The Elusive p-air cross section

For the \(\bar pp\) and pp systems, we have used all of the extensive data of the Particle Data Group K. Hagiwara et al. (Particle Data Group), Phys. Rev. D 66, 010001 (2002)]. We then subject these data to a screening process, the “Sieve” algorithm M. M. Block, physics/0506010], in order to eliminate “ outliers” that can skew a χ² fit. With the “Sieve” algorithm, a robust fit using a Lorentzian distribution is first made to all of the data to sieve out abnormally high Δχ _i ² , the individual i^th point’s contribution to the total χ². The χ² fits are then made to the sieved data. We demonstrate that we cleanly discriminate between asymptotic ln s and ln² s behavior of total hadronic cross sections when we require that these amplitudes also describe, on average, low energy data dominated by resonances. We simultaneously fit real analytic amplitudes to the “sieved” high energy measurements of \(\bar pp\) and pp total cross sections and ρ-values for \(\sqrt s \) ≥ GeV, while requiring that their asymptotic fits smoothly join the the σ _pp and σ_pp total cross sections at \(\sqrt s \) = 4.0 GeV—again both in magnitude and slope. Our results strongly favor a high energy ln² s fit, basically excluding a ln s fit. Finally, we make a screened Glauber fit for the p-air cross section, using as input our precisely-determined pp cross sections at cosmic ray energies.