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 ${\ensuremath{\sigma}}_{\mathrm{tot}}$ and the $\ensuremath{\rho}$ 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 $\mathrm{pp}$ and $\overline{p}p$ scattering, from accelerator to cosmic-ray energies: (1) the effect of different estimations for ${\ensuremath{\sigma}}_{\mathrm{tot}}$ from cosmic-ray experiments; (2) the differences between individual and global (simultaneous) fits to ${\ensuremath{\sigma}}_{\mathrm{tot}}$ and $\ensuremath{\rho};$ (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: $1+\ensuremath{\epsilon}=1.094;$ (2) although global fits present good statistical results, in general, this procedure constrains the rise of ${\ensuremath{\sigma}}_{\mathrm{tot}};$ (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 $\sqrt{s}\ensuremath{\approx}70\mathrm{GeV},$ ${\ensuremath{\rho}}_{\mathrm{pp}}(s)$ becomes greater than ${\ensuremath{\rho}}_{\overline{p}p}(s),$ and this result is in complete agreement with all the data presently available. In particular, we infer ${\ensuremath{\rho}}_{\mathrm{pp}}=0.134\ifmmode\pm\else\textpm\fi{}0.005$ at $\sqrt{s}=200\mathrm{GeV}$ and $0.151\ifmmode\pm\else\textpm\fi{}0.007$ at 500 GeV (BNL RHIC energies). A detailed discussion of the procedures used and all the results obtained is also presented.