Extended Derivative Dispersion Relations

It is shown that, for a wide class of functions with physical interest as forward scattering amplitudes, integral dispersion relations can be replaced by derivative forms without any high-energy approximation. The applicability of these extended derivative relations, in the investigation of forward proton-proton and antiproton-proton elastic scattering, is exemplified by means of a Pomeron-Reggeon model with totally nondegenerate trajectories.Comment: 7 pages, 1 figure, contribution to "Sense of Beauty in Physics", Miniconference in Honor of Adriano Di Giacomo on his 70th Birthday, Pisa, Italy, Jan. 26-27, 200

Derivative dispersion relations above the physical threshold

We discuss some formal and practical aspects related to the replacement of Integral Dispersion Relations (IDR) by derivative forms, without high-energy approximations. We first demonstrate that, for a class of functions with physical interest as forward scattering amplitudes, this replacement can be analytically performed, leading to novel Extended Derivative Dispersion Relations (EDDR), which, in principle, are valid for any energy above the physical threshold. We then verify the equivalence between the IDR and EDDR by means of a popular parametrization for total cross sections from proton-proton and antiproton-proton scattering and compare the results with those obtained through other representations for the derivative relations. Critical aspects on the limitations of the whole analysis, from both formal and practical points of view, are also discussed in some detail.Comment: Final version, published in Brazilian Journal of Physics, V. 37, 358 (2007

Selected applications of optoacoustic spectrometry to the examination of solids

Imperial Users onl

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