Proton-proton total cross section above 104 GeV: Can cosmic rays give the answer

From Glauber calculations of the absorption cross section of nucleons on air (σₐbs) we find that present extensive-air-shower data cannot resolve the question of the asymptotic energy behavior of the nucleon-nucleon total cross section [σ_t(NN)]. Relative differences between various asymptotic extrapolations for σ_t(NN) are reduced by about a factor of 3 in σₐbs through the Glauber conversion. Novel techniques or conventional experiments with a better determination of electron and muon numbers in extensive air showers will be required in order to obtain useful information on proton-proton cross sections in the asymptotic region.