An even lighter QCD axion

We explore whether the axion which solves strong CP problem can naturally be much lighter than canonical QCD axion. The $Z_\mathcal{N}$ symmetry proposed by Hook, with $\mathcal{N}$ mirror and degenerate worlds coexisting in Nature linked field, is considered terms of generic effective couplings. show that total potential safely approximated a single cosine large limit, we determine analytical formula for exponentially suppressed mass. resulting universal enhancement all interactions relative to those has impact on prospects axion-like particle experiments such as ALPS II, IAXO many others. finite density also analyzed asymmetric background high-density stellar environments sets already significant model-independent constraints: $3\le\mathcal{N}\lesssim47$ an scale $f_a\lesssim 2.4\times10^{15}$ GeV, tantalizing discovery any value $f_a$ down $\mathcal{N}\sim9$ future neutron star gravitational wave data, ultra-light mass region. In addition, two specific ultraviolet completions are developed: composite one KSVZ-like model improved Peccei-Quinn quality.