Attempts to solve naturalness by having the weak scale as the only breaking of classical scale invariance in 4-dimensional Quantum Field Theories satisfy Total Asymptotic Freedom (TAF): the theory holds up to infinite energy, where all coupling constants flow to zero and is devoid of any Landau poles. Specifically we will discuss a fundamental field theory of the QCD axion in the totally asymptotically free (TAF) scenario, and the dynamics of the Peccei-Quinn (PQ) phase transition there-in.

Cosmic ray nuclei arrive on Earth with energies of up to 3x10^20 eV (~50Joules), a macroscopic energy focused on a single sub-atomic particle. Despite nearly 100 years since their first observations, little is still known about the sources of these particles and the processes by which they acquire such tremendous energies. At rates of < 1 / km^2 / century, detecting these particles and extracting information from them requires detector arrays the size of small nations.