pp interaction at very high energies in cosmic ray experiments

An analysis of p-air cross section data from extensive air shower measurements is presented, based on an analytical representation of the pp scattering amplitudes that describes with high precision all available accelerator data at ISR, SPS and LHC energies. The theoretical basis of the representation, together with the very smooth energy dependence of parameters controlled by unitarity and dispersion relations, permits reliable extrapolation to high energy cosmic ray (CR) and asymptotic energy ranges. Calculations of σp−airprod based on Glauber formalism are made using the input values of the quantities σ, ρ, BI and BR at high energies, with attention given to the independence of the slope parameters, with BR≠BI. The influence of contributions of diffractive intermediate states, according to Good–Walker formalism, is examined. The comparison with CR data is very satisfactory in the whole pp energy interval from 1 to 100 TeV. High energy asymptotic behaviour of cross sections is investigated in view of the geometric scaling property of the amplitudes. The observed energy dependence of the ratio between p-air and pp cross sections in the data is shown to be related to the nature of the pp cross section at high energies, that does not agree with the black disk image. (paper)