High-Energy Proton-Proton Forward Scattering and Derivative Analyticity Relations

Abstract

We present the results of several parametrizations to two different ensemble of data on $pp$ total cross sections $σ_{tot}^{pp}$ at the highest center-of-mass energies (including cosmic-ray information). The results are statistically consistent with two distinct scenarios at high energies. From one ensemble the prediction for the LHC ($\sqrt s = 14$ TeV) is $σ_{tot}^{pp} = 113 \pm 5$ mb and from the other, $σ_{tot}^{pp}=140 \pm 7$ mb. From each parametrization, and making use of derivative analyticity relations (DAR), we determine $ρ(s)$ (ratio between the forward real and imaginary parts of the elastic scattering amplitude). A discussion on the optimization of the DAR in terms of a free parameter is also presented.In all cases good descriptions of the experimental data are obtained.

One formula added, one unit changed, small misprints corrected, final version to be published in Brazilian Journal of Physics; 13 pages, 8 figures, aps-revtex