Strong and weakCPin a model with a new gauged U(1) symmetry

We discuss a natural solution to the strong CP problem with spontaneous CP breaking in the context of $S{U}C(3)×{}S{U}L(2)×{}{U}Y(1)×{}{U}new(1)$ with two vectorlike quarks. The gauged ${U}new$(1) symmetry is imposed such that ${{θ}}$ remains zero at the tree level when $CP$ and ${U}new$(1) are broken by singlet Higgs scalars. Flavor-changing neutral currents at the tree level are naturally suppressed because only singlet Higgs scalars are introduced. In order to agree with the experimental measurement of ε and ε^'ε, we find that the CP-breaking scale and the masses of the new quarks are less than 2.0 TeV and 530 GeV, respectively.