Measurement of the Proton-Air Cross Section with Telescope Array's Black Rock Mesa and Long Ridge Fluorescence Detectors, and Surface Array in Hybrid Mode

Abstract: Ultra high energy cosmic rays provide the highest known energy source in the universe to measure proton cross sections. Though conditions for collecting such data are less controlled than an accelerator environment, current generation cosmic ray observatories have large enough exposures to collect significant statistics for a reliable measurement for energies above what can be attained in the lab. Cosmic ray measurements of cross section use atmospheric calorimetry to measure depth of air shower maximum ($X_{\mathrm{max}}$), which is related to the primary particle's energy and mass. The tail of the $X_{\mathrm{max}}$ distribution is assumed to be dominated by showers generated by protons, allowing measurement of the inelastic proton-air cross section. In this work the proton-air inelastic cross section measurement, $\sigma^{\mathrm{inel}}_{\mathrm{p-air}}$, using data observed by Telescope Array's Black Rock Mesa and Long Ridge fluorescence detectors and surface detector array in hybrid mode is presented. $\sigma^{\mathrm{inel}}_{\mathrm{p-air}}$ is observed to be $520.1 \pm 35.8$[Stat.] $^{+25.0}_{-40}$[Sys.]~mb at $\sqrt{s} = 73$ TeV. The total proton-proton cross section is subsequently inferred from Glauber formalism and is found to be $\sigma^{\mathrm{tot}}_{\mathrm{pp}} = 139.4 ^{+23.4}_{-21.3}$ [Stat.]$ ^{+15.0}_{-24.0}$[Sys.]~mb.