Window for preferred axion models

We discuss phenomenological criteria for defining "axion windows," namely regions in the parameter space of the axion-photon coupling where realistic models live. Currently, the boundaries of this region depend on somewhat arbitrary criteria, and it would be highly desirable to specify them in terms of precise phenomenological requirements. We first focus on hadronic axion models within post-inflationary scenarios, in which the initial abundance of the new vectorlike quarks Q is thermal. We classify their representations RQ by requiring that (i) the Q are sufficiently short lived to avoid issues with long-lived strongly interacting relics, (ii) the theory remains weakly coupled up to the Planck scale. The more general case of multiple RQ is also studied, and the absolute upper and lower bounds on the axion-photon coupling as a function of the axion mass is identified. Pre-inflationary scenarios in which the axion decay constant remains bounded as fa≤5×1011 GeV allow for axion-photon couplings only about 20% larger. Realistic Dine-Fischler-Srednicki-Zhitnitsky type of axion models also remain encompassed within the hadronic axion window. Some mechanisms that can allow to enhance the axion-photon coupling to values sizeably above the preferred window are discussed.