Particle Physics at Ultrahigh Energies

We explore particle physics beyond accelerator energies, motivated by questions exposed in astroparticle physics observations: 1) Are there reasonable modifications to the standard extrapolations of LHC-tuned hadronic interaction models, so that ultrahigh energy cosmic ray (UHECR) showers are well-described with a purely protonic primary composition rather than requiring a tuned, energy-dependent composition mixture as needed in conventional models? 2) What modifications to standard models can solve the deficiency in the predicted ground signal found in hybrid UHECR observations? We find that a pure proton composition provides an excellent fit to shower observations, if the QCD inelastic cross section increases more rapidly above $E_{\rm cm} \approx 60$ TeV than in conventional models, and speculate as to possible reasons this may happen; the "muon deficiency" can be cured by relatively minor modifications to particle ratios in unexplored kinematic regimes below and above LHC energies.