Abstract
We analyze the strong CP problem and the implications for axion physics in the context ofU1vector leptoquark models, recently put forward as an elegant solution to the hints of lepton flavoruniversality violation inB-meson decays. It is shown that in minimal gauge models containing theU1as a gauge boson, the Peccei-Quinn solution of the strong CP problem requires the introductionof two axions. Characteristic predictions for the associated axions can be deduced from the modelparameter space hinted byB-physics, allowing the new axion sector to account for the dark matterof the Universe. We also provide a specific ultraviolet completion of the axion sector that connectsthe Peccei-Quinn mechanism to the generation of neutrino masses