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

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