Solution (source code)

= Solution

CP conjugates the charged-current coupling and replaces $V_{\rm CKM}$ by $V_{\rm CKM}^*$. CP is conserved only if quark-field rephasings can make the entire matrix real. For three generations an irreducible phase prevents this. Equivalently, the rephasing-invariant <Jarlskog invariant>
$$
J=\operatorname{Im}(V_{ij}V_{k\ell}V_{i\ell}^*V_{kj}^*)
$$
is nonzero for distinct rows and columns. Since $J$ changes sign under complex conjugation, $J\neq0$ proves <CP violation> in electroweak interactions.