pp interactions in extended air showers

Abstract

Abstract. Applying the recently constructed analytic representation for the pp scattering amplitudes, we present a study of p-air cross sections, with comparison to the data from Extensive Air Shower (EAS) measurements. The amplitudes describe with precision all available accelerator data at ISR, SPS and LHC energies, and its theoretical basis, together with the very smooth energy dependence of parameters controlled by unitarity and dispersion relations, permit reliable extrapolation to higher energies and to asymptotic ranges. The comparison with cosmic ray 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 amplitudes predict that the proton does not behave as a black disk even at asymptotically high enegies, and we discuss possible non-trivial consequences of this fact for pA collision cross sections at higher energies.

pp Interaction in Extended Air Showers

“…Our analysis of energy dependence of amplitudes and observables in pp collisions shows that the total cross section has a neat log 2 s form [5], as already indicated in sev-eral analyses [8]. An important new feature is that the slope parameters, B I and B R , also have a log 2 s dependence.…”

“…In our description of the pp system, as given by the energy dependences in Eqs. (2)(3)(4)(5), this ratio has the high energy behaviour…”

“…Recent detailed analyses [1][2][3][4][5] of the experimental pp and pp scattering data based on a QCD inspired model [6,7] reproduces the observed cross sections for all energies with high accuracy. These analyses lead to a precise analytic representation of the elastic scattering amplitudes, disentangling the real and imaginary parts, respecting unitarity and causality conditions, with regular energy dependence that gives confidence in extrapolation to higher energies.…”

“…The relevant parameters are then the total cross section σ, the ratio ρ between real and imaginary parts at t = 0, and the slopes B I and B R of each of the two parts. Our full-t analysis [5] provides the energy dependence of these quantities with simple analytical forms that are appropriate for the whole energy range from 50 GeV to 100 TeV.…”

Elastic amplitudes and observables in pp scattering

“…At 57 TeV the Auger Cosmic Ray experiment [14], using other models for pp input, obtains σ inel = 92 ± 14.8 mb , while our extrapolation gives 101 mb. This measurement [15] is discussed together with other CR Extended Air Showers (EAS) experiments, using our inputs and a basic Glauber method to connect pp and p-air processes. Our calculation reproduces well all CR data for p-air cross sections with energies √ s (in the pp system) up to 100 TeV.…”