Six fixed points exist for the massless one-loop RG running of three-generation fermion mixing matrices, remaining fixed points to all orders via geometric properties of vector fields on the space of mixing matrices.
The Renormalization Group Evolution of the CKM Matrix
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abstract
We compute the renormalization of the complete CKM matrix in the MSbar scheme and perform a renormalization group analysis of the CKM parameters. The calculation is simplified by studying only the Higgs sector, which for the \beta-function of the CKM matrix is at one loop the same as in the full Standard Model. The renormalization group flow including QCD corrections can be computed analytically using the hierarchy of the CKM parameters and the large mass differences between the quarks. While the evolution of the Cabibbo angle is tiny V_{ub} and V_{cb} increase sizably. We compare our results with the ones in the full Standard Model.
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Fixed points of the renormalisation group running of quark and fermion mixing matrices in the Standard Model and beyond
Six fixed points exist for the massless one-loop RG running of three-generation fermion mixing matrices, remaining fixed points to all orders via geometric properties of vector fields on the space of mixing matrices.