Tatsuo Kobayashi, Hajime Otsuka, Morimitsu Tanimoto, Tsutomu T. Yanagida
The unsuppressed C P violation in QCD is a problem in the standard model. If we have some mechanism to guarantee real determinants of the quark mass matrices, the vanishing physical vacuum angle θ ¯ indicates the C P invariance at the fundamental level. Thus, the small θ ¯ is technically natural, since we have an enhanced C P symmetry in the limit of the vanishing θ ¯ = 0 . In fact, it was proved that the vacuum angle is never renormalized up to the four-loop level once it is fixed at 0 value at some high energy scale. The purpose of this paper is to construct a model that guarantees the real determinants of the quark mass matrices assuming a noninvertible symmetry. In the present model, we have only one C P violating phase and hence all observable phases such as phases in the Cabibbo-Kobayashi-Maskawa matrix, in the neutrino oscillation and in the leptogenesis are related. It should be remarkable that the correct sign of the baryon-number asymmetry in the present Universe is obtained and a narrow region for the C P violating phase δ CP ≃ 19 2 ° – 19 7 ° is predicted.