We demonstrate that integral dispersion relations for hadron-hadron scattering amplitudes can be replaced by differential relations, without the usual high-energy approximation. We obtain analytical expressions for the corrections associated with the low energy region and exemplify the applicability of the novel relations in the context of an analytical parametrization for proton-proton and antiproton-proton total cross sections.

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.

Making use of a model-independent analytical fit for the elastic hadron-hadron amplitude, recently developed, we investigate the slope of the proton-proton and antiproton-proton differential cross sections, as a function of the energy and the momentum transfer. We show that the predictions for these quantities are in agreement with the experimental data available and discuss the effect of the slope position as function of the momentum transfer.

After reviewing the main aspects of the model-independent analysis on elastic proton-proton scattering, developed by França and Hama in the seventies, we argue that the work can be considered a paradigm for empirical analysis on elastic hadron interactions (the inverse problem). We discuss some further developments, consequences and results that have been recently obtained on the subject and which have been based on the original strategy by França and Hama.

We review the main results we have obtained in the area of high-energy elastic hadron scattering and presented in this series of Workshops on Hadron Interactions. After an introduction to some basic experimental and theoretical concepts, we survey the results reached by means of four approaches: analytic models, model-independent analyses, eikonal models and nonperturbative QCD. Some of the ongoing researches and future perspectives are also outlined.

Making use of the extrema bounds for the soft pomeron intercept, recently determined by fits to pp and <img id="_x0000_i1026" src="../../img/revistas/bjp/v34n1a/a25img08.gif" align=absbottom>data (from both accelerator and cosmic-ray experiments), we investigate the total cross sections for pion-proton, kaon-proton, gamma-proton and gamma-gamma scattering. We show that by means of global fits, the extrema bounds are in agreement with the bulk of experimental data presently available, and that extrapolations to higher energies indicate different behaviors for the rise of the total cross sections. We also discuss factorization and quark counting, showing that both bounds are in agreement with these properties.

We investigate correlations between the total cross section and the slope of the elastic differential cross section for proton-proton and antiproton-proton scattering at the highest energies. Based on the empirical behavior of these quantities as function of the energy, we select two different analytical parametrizations connecting them, and obtain the correlations through fits to the experimental data available. We present and discuss practical uses of extrapolations and interpolations of the results. In the former case we refer to the estimation of the proton-proton total cross sections from the proton-air cross sections (obtained from cosmic-ray experiments), and in the later case, we critically discuss the recent measurement of the slope parameter at the BNL RHIC at 200 GeV by the pp2pp Collaboration.

We present the results of several parametrizations to two different ensemble of data on pp total cross sections (<FONT FACE=Symbol>s<img SRC="http:/img/fbpe/bjp/v31n4/07eq01.gif" ></FONT>) at the highest center-of-mass energies (including cosmic-ray information). The results are statistically consistent with two distinct scenarios at high energies. From one ensemble the prediction for the LHC (<img SRC="http:/img/fbpe/bjp/v31n4/07eq02.gif"> = 14 TeV) is<FONT FACE=Symbol>s<img SRC="http:/img/fbpe/bjp/v31n4/07eq01.gif" ></FONT> = 113 ± 5 mb and from the other, <FONT FACE=Symbol>s<img SRC="http:/img/fbpe/bjp/v31n4/07eq01.gif"></FONT> = 140 ± 7 mb. From each parametrization, and making use of derivative analyticity relations (DAR), we determine rho(s) (ratio between the forward real and imaginary parts of the elastic scattering amplitude). A discussion on the optimization of the DAR in terms of a free parameter is also presented. In all cases good descriptions of the experimental data are obtained.