The Elusive p-air Cross Section

Abstract

For the $\pbar p$ and $pp$ systems, we have used all of the extensive data of the Particle Data Group[K. Hagiwara {\em 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 ${\chi }^2$ 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 $\delchi$, the individual i${}^{\mathrm{th}}$ point's contribution to the total ${\chi }^2$. The ${\chi }^2$ fits are then made to the sieved data. We demonstrate that we cleanly discriminate between asymptotic $\ln s$ and ${\ln }^{2}s$ behavior of total hadronic cross sections when we require that these amplitudes {\em also} describe, on average, low energy data dominated by resonances. We simultaneously fit real analytic amplitudes to the ``sieved'' high energy measurements of $\bar{p}p$ and $pp$ total cross sections and $\rho$-values for $\sqrt{s}\ge 6$ GeV, while requiring that their asymptotic fits smoothly join the the ${\sigma }_{\bar{p}p}$ and ${\sigma }_{pp}$ total cross sections at $\sqrt{s}=$4.0 GeV--again {\em both} in magnitude and slope. Our results strongly favor a high energy ${\ln }^{2}s$ 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.

15 pages, 6 figures, 2 table,Paper delivered at c2cr2005 Conference, Prague, September 7-13, 2005. Fig. 2 was missing from V1. V3 fixes all figures