Predicting Proton - air Cross Sections at √ s ∼ 30 TeV , using Accelerator and Cosmic Ray Data

We use the high energy predictions of a QCD-inspired parameterization of all accelerator data on forward proton-proton and antiproton-proton scattering amplitudes, along with Glauber theory, to predict proton–air cross sections at energies near √ s ≈ 30 TeV. The parameterization of the proton-proton cross section incorporates analyticity and unitarity, and demands that the asymptotic proton is a black disk of soft partons. By comparing with the p-air cosmic ray measurements, our analysis results in a constraint on the inclusive particle production cross section. Cosmic ray experiments measure the penetration in the atmosphere of particles with energies in excess of those accelerated by existing machines—interestingly, their energy range covers the energy of the Large Hadron Collider (LHC) and extends beyond it. However, extracting proton–proton cross sections from cosmic ray observations is far from straightforward [1]. By a variety of experimental techniques, cosmic ray experiments map the atmospheric depth at which cosmic ray initiated showers develop. The measured shower attenuation length (Λm) is not only sensitive to the interaction length of the protons in the atmosphere (λp−air), with Λm = kλp−air = k 14.5mp σ p−air , (1) but also depends on the rate at which the energy of the primary proton is dissipated into electromagnetic shower energy observed in the experiment. The latter effect is parameterized in Eq. (1) by the parameter k; mp is the proton mass and σ inel p−air the inelastic proton-air cross section. The value of k depends on the inclusive particle production cross section in nucleon and meson interactions on the light nuclear target of the atmosphere and its energy dependence. We here ignored the fact that particles in the cosmic ray ”beam” may be nuclei, not just protons. Experiments allow for this by omitting from their analysis showers which dissipate their energy high in the atmosphere, a signature that the initial energy is distributed over the constituents of a nucleus. The extraction of the pp cross section from the cosmic ray data is a two step process. First, one calculates the p-air total cross section from the measured inelastic cross section σ p−air = σp−air − σ p−air − σ q−el p−air . (2) Next, the Glauber method [2] is used to transform the measured value of σ p−air into a proton–proton total cross section σpp; all the necessary steps are calculable in the theory. In Eq. (2) the measured cross section for particle production is supplemented with the elastic and quasi-elastic cross section, as calculated by the Glauber theory, to obtain the total cross section σp−air. The subsequent relation between σ inel p−air and σpp involves the slope of the forward scattering amplitude for elastic pp scattering, B = [