New Constraint on Weak CP Phase Rephasing Invariant and Maximal CP Violation

By using the relation between CP-violation phase and the mixing angles in CabibboKobayashi-Maskawa matrix postulated by us before, the rephasing invariant is recalculated. Furthermore, the problem about maximal CP violation is discussed. We find that the maximal value of Jarlskog’s invariant is about 0.038. And it presents at α ≃ 71.00, β ≃ 90.20 and γ ≃ 18.80 in triangle db. PACS number(s): 11.30.Er, 12.10.Ck, 13.25.+m New Constraint on Weak CP Phase Rephasing Invariant and Maximal CP Violation Since the discovery of CP-violation in neutral kaon system in 1964 [1], more than thirty years have passed. Although a great progress has been made during these years [2-6], such as establishing the phenomenological structure of the effects, classifying the CP parameters and contructing the gauge theory models [7-14], our understanding about CP violation is still very poor. On the experimental side, the kaon system remains the only place where CP violaion is observed, though the B meson system is the best probe to it as is widely accepted [15-16]. On the theoretical side, the origin of CP violation is not so clear, and the correctness of the standard Cabibbo-Kobayashi-Maskawa mechanism is far from being proved. In the standard model of three generations, CP violation originates from the phase angle present in the unitary Cabibbo-Kobayashi-Maskawa matrix. Mathematically, it is permited that, only one phase angle exists in a three by three unitary matrix with the exception of three Eulerian angles. However, the weak CP phase which cannot be eliminated by any means, is introduced somewhat artificially. The requirement that it has nothing to do with the three mixing angles is only due to the mathematical rather than a physical reason. It is naturally to ask whether there is an intrinsic relation between the phase and the three mixing angles. Recently, we found that the CP-violation phase and the other three mixing angles satisfy the following relation [17-18]