Abstract
A global $\mathrm{U}{(1)}_{A}$ symmetry is used to solve both the fermion-mass-hierarchy problem and the strong $\mathrm{CP}$ problem. A domain-wall-free invisible-axion model requires heavy fermions at the axion scale. The dominant contribution to the off-diagonal elements of the fermion mass matrix comes from the small vacuum expectation value of superheavy scalar doublets, which is guaranteed by the Peccei-Quinn symmetry.
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