Let us rephase the $R_2$ factors for the CKM matrix, so that each factor is a nice matrix of determinant $\pm 1$. That is, one parameter appears in a factor of the form
The correct phase for the triplet of such factors is
where the numerator and denominator each contribute a phase of $\pi/12 + x$ for $x = 0.003$ a small parameter. In this form, the triple product is more clearly associated to triality. Note that the numerator of $\phi$ cancels the phasing of each factor, so we have simply modified the complex matrix by the phase $\pi/12 + x$.
6 years ago