Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 305 / 4 / b / Solution

CP conjugates the charged-current coupling and replaces $V_{\mathrm{CKM}}$ by $V_{\mathrm{CKM}}^{\ast }$. 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 invariantis nonzero for distinct rows and columns. Since $J$ changes sign under complex conjugation, $J\ne 0$ proves CP violation in electroweak interactions.