Analytic models and forward scattering from accelerator to cosmic-ray energies

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Analytic models for hadron-hadron scattering are characterized by analytical parametrizations for the forward amplitudes and the use of dispersion relation techniques to study the total cross section σtot and the ρ parameter. In this paper we investigate four aspects related to the application of the model to pp and pp scattering, from accelerator to cosmic-ray energies: 1) the effect of different estimations for σtot from cosmic-ray experiments; 2) the differences between individual and global (simultaneous) fits to σtot and ρ; 3) the role of the subtraction constant in the dispersion relations; 4) the effect of distinct asymptotic inputs from different analytic models. This is done by using as a framework the single Pomeron and the maximal Odderon parametrizations for the total cross section. Our main conclusions are the following: 1) Despite the small influence from different cosmic-ray estimations, the results allow us to extract an upper bound for the soft pomeron intercept: 1 + ε= 1.094; 2) although global fits present good statistical results, in general, this procedure constrains the rise of σtot; 3) the subtraction constant as a free parameter affects the fit results at both low and high energies; 4) independently of the cosmic-ray information used and the subtraction constant, global fits with the odderon parametrization predict that, above √ s ≈ 70 GeV, ρpp(s) becomes greater than ρpp(s), and this result is in complete agreement with all the data presently available. In particular, we infer ρpp = 0.134 ± 0.005 at √ s = 200 GeV and 0.151 ± 0.007 at 500 GeV (BNL RHIC energies).