We propose a minimal model in which the flavour anomaly in the $b to s mu^+ mu^-$ transition is connected to the breaking of Peccei-Quinn (PQ) symmetry. The flavour anomaly is explained from new physics contribution by introducing one generation of heavy quark and heavy lepton which are vector-like under the standard model (SM) gauge group but charged under a local $U(1)_X$ group. They mix with the SM quarks and leptons, inducing flavour-changing $Z^prime$ couplings, which generates the $b to s mu^+mu^-$ anomaly at tree level. On the other hand the new fermions are chiral under the global Peccei-Quinn(PQ) symmetry. The pseudo-Goldstone boson coming from the spontaneous breaking of the PQ symmetry becomes an axion, solving the strong CP problem and providing a cold dark matter candidate. The same symmetry prevents the right-handed neutrino from having a Majorana mass term. But the introduction of a neutrino-specific Higgs doublet allows neutrino to have Dirac mass term without fine-tuning problem. The model shows an interplay between axion, neutrino, dark matter, and flavour physics.
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