CKM Substructure

Abstract

The CKM matrix is not generic. The Wolfenstein parametrization encodes structure by having one small parameter, $\lambda \approx 0.22$. We pose the question: is there substructure in the CKM matrix that goes beyond the single small parameter of the Wolfenstein parameterization? We find two relations that are approximately satisfied: $|V_{td}{|}^2=|V_{cb}{|}^3$ and $|V_{ub}{|}^2|V_{us}|=|V_{cb}{|}^4$. We discuss the statistical significance of these relations and find that they may indicate deeper structure in the CKM matrix. The current precision, however, cannot exclude an $\mathcal{O}(10\%)$ accident.

Comments: 10 pages, 3 figures