We derive the two-loop evolution equations for the Cabibbo-Kobayashi-Maskawa matrix. We show that to leading order in the mass and CKM hierarchies the scaling of the mixings $|V_{ ub}|^2$, $|V_{ cb}|^2$, $|V_{ td}|^2$, $|V_{ ts}|^2$ and of the rephase-invariant CP-violating parameter $J$ is universal to all orders in perturbation theory. In leading order the other CKM elements do not scale. Imposing the constraint $\lambda _b=\lambda _{ \tau}$ at the GUT scale determines the CKM scaling factor to be $\simeq 0.58$ in the MSSM.
Categories: hep-ph
