We derive the two-loop evolution equations for the Cabibbo-Kobayashi-Masakawa (CKM) matrix. We show that to leading order in the mass and CKM hierarchies the scaling of the mixings |Vub|², |Vcb|², |Vtd|², |Vₜₛ|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 λb=λ_τ at the grand unified theory scale determines the CKM scaling factor to be {∥}0.58 in the minimal supersymmetric standard model.
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Barger et al. (1993) studied this question.
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