ar X iv : h ep - p h / 04 08 08 6 v 1 6 A ug 2 00 4 P - P Total Cross Sections at VHE from Accelerator Data

Up today estimations of proton-proton total cross sections, σ pp tot , at very high energies are obtained from cosmic rays (> 10 17 eV) by means of some approximations and the knowledge of the measured proton-air cross section at these energies. Besides, σ pp tot are measured with present day high energy colliders up to nearly 2 TeV in the center of mass (∼ 10 15 eV in the laboratory). Several theoretical, empirical or semi-empirical parameterizations, very successful for interpolation at accelerator energies, can then be used to extrapolate the measured value to cosmic ray energies and get a reasonable estimation of cross sections at higher energies (∼ 10 17 eV). When both cross section estimations-from accelerators and cosmic rays-are compared, a disagreement is observed, amounting to more than 10%, showing a discrepancy beyond statistical errors. Here we use a phenomenological model based on the Multiple-Diffraction approach to successfully describe data at accelerator energies. Then we estimate with this model σ pp tot at cosmic ray energies. The employed fitting method associates the model free-parameters to the data of only two physical observable: the differential cross-section and the parameter ρ. The model predictions for estimations of σ pp tot are then compared with data of total cross-sections. On the basis of regression analysis we determine confident error bands, analyzing the sensitivity of our predictions to the employed data for extrapolation. : using data at 546 and 1.8 TeV, our extrapolations for σ pp tot are only compatible with the Akeno cosmic ray data, predicting a slower rise with energy than other cosmic ray results and other extrapolation methods. We discuss our results within the context of constraints in the light of future accelerator and cosmic ray experimental results.