Extending the Frontiers—Reconciling Accelerator and Cosmic Ray p-p Cross Sections

We simultaneously fit a QCD-inspired parameterization of all accelerator data on forward protonproton and antiproton-proton scattering amplitudes, together with cosmic ray data (using Glauber theory), to predict proton-air and proton-proton cross sections at energies near √ s ≈ 30 TeV. The p-air cosmic ray measurements provide a strong constraint on the inclusive particle production cross section, as well as greatly reducing the errors on the fit parameters—in turn, greatly reducing the errors in the high energy proton-proton and proton-air cross section predictions. Work partially supported by Department of Energy contract DA-AC02-76-Er02289 Task B. Work partially supported by Department of Energy Grant No. DE-FG02-95ER40896 and the University of Wisconsin Research Committee with funds granted by the Wisconsin Alumni Research Foundation. Work partially supported by the U.S. Department of Energy under Grant No. DE-FG02-91ER40626. The energy range of cosmic ray experiments covers not only the energy of the Large Hadron Collider (LHC), but extends beyond it. Cosmic ray experiments can measure the penetration in the atmosphere of these very high energy protons—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 quantity is the shower attenuation length (Λm), which 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 critically on the inelasticity, which determines the rate at which the energy of the primary proton is dissipated into electromagnetic shower energy observed in the experiment. The latter effect is taken into account in Eq. (1) by the parameter k; mp is the proton mass and σ inel p−air the inelastic proton-air cross section. The departure of k from unity 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. The extraction of the pp cross section from the cosmic ray data is a two stage process. First, one calculates the p-air total cross section from the inelastic cross section inferred in Eq. (1), where σ p−air = σp−air − σ p−air − σ q−el p−air . (2) Next, the Glauber method [2] transforms the value of σ p−air into a proton-proton total cross section σpp; all the necessary steps are calculable in the theory, but depend sensitively on a knowledge of B, the slope of dσ pp dt , the pp differential elastic scattering cross section, where