Empirical Determination of the Very High Energy Heavy Quark Cross Section from Non-Accelerator Data

To cosmic rays incident near the horizon the Earth's atmosphere represents a beam dump with a slant depth reaching 36000~g~cm$^{-2}$ at $90^\circ$. The prompt decay of a heavy quark produced by very high energy cosmic ray showers will leave an unmistakable signature in this dump. We translate the failure of experiments to detect such a signal into an upper limit on the heavy quark hadroproduction cross section in the energy region beyond existing accelerators. Our results disfavor any rapid growth of the cross section or the gluon structure function beyond very conservative estimates based on perturbative QCD.Comment: (8 pages, latex file, 3 figures available upon request) MAD/PH/74