Eikonal zeros in the momentum transfer space from proton-proton scattering: An empirical analysis

By means of improved empirical fits to the differential cross section data on $pp$ elastic scattering at $19.4 \le\sqrt{s}\le 62.5$ GeV and making use of a semi-analytical method, we determine the eikonal in the momentum transfer space (the inverse scattering problem). This method allows the propagation of the uncertainties from the fit parameters up to the extracted eikonal, providing statistical evidence that the imaginary part of the eikonal (real part of the opacity function) presents a zero (change of signal) in the momentum space, at $q^2 \approx 7 \pm 1$ GeV$^2$. We discuss the implication of this change of signal in the phenomenological context, showing that eikonal models with one zero provide good descriptions of the differential cross sections in the full momentum transfer range, but that is not the case for models without zero. Empirical connections between the extracted eikonal and results from a recent global analysis on the proton electric form factor are also discussed, in special the Wu-Yang conjecture. In addition, we present a critical review on the $pp$ differential cross section data presently available at high energies.Comment: Two references and some misprints corrected, 22 pages; final version to be published in Eur.Phys. J. C (2008

Total factor productividty growth in agriculture: the role of technological capital.

In this chapter we compute measures of total factor productivity (TFP) growth for developing countries and then contrast TFP growth with technological capital indexes. In developing these indexes, we incorporate schooling capital to yield two new indexes: Invention-Innovation Capital and Technology Mastery. We find that TFP performance is strongly related to technological capital and that technological capital is required for TFP and cost reduction growth. Investments in technological capital require long-term (20- to 40-year) investments, which are typically made by governments and aid agencies and are the only viable escape route from mass poverty

On model-independent analyses of elastic hadron scattering

By means of an almost model-independent parametrization for the elastic hadron-hadron amplitude, as a function of the energy and the momentum transfer, we obtain good descriptions of the physical quantities that characterize elastic proton-proton and antiproton-proton scattering (total cross section, r parameter and differential cross section). The parametrization is inferred on empirical grounds and selected according to high energy theorems and limits from axiomatic quantum field theory. Based on the predictive character of the approach we present predictions for the above physical quantities at the Brookhaven RHIC, Fermilab Tevatron and CERN LHC energies.67567

Creation of blenders in the conservative setting

In this work we prove that each C^r conservative diffeomorphism with a pair of hyperbolic periodic points of co-index one can be C^1-approximated by C^r conservative diffeomorphisms having a blender.Comment: 4 figures, 16 figure