Phenomenological implications of fundamental theories of axions and how to probe them

The axion represents one of the most compelling extensions of the Standard Model (SM), by simultaneously solving the strong-CP problem and providing an excellent dark matter candidate. Nevertheless, the global Peccei-Quinn (PQ) symmetry, invoked to deliver the axion, cannot be a fundamental symmetry of Nature, since it is broken by quantum corrections at high energies. Moreover, a credible description of the origin of the PQ symmetry from high energy dynamics is currently also lacking. This project aims to use these problems as a guide to find possible complete theories of the axion. The implications of these theories will be investigated in conjunction with other unsolved problems of the SM such as the flavor hierarchy problem and the observed lepton-flavour non-universality. Moreover, the extra imprints on low energy collider observables and cosmological signatures as well as the possibility of breaking the large degeneracy in the axion parameter space will also be carefully studied.