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v3.3.4-pre
We highlight general issues associated with quality and naturalness problems in theories of light QCD-axions. We then move to discuss relaxion models, explaining why the classical QCD-(rel)axion realization suffers from CP and quality problems, and along the way introduce the concept of relaxed-relaxion. We then briefly introduce Hook’s $Z_N$ QCD model, which is naturally extra-visible, and of high quality. Then we integrate the latter model with theb framework relaxation and show that this can in principle address both the QCD relaxion CP problem, as well as its quality problem. This new class of models also leads to interesting experimental signatures, which can be searched for at the precision frontier.
We revisit the original proposal of cosmological relaxation of the electroweak scale by Graham, Kaplan and Rajendran in which the Higgs mass is scanned during inflation by an axion-like field, the relaxion. We investigate the regime where the relaxion is subject to large fluctuations during inflation, including the “quantum-beats-classical” regime. The stochastic dynamics is described by means of the Fokker-Planck formalism. We derive a new stopping condition for the relaxion taking into account the transitions between the local minima. For a large Hubble scale during inflation the field can stop much further away from the first minimum, where the potential is less shallow. We investigate the consequences both for the QCD relaxion and the strong CP problem, as well as for non-QCD models. We identify a new region of the parameter space where the stochastic misalignment of the relaxion from its local minimum due to fluctuations can naturally explain the observed dark matter density in the universe.