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 ${\sigma }_{tot}$ and the $\rho$ 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 ${\sigma }_{tot}$ 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: $1+ϵ=1.094$; 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 $\sqrt{s}\approx 70$ GeV, ${\rho }_{pp}(s)$ becomes greater than ${\rho }_{\bar{p}p}(s)$, and this result is in complete agreement with all the data presently available. In particular, we infer ${\rho }_{pp}=0.134\pm 0.005$ at $\sqrt{s}=200$ GeV and $0.151\pm 0.007$ at 500 GeV (BNL RHIC energies).

Comments: 16 pages, 7 figures, aps-revtex, wording changes, corrected typos, to appear in Physical Review D