Universal Evolution of CKM Matrix Elements

Abstract

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.

Comments: 17 pages + 2 figures not included (available upon request), revised version fixes discrepancy between S and S^{1/2}, no other changes, MAD/PH/722