A Flavorful Factoring of the Strong CP Problem

Motivated by the intimate connection between the strong CP problemand the flavor structure of the Standard Model, we present a flavor model that revives and extends the classic ${m_u=0}$ solution to the strong CP problem. QCD is embedded into a $SU(3)_1\times SU(3)_2 \times SU(3)_3$ gauge group, with each generation of quarkscharged under the respective $SU(3)$. The non-zero value of the up-quarkYukawa coupling (along with the strange quarkand bottom-quarkYukawas) is generated by contributions from small instantonsat a new scale $M \gg \Lambda_{QCD}$. The Higgsing of $SU(3)^3\to SU(3)_c$ allows dimension-5 operators that generate the Standard Model flavor structure and can be completed in a simple renormalizable theory. The smallness of the third generation mixing angles can naturally emerge in this picture, and is connected to the smallness of threshold corrections to $\bar\theta$. Remarkably, $\bar\theta$ is essentially fixed by the measured quarkmasses and mixings, and is estimated to be close to the current experimental bound and well within reach of the next generation of neutron and proton EDM experiments.