Proton-Air Cross Section and Composition of Ultra High Energy Cosmic Rays Observed by Telescope Array

Ultra high energy cosmic rays (UHECRs) provide a natural source of particles accelerated to energies beyond those that can be attained in the laboratory. UHECRs have been observed with energies exceeding $10^{20}$ eV, which is equivalent to 433 TeV in the center-of-momentum frame. Using this natural source of particles physicists can extend the measurement of the $pp$ cross section an order of magnitude above what is achievable in the lab, possibly identifying hints of new physics. The proton-air cross section and other properties of UHECR QCD physics are also important in their own right to the study of the sources and composition of UHECRs, but hadronic modelling at these energies is still reliant upon phenomenological and the theoretical extrapolations based upon terrestrial accelerator data. UHECR data can be used to improve these extrapolations of the proton-air cross section, but large uncertainties remain for other hadronic model parameters. We present the most recent measurement of the inelastic proton-air cross section at $\sqrt{s} = 95$ TeV measured by Telescope Array using high quality $X_{\mathrm{max}}$ data collected in hybrid observing mode. This measurement is also used to infer the total proton-proton cross section.