Amplitudes Fitted to Experimental Data and to Roy's Equations

The scalar-isoscalar, scalar-isotensor and vector-isovector pi-pi amplitudes are fitted simultaneously to experimental data and to Roy's equations. The resulting amplitudes are compared with those fitted only to experimental data. No additional constraints for the pi-pi threshold behaviour of the amplitudes are imposed. Threshold parameters are calculated for the amplitudes in the three waves. Spectrum of scalar mesons below 1.8 GeV is found from the analysis of the analytical structure of the fitted amplitudes.Comment: 3 pages, 1 figure. Talk given at MESON 2004: 8th International Workshop on Meson Production, Properties and Interactions, Cracow, Poland, 4-8 Jun 2004. Submitted to Int.J.Mod.Phys.

Properties of scalar--isoscalar mesons from multichannel interaction analysis below 1800 MeV

Scalar-isoscalar mesons are studied using an unitary model in three channels: pi-pi, K-anti K and an effective 2pi-2pi. All the solutions, fitted to the pi-pi and K-anti K data, exhibit a wide f0(500), a narrow f0(980) and two relatively narrow resonances, lying on different sheets between 1300 MeV and 1500 MeV. These latter states are similar to the f0(1370) and f0(1500) seen in experiments at CERN. Branching ratios are compared with available data. We have started investigations of some crossing symmetry and chiral constraints imposed near the pi-pi threshold on the scalar-isoscalar, scalar-isotensor and P-wave pi-pi amplitudes.Comment: Talk given at XVth Particles and Nuclei Int. Conf. (PANIC99), Uppsala, Sweden, June 10-16, 1999; 4 pages, 3 figures, file espcrc1.sty include

Multichannel Interaction Analysis of Scalar Mesons Below 1800 MeV

Properties of scalar--isoscalar mesons in a mass range from pi-pi threshold up to 1800 MeV are analysed using an unitary model with separable interactions in three decay channels: pi-pi, K-anti K and an effective 2pi-2pi. Different solutions are obtained by fitting pi-pi and K-anti K data. Analytical structure of the meson-meson multichannel amplitudes is studied with a special emphasis on the important role played by the S-matrix zeroes. The dependence of the positions of S-matrix singularities on the interchannel coupling strength is investigated. Poles, located in the complex energy plane not too far from the physical region, are interpreted as scalar resonances: a wide f0(500), a narrow f0(980) and a relatively narrow f0(1400). In all our solutions two resonances, lying on different sheets, in the energy region between 1300 MeV and 1500 MeV are found. These states may be compared with the resonances f0(1370) and f0(1500) seen in the experiments at CERN. Total, elastic and inelastic channel cross sections, branching ratios and coupling constants are evaluated and compared with available data.Comment: Talk given at Workshop on Hadron Spectroscopy, Frascati (Rome) - Italy, March 8-12, 1999. To be published in Frascati Physics Series, 8 pages, 4 figures, included file frascatiphys.st

Space-time directional Lyapunov exponents for cellular automata

Space-time directional Lyapunov exponents are introduced. They describe the maximal velocity of propagation to the right or to the left of fronts of perturbations in a frame moving with a given velocity. The continuity of these exponents as function of the velocity and an inequality relating them to the directional entropy is proved

Three channel model of meson-meson scattering and scalar meson spectroscopy

New solutions on the scalar -- isoscalar $\pi\pi$ phase shifts are analysed together with previous $K\bar{K}$ results using a separable potential model of three coupled channels ($\pi\pi$, $K\bar{K}$ and an effective $2\pi 2\pi$ system). Model parameters are fitted to two sets of solutions obtained in a recent analysis of the CERN-Cracow-Munich measurements of the $\pi^- p_{\uparrow} \to \pi^+ \pi^- n$ reaction on a polarized target. A relatively narrow (90 -- 180 MeV) scalar resonance $f_0(1400-1460)$ is found, in contrast to a much broader ($\Gamma \approx 500$ MeV) state emerging from the analysis of previous unpolarized target data.Comment: 10 Latex pages + 6 postscript figure

Elimination of ambiguities in pion-pion phase shifts using crossing symmetry

Roy's equations, which incorporate crossing symmetry of the pion-pion scattering amplitudes, are used to resolve the present ambiguity between two solutions for the scalar-isoscalar phase shifts below 1 GeV. It is shown that the "down-flat" solution satisfies well Roy's equations and consequently crossing symmetry while the other solution called "up-flat" does not and thus should be eliminated.Comment: 14 pages, 4 figure

Quantum constraints, Dirac observables and evolution: group averaging versus Schroedinger picture in LQC

A general quantum constraint of the form $C= - \partial_T^2 \otimes B - I\otimes H$ (realized in particular in Loop Quantum Cosmology models) is studied. Group Averaging is applied to define the Hilbert space of solutions and the relational Dirac observables. Two cases are considered. In the first case, the spectrum of the operator $(1/2)\pi^2 B - H$ is assumed to be discrete. The quantum theory defined by the constraint takes the form of a Schroedinger-like quantum mechanics with a generalized Hamiltonian $\sqrt{B^{-1} H}$. In the second case, the spectrum is absolutely continuous and some peculiar asymptotic properties of the eigenfunctions are assumed. The resulting Hilbert space and the dynamics are characterized by a continuous family of the Schroedinger-like quantum theories. However, the relational observables mix different members of the family. Our assumptions are motivated by new Loop Quantum Cosmology models of quantum FRW spacetime. The two cases considered in the paper correspond to the negative and, respectively, positive cosmological constant. Our results should be also applicable in many other general relativistic contexts.Comment: RevTex4, 32 page

The kernel and the injectivity of the EPRL map

In this paper we prove injectivity of the EPRL map for |\gamma|<1, filling the gap of our previous paper.Comment: 17 pages, 3 figure

Strong and Weak Interactions in B to pi+ pi- K Decays

To describe the weak three-body B decays into pi+ pi- K, we recently derived amplitudes based on two-body QCD factorization followed by pi+ pi- final state interactions in isoscalar S- and isovector P-waves. We study here the sensitivity of the results to the values of the B to f0(980) transition form factor and to the effective decay constant of the f0(980).Comment: Contribution to the Few Body 18 conference in Santos, Brazil, August 21-26, 2006, 5 pages, to be published in Nuclear Physics