A How to draw the angles of the CKM matrix?

[Heidi]

Hi Pfs,
please look at the CKM article on wikipedia
https://en.wikipedia.org/wiki/Cabibbo–Kobayashi–Maskawa_matrix

It begins with the case of two generation (with the Cabibbo angle)
We have two orthonorma basis related by a rotation
https://en.wikipedia.org/wiki/File:Cabibbo_angle.svg

I wonder if such a graphical representation exists with the CKM matrix (with three angles)
we would have two (three dimensional) basis and each of of vector eigenstate woul be associated to the 3 angles. Have you ever seen such a picture?

 

[Vanadium 50]

Such a body would have 8 dihedral angles and 5 constraints on these angles. That ignores the phase. What would such a thing even look like?

 

[Heidi]

I read this in the wikipedia article about the CKM matrix:
For the Standard Model case (n = 3), there are three mixing angles and one CP-violating complex phase.

 

[Heidi]

In the general case of a CKM matrix with n generation (n * n matrix)
the standard parameterization gives n(n-1)/2 angles but as it is a choice, it is not obvious
that the Euler angles appear clearly in a picture likr in tbe 2 * 2 case with its unique angle.