The fact that $0.999133^2 = 24^2 / (24^2 + 1)$ in
this parameterisation suggests looking for a
CKM representation with a denominator of $24^2 + 1$. That is, if we subtract $24^2$ from the three large CKM entries on the diagonal, the remaining entries should have row and column sums of $1$. Let us look for two components: a sum $1$ piece and a zero sum piece. This can be done with a sum $1$ piece given by:
leaving zero sum corrections given by
where $\epsilon$ can be zero to within experimental precision. Note that the $704/24$ is just $29$ and a third. This is the norm square matrix, so on taking square roots, the $144$ becomes $12$ and so on. Numerology, maybe, but $0.999133$ still matches an $R_2$ factor at $r = 24$.
leaving zero sum corrections given by 
where $\epsilon$ can be zero to within experimental precision. Note that the $704/24$ is just $29$ and a third. This is the norm square matrix, so on taking square roots, the $144$ becomes $12$ and so on. Numerology, maybe, but $0.999133$ still matches an $R_2$ factor at $r = 24$.
Um, OK, so that is supposed to be a minus sign for the ts.ud factor. Anyway, the resulting matrix:
ReplyDelete0.974206387725,0.225632175637,0.00346921205934;
0.225498783858,0.973359764762,0.04148574238;
0.00849779935491,0.0407540140251,0.999133073092.
... which gives a Cabibbo angle of 13.04013499 degrees.
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