The Weak Mixing Matrix

We show that the Weak Mixing Matrix, $ \left( {\begin{array}{*{20}c} {U_{ud} } & {U_{us} } & {U_{ub} } \\ {U_{cd} } & {U_{cs} } & {U_{cb} } \\ {U_{td} } & {U_{ts} } & {U_{tb} } \\ \end{array}} \right)$ , is not equal to the product of rotations, and in particular, it is not equal to the KM, or the PDG Matrices. \par \noindent At most, we may find an approximating matrix for the Weak Mixing Matrix that is based on the rotation matrices. \par \noindent We show that one such approximating matrix for the Real part of the Weak Mixing Matrix is $$\left( {\begin{array}{*{20}c} {\cos \theta _C \cos \theta _C^3 } & {\sin \theta _C \cos \theta _C^3 } & {\sin ^3 \theta _C \cos \theta _C^2 } \\ { - \sin \theta _C \cos \theta _C^2 } & {\cos \theta _C \cos \theta _C^2 } & {\sin ^2 \theta _C } \\ { - \cos \theta _C \sin ^3 \theta _C } & { - \cos \theta _C \cos \theta _C^3 \sin ^2 \theta _C } & {\cos \theta _C^2 \cos \theta _C^3 } \\ \end{array}} \right),$$ where $\theta _C $ is the Cabbibo angle. \par \noindent The approximating matrix depends on $\theta _C $ alone, and predicts the Real part of the Weak Mixing Matrix to a high degree of accuracy. \par \noindent We establish, with a Chi-Squared Goodness-of- Fitness-Test, that our approximating matrix can be used with extremely high level of statistical confidence.