M Theory Lesson 344

Last time we generated the norm of a Koide matrix from a symmetrisation of the $1$-circulant piece of the neutrino mixing matrix. Recall that the CKM quark mixing matrix could also be approximated by a pair of $R_2$ factors, which we can choose to have norm less than one, as in $(a, 1/b)$ $=$ $(-0.231, 1/24)$. The Koide norm obtained in this case happens to give

$r^{-1} = 0.0193$

which is rather bizarre, since this is the CP violating phase $\beta_s$. Using this coincidence to define the third $R_2$ factor $c$ in terms of $\beta_s = abc$, we get

$c = \frac{2}{b^2} = 0.0035$

and it remains to wonder how the parameter $a$ is related to $b = 24$.