An even lighter QCD axion

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