GeV-scale QCD Axion

Abstract: In order to solve the strong CP problem, we study the possibility that the Peccei--Quinn symmetry is broken {\it below}\/ the QCD scale. We find that a QCD axion can be above GeV, and may be among the observed $η$ resonances. It is immune to quantum gravity corrections. The only fermion that has a $U(1)$ Peccei--Quinn charge is the right-handed up quark. Flavor-changing neutral currents are surprisingly small, except for a possible but not necessary contribution to $D<sup>0$--$\overline{D}<sup>0$ mixing. All accelerator and astrophysical limits can be evaded. The most significant constraint is the mass splitting between $π<sup>\pm$ and $π<sup>0$. In a UV completed model, LHC can look for a dijet resonance in $u\bar{u}$, $u\bar{d}$, $d\bar{u}$ channels.