Exploring the Origin of CP Violation in the Standard Model

In this article, we present a very general but not ultimate solution of CPV problem in the standard model. Our study starts from a naturally Hermitian M 2 ≡ M q · M q † rather than the previously assumed Hermitian M q . The only assumption employed here is that the real part and imaginary part of M 2 can be, respectively, diagonalized by a common U q matrix. Such an assumption leads to a M 2 pattern which depends on only five parameters and can be diagonalized analytically by a U q matrix which depends on only two of the parameters. Two of the derived mass eigenvalues are predicted degenerate if one of the parameters C ( C ′ ) in up- (down-) quark sector is zero. As the U q patterns are obtained, thirty-six V CKM candidates are yielded and only eight of them, classified into two groups, fit empirical data within the order of O ( λ ). One of the groups is further excluded in a numerical test, and the surviving group predicts that the degenerate pair in a quark type are the lightest and the heaviest generations rather than the lighter two generations assumed in previous researches. However, there is still one unsatisfactory prediction in this research, a quadruple equality in which four CKM elements of very di ff erent values are predicted to be equal. It indicates the M 2 pattern studied here is still oversimplified by that employed assumption and the ultimate solution can only be obtained by diagonalizing the unsimplified M 2 matrix containing nine parameters directly. The V CKM presented here is already very close to such an ultimate CPV solution.