Catalogues of cosmologically self-consistent hadronic QCD axion models

We extend the catalogue of “phenomenologically preferred” hadronic axion models to include heavy fermion representations associated with higher-dimensional decay operators. The latter have recently been shown to self-consistently trigger a period of early matter domination, making the underlying axion models cosmologically viable. After identifying all possible representations up to decay operator dimension d ≤ 9, we update the hadronic axion band for the axion-photon coupling. The central regions of the axion band are similar to those found previously and approximately independent of the axion decay constant f_a , suggesting that they are robust predictions and targets for future axion searches. Moreover, we find that d = 6 and d = 7 operators can lead to two new viable “model islands” around f_a ∼ 10¹² GeV and f_a ∼ 10¹⁴ GeV, i.e., beyond the standard post-inflationary mass region.