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In this manuscript, a general FCNC-free and CP-violating pattern ofquark-mass matrices in the 2HDM derived in our previous investigations isrevised. This revised pattern is to be diagonalized analytically with nosymmetries imposed. The unitary transformation matrices thus derived depend ononly two parameters in each quark type and subsequently lead to a CKM matrixwhich depends on at most four parameters. The fitting of theoretically derivedCKM elements and their corresponding empirical values are as good as ${\bfO}(10^{-2})$ at tree-level. In a phenomenological way which imposes severalfine-tuning parameters into the CKM matrix suitably, the fitting is furtherimproved to ${\bf O}(10^{-4})$. After the derivation, we find this hypothesisalso applies to the Standard Model and even a model with three Higgs doublets.This will be a big progress in the derivation of a theoretical origin of CPviolation.

Theoretical Origin of CP violation in the FCNC-free 2HDM and Its Extensions to the Standard Model and 3HDM