Factoring the Strong CP Problem

We present a new mechanism to solve the strong CP problem using $N\geq2$ axions, each dynamically relaxing part of the $\bar\theta$ parameter. At high energies $M\gg\Lambda_{QCD}$ the $SU(3)_{c}$ group becomes the diagonal subgroup of an $SU(3)^{N}$ gauge group, and the non-perturbative effects in each individual $SU(3)$ factor generate a potential for the corresponding axion. The vacuum is naturally aligned to ensure $\bar\theta=0$ at low energies, and the masses of these axions can be much larger than for the standard QCD axion. This mechanism avoids the introduction of a discrete $Z_2$ symmetry and associated 'mirror' copies of the SM fermions, and also avoids the introduction and stabilization of new light colored states to modify the running of the QCD gauge coupling found in other heavy axion models. This strengthens the motivation for axion-like particles solving the strong CP problem at points beyond the standard QCD axion curve in the $(m_a, f_a)$ plane.