## Thursday, June 10, 2010

### M Theory Lesson 336

Recall that the two factor mixing products corresponded to a new kind of magic matrix. For example, the tribimaximal values may be rearranged as where the number $6$ replaces the zero entry of the matrix. Such magic squares have both sum and product rules. For example, the tribimaximal values give us
$\frac{2}{3} \times \frac{1}{2} = \frac{1}{3}$
$\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$.
Similarly, the CKM values give us the product rules
$(ud) \times (tb) = (cs)$
$(us) \times (cb) = (td)$.
The probability matrices are obtained from these magic squares by rearranging only a few values. One way that we might draw such a magic square is: