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 supersynunetric SO(10) grand unified embedding of this idea with Yukawa couplings generated by 10, (126) over bar and 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 them 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.