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

Abstract

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 $σ_{tot}$ and the $ρ$ parameter. In this paper we investigate four aspects related to the application of the model to $pp$ and $\bar{p}p$ scattering, from accelerator to cosmic-ray energies: 1) the effect of different estimations for $σ_{tot}$ from cosmic-ray experiments; 2) the differences between individual and global (simultaneous) fits to $σ_{tot}$ 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 $σ_{tot}$; 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 $\sqrt s \approx 70$ GeV, $ρ_{pp}(s)$ becomes greater than $ρ_{\bar{p}p}(s)$, and this result is in complete agreement with all the data presently available. In particular, we infer $ρ_{pp} = 0.134 \pm 0.005$ at $\sqrt s = 200$ GeV and $0.151 \pm 0.007$ at 500 GeV (BNL RHIC energies).