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

Analytic models for hadron-hadron scattering are characterized by simple analytical parametrizations for the forward amplitudes and the use of dispersion relation techniques to study the total cross section sigma(tot) and the rho parameter (the ratio between the real and imaginary parts of the forward amplitude). In this paper we investigate simultaneously four aspects related to the application of the model to pp and (p) over barp scattering, from accelerator to cosmic-ray energies: (1) the effect of different estimations for sigma(tot) from cosmic-ray experiments; (2) the differences between individual and global (simultaneous) fits to sigma(tot) and rho; (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 + epsilon = 1.094; (2) although global fits present good statistical results, in general, this procedure constrains the rise of sigma(tot); (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 roots approximate to 70 GeV, rho(pp)(s) becomes greater than rho((p) over barp)(s), and this result is in complete agreement with all the data presently available. In particular, we infer rho(pp)=0.134+/-0.005 at roots = 200 GeV and 0.151+/-0.007 at 500 GeV (BNL RHIC energies). A detailed discussion of the procedures used and all the results obtained is also presented.