Proton-proton total cross sections estimations at very high energies

Proton-proton total cross sections are measured with present day high energy colliders up to 2 TeV in the centre-of-mass of the system (10^{15}) eV in the laboratory). Several parameterizations, very succesful at low energies, can then be used to extrapolate the measured values and get estimations of cross sections to higher energies (10^{17} eV). On the other hand, from very high energetic cosmic rays (> 10^{17} eV) and using some approximations, it is possible to get a value for proton-proton total cross section from the knowledge of the proton-proton total cross section at these energies. Here we use a phenomenological model to estimate proton-proton total cross section at cosmic ray energies. On the basis of regression analysis we show that the predictions are highly sensitive to the employed data for extrapolation. Using data at 1.8 TeV our extrapolations for proton-proton total cross section are incompatible with most of cosmic ray results