using the large-$N_c$ consistency conditions between the unitarization and resonance saturation. The obtained $\pi\pi$-scattering length $a_0^0$ in case when we restrict to the analysis of the $\pi\pi$ scattering or consider so-called A-solution (with a lower mass and width of $f_0(600)$ meson) agrees well with prediction of chiral perturbation theory (ChPT) and with data extracted at CERN by the NA48/2 Collaboration from the analysis of the $K_{e4}$ decay and by the DIRAC Collaboration from the measurement of the $\pi^+\pi^-$ lifetime.Comment: 21 pages, 3 figures, 6 table

Electromagnetic Energy, Momentum, and Angular Momentum in an Inhomogeneous Linear Dielectric

In a previous work, Optics Communications 284 (2011) 2460--2465, we considered a dielectric medium with an anti-reflection coating and a spatially uniform index of refraction illuminated at normal incidence by a quasimonochromatic field. Using the continuity equations for the electromagnetic energy density and the Gordon momentum density, we constructed a traceless, symmetric energy--momentum tensor for the closed system. In this work, we relax the condition of a uniform index of refraction and consider a dielectric medium with a spatially varying index of refraction that is independent of time, which essentially represents a mechanically rigid dielectric medium due to external constraints. Using continuity equations for energy density and for Gordon momentum density, we construct a symmetric energy--momentum matrix, whose four-divergence is equal to a generalized Helmholtz force density four-vector. Assuming that the energy-momentum matrix has tensor transformation properties under a symmetry group of space-time coordinate transformations, we derive the global conservation laws for the total energy, momentum, and angular momentum.Comment: added publication informatio

QCD Tests of the Puzzling Scalar Mesons

Motivated by several recent data, we test the QCD spectral sum rules (QSSR) predictions based on different proposals (\bar qq, \bar q\bar q qq, and gluonium) for the nature of scalar mesons. In the I=1 and 1/2 channels, the unusual (wrong) splitting between the a_0(980) and \kappa(900) and the a_0(980) width can be understood from QSSR within a \bar qq assignement. However, none of the \bar qq and \bar q\bar q qq results can explain the large \kappa width, which may suggest that it can result from a strong interference with non-resonant backgrounds. In the I=0 channel, QSSR and some low-energy theorems (LET) require the existence of a low mass gluonium \sigma_B(1 GeV) coupled strongly to Goldstone boson pairs which plays in the U(1)_V channel, a similar role than the \eta' for the value of the U(1)_A topological charge. The observed \sigma(600) and f_0(980) mesons result from a maximal mixing between the gluonium \sigma_B and \bar qq(1 GeV) mesons, a mixing scheme which passes several experimental tests. OZI violating J/\psi--> \phi\pi^+\pi^-, D_s--> 3\pi decays and J/\psi--> \gamma S glueball filter processes may indicate that most of the I=0 mesons above 1 GeV have important gluonium in their wave functions. We expect that the f_0(1500), f_0(1710) and f_0(1790) have significant gluonium component in their wave functions, while the f_0(1370) is mostly \bar qq. Tests of these results can be provided by the measurements of the pure gluonium \eta'\eta and 4\pi specific U(1)_A decay channels.Comment: Version to appear in Phys. Rev. D (one previous figure corrupted

The evolution of pebble size and shape in space and time

We propose a mathematical model which suggests that the two main geological observations about shingle beaches, i.e. the emergence of predominant pebble size ratios and strong segregation by size are interrelated. Our model is a based on a system of ODEs called the box equations, describing the evolution of pebble ratios. We derive these ODEs as a heuristic approximation of Bloore's PDE describing collisional abrasion. While representing a radical simplification of the latter, our system admits the inclusion of additional terms related to frictional abrasion. We show that nontrivial attractors (corresponding to predominant pebble size ratios) only exist in the presence of friction. By interpreting our equations as a Markov process, we illustrate by direct simulation that these attractors may only stabilized by the ongoing segregation process.Comment: 22 pages, 8 figure

