The CKM matrix with maximal CP violation from Z(12) symmetry

Abstract

The recent accurate determination of the CKM parameters including the maximal CP phase π 2 enables us to write down the up-type and down-type quark mass matrices to a high degree of accuracy. The lightest element(ūu element) of the quark mass texture (not the mass eigenvalue) has a power λ 6 where λ = sin θC. The CP phase of 2π divided by an integer hints a discrete symmetry. Since λ 6 is the highest power of λ among the quark mass matrix elements, we present as an example a possibility that the maximal CP phase π 2 is obtainable from a supersymmetric Z12 discrete symmetry model.

Strong CP problem, axions, and cosmological implications of CP violation

“…Indeed, this has been shown in Ref. [19] where the weak CP violation is spontaneous and one unremovable phase is located at the weak interaction singlet à la the Froggatt-Nielsen(FN) mechanism [20]. 2 In the supersymmetric model, it was shown that one phase in the ultra-violet completion gives [14]: δ PMNS = ±δ CKM .…”

Leptogenesis with high-scale electroweak symmetry breaking and an extended Higgs sector

“…To obtain a calculable theory for phases, we introduce a single Froggatt-Nielsen(FN) field [22] X developing a complex VEV, X = x e iδX [23,24]. The Yukawa coupling matrix of the doublet h u include powers of X such that some symmetry behind the Yukawa couplings is satisfied.…”

Unifying CP violations of quark and lepton sectors

“…Effectively, it amounts to intoducing many H u 's but the FCNCs are suppressed by superheavy masses of X. By some symmetry structure of the theory, the X coupling can be made flavor-dependent [33]. Now, let us proceed in this scheme to relate δ CKM and δ PMNS .…”

“…To have a relation without any other parameters, such as in the relation δ PMNS = ±δ CKM , only one phase must be introduced in the whole theory such as in the unification of GUT families. To mimick the KM weak CP at low energy, the complex VEV must be that of a SM singlet [26] as performed in [27].…”