Anomalous Solutions to the Strong $CP$ Problem

We present a new mechanism for solving the strong $CP$ problem using a ${\mathbb{Z}}_2$ discrete symmetry and an anomalous $U(1)$ symmetry. A ${\mathbb{Z}}_2$ symmetry is used so that two gauge groups have the same theta angle. An anomalous $U(1)$ symmetry makes the difference between the two theta angles physical and the sum unphysical. Two models are presented where the anomalous symmetry manifests itself in the IR in different ways. In the first model, there are massless bifundamental quarks, a solution reminiscent of the massless up quark solution. In the IR of this model, the ${\eta }^{\prime }$ boson relaxes the QCD theta angle to the difference between the two theta angles—in this case zero. In the second model, the anomalous $U(1)$ symmetry is realized in the IR as a dynamically generated mass term that has exactly the phase needed to cancel the theta angle. Both of these models make the extremely concrete prediction that there exist new colored particles at the TeV scale.

Figure 1

The mass of the ${\rho }^{\prime }$ meson in the mirror sector as a function of the mirror Higgs VEV. The mass of the scalar color octet will be a factor of a few below the mass of the ${\rho }^{\prime }$.

Figure 2

${\mathrm{\Lambda }}_{{\mathrm{QCD}}^{\prime }}$ as a function of the mass of the $N_f$ flavors of quarks ${\psi }_Q^i$. The VEV of the mirror Higgs field is set to be ${10}^{14}\mathrm{GeV}$. The mass of the $N_f$ flavor of quarks is bounded by about 3 TeV. The black, blue, and red lines are $N_f=1,5$, and 10, respectively.