Maximal CP and Bounds on the Neutron Electric Dipole Moment from P and CP Breaking

Abstract

We find in theories with spontaneous P and CP violation that symmetries needed to set the tree level strong CP phase to zero can also set all non-zero tree level CP violating phases to the maximal value π/ 2 in the symmetry basis simultaneously explaining the smallness of \barθ and the largeness of the CKM CP violating phase. In these models we find the one loop lower bound \barθ > 10^{-11} relevant for early discovery of neutron edm d_n > 10^{-27} ecm. The lower bound relaxes to \barθ > 10^{-13} or d_n > 10^{-29} ecm for the case where the CP phases are non-maximal. Interestingly the spontaneous CP phase appears in the quark sector, not the Higgs sector, and is enabled by a heavy left-right symmetric vectorlike quark family with mass M. These results do not vanish in the decoupling limit of M_{H_2^+} > M \rightarrow \infty (where M_{H_2^+} is the mass of heavy Higgs at the parity breaking scale) and the age-old expectation that laws of nature (or its Lagrangian) are parity and matter-antimatter symmetric may be testable by the above predictions and EDM experiments, even if new physics occurs only at see-saw, GUT or Planck scales. There is also a region in parameter space with M_{H_2^+} < M where the above bounds are dampened by the factor (M_{H_2^+}/M)^2. By using flavour symmetries and texture arguments we also make predictions for the CKM phase that arises from the maximal phase on diagonalization to the physical basis. There are no axions predicted in this model.