Question regarding CP violation in the CKM matrix

[jossives]

Could somebody explain how an imaginary phase in some of the CKM matrix elements represents a CP-violation factor?

 

[hamster143]

My theory is a bit rusty but here's the essence of it.

CKM matrix couples gauge bosons, up-type quarks, and down-type quarks. For example, there's a term in the Lagrangian that couples right-handed anti-up with left-handed strange quark, and it is proportional to $$V_{us}$$, its hermitean conjugate couples left-handed up with right-handed anti-strange, and it is proportional to $$V^*_{us}$$. CP transformation flips charges and spins, so the sum of two terms is invariant under CP only if $$V_{us}$$ is real. If you only have two families, you can fiddle with quark phases and redefine their wave functions to absorb all imaginary numbers, but with three families 'i''s will pop up somewhere. It's convenient to pick quark phases so that all elements connecting with the first family (up & down quarks) are real.