Perspectives: Quantum Mechanics on Phase Space

The basic ideas in the theory of quantum mechanics on phase space are illustrated through an introduction of generalities, which seem to underlie most if not all such formulations and follow with examples taken primarily from kinematical particle model descriptions exhibiting either Galileian or Lorentzian symmetry. The structures of fundamental importance are the relevant (Lie) groups of symmetries and their homogeneous (and associated) spaces that, in the situations of interest, also possess Hamiltonian structures. Comments are made on the relation between the theory outlined and a recent paper by Carmeli, Cassinelli, Toigo, and Vacchini.Comment: "Quantum Structures 2004" - Meeting of the International Quantum Structures Association; Denver, Colorado; 17-22 July, 200

Nature of the light scalar mesons

Despite the apparent simplicity of meson spectroscopy, light scalar mesons cannot be accommodated in the usual $q\bar q$ structure. We study the description of the scalar mesons below 2 GeV in terms of the mixing of a chiral nonet of tetraquarks with conventional $q\bar q$ states. A strong diquark-antidiquark component is found for several states. The consideration of a glueball as dictated by quenched lattice QCD drives a coherent picture of the isoscalar mesons.Comment: 14 pages, 1 figure, accepted for publication in Phys. Rev.

Energy-Momentum Tensor for the Electromagnetic Field in a Dielectric

The total momentum of a thermodynamically closed system is unique, as is the total energy. Nevertheless, there is continuing confusion concerning the correct form of the momentum and the energy-momentum tensor for an electromagnetic field interacting with a linear dielectric medium. Here we investigate the energy and momentum in a closed system composed of a propagating electromagnetic field and a negligibly reflecting dielectric. The Gordon momentum is easily identified as the total momentum by the fact that it is, by virtue of being invariant in time, conserved. We construct continuity equations for the energy and the Gordon momentum and use the continuity equations to construct an array that has the properties of a traceless, diagonally symmetric energy-momentum tensor. Then the century-old Abraham-Minkowski momentum controversy can be viewed as a consequence of attempting to construct an energy-momentum tensor from continuity equations that contain densities that correspond to nonconserved quantities.Comment: added publication informatio

Quantum Vacuum Contribution to the Momentum of the Dielectric Media

Momentum transfer between matter and electromagnetic field is analyzed. The related equations of motion and conservation laws are derived using relativistic formalism. Their correspondence to various, at first sight self-contradicting, experimental data (the so called Abraham-Minkowski controversy) is demonstrated. A new, Casimir like, quantum phenomenon is predicted: contribution of vacuum fluctuations to the motion of dielectric liquids in crossed electric and magnetic fields. Velocities about $50nm/s$ can be expected due to the contribution of high frequency vacuum modes

Is the Cygnus Loop two supernova remnants?

The Cygnus Loop is classified as a middle-aged supernova remnant (SNR) located below the Galactic equator (l=74, b=-8.6) and 770 pc away from us. Its large size and little confusion with Galactic emission makes it an ideal test ground for evolutionary and structural theories of SNRs. New radio continuum mapping of the Cygnus Loop at 2695 MHz with the Effelsberg 100-m telescope provides indications that the Cygnus Loop consists of two separate SNRs. Combining this result with data from the literature we argue that a secondary SNR exists in the south with a recently detected neutron star close to its center. Two interacting SNRs seem to be the best explanation to account for the Cygnus Loop observations at all wavelengths.Comment: 4 pages, 2 figures, Astron. Astrophys., accepte

Bohr-Sommerfeld Quantization of Space

We introduce semiclassical methods into the study of the volume spectrum in loop gravity. The classical system behind a 4-valent spinnetwork node is a Euclidean tetrahedron. We investigate the tetrahedral volume dynamics on phase space and apply Bohr-Sommerfeld quantization to find the volume spectrum. The analysis shows a remarkable quantitative agreement with the volume spectrum computed in loop gravity. Moreover, it provides new geometrical insights into the degeneracy of this spectrum and the maximum and minimum eigenvalues of the volume on intertwiner space.Comment: 32 pages, 10 figure