Grand unified parity solution to the strong $CP$ problem

A beyond the standard model theory that respects parity symmetry at short distances is known to provide a solution to the strong $CP$ problem without the need for an axion, while keeping the Cabibbo-Kobayashi-Maskawa phase unconstrained. In this paper we present a supersymmetric SO(10) grand unified embedding of this idea with Yukawa couplings generated by $\mathbf{10}$, $\overline{\mathbf{126}}$ and $\mathbf{120}$ Higgs fields. This model is known to provide a unified description of masses and mixings of quarks and leptons. When $CP$ symmetry is imposed on this model, the discrete gauge subgroup C of SO(10) combines with it to generate an effective parity symmetry, leading to Hermitian quark mass matrices. Imposing an additional discrete symmetry, $G$, we show that there are no other tree level sources of $\theta$ in the model; $G$ also guarantees that the one- and two-loop contributions to $\theta$ vanish. We then show that the leading three-loop effects and the effect of higher-dimensional operators invariant under $G$ give rise to $\theta$ near the current experimental bound, making the model testable in the current searches for neutron electric dipole moment.

Figure 1

The 3-loop diagram which induces the phase of the gluino mass. There are also diagrams in which $u^c{e}^c‐q\ell$ and ${\nu }^c{d}^c‐\ell q$ propagate. In 126 and 120, there are other colored components, e.g., ($\mathbf{8}$, $\mathbf{2}$, $1/2$), which have bifermion couplings, and there are similar loop-diagrams in which the other colored components propagate for the gluino mass correction.