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Finite Supersymmetric Threshold Corrections to CKM Matrix Elements in the Large $tanβ$ Regime

We evaluate the finite 1-loop threshold corrections, proportional to $tanβ$, to the down quark mass matrix. These result in corrections to down quark masses and to Cabibbo-Kobayashi-Maskawa [CKM] matrix elements. The corrections to CKM matrix elements are the novel feature of this paper. For grand unified theories with large $\tanβ$ these corrections may significantly alter the low energy predictions of four of the CKM matrix elements and the Jarlskog parameter J, a measure of CP violation. The angles $α,\: β$ and $γ$ of the unitarity triangle and the ratio $|{V_{ub} \over V_{cb}}|$, however, are not corrected to this order. We also discuss these corrections in the light of recent models for fermion masses. Here the corrections may be useful in selecting among the various models. Moreover, if one model fits the data, it will only do so for a particular range of SUSY parameters.