MINOS Neutrinos II

Expanding on my last comment, recall that Carl Brannen's phase for the neutrino Koide mass matrix is

$\delta = \frac{2}{9} + \frac{\pi}{12}$

which results in the eigenvalue set

$\sqrt{m_{i}} = \mu (1 + \sqrt{2} \textrm{cos} (\delta + \omega_i))$

for $i = 1,2,3$ and $\omega_i$ the three cubed roots of unity. The value $2/9$ and the factor $\sqrt{2}$ are shared by both neutrinos and charged leptons. This $\delta$ gives three neutrino masses and a $\Delta m^2$ in agreement with known measurements. If, on the other hand, we took a phase

$\delta = \frac{2}{9} - \frac{\pi}{12}$

for the same scale $\mu$ and same eigenvalue equation, we obtain three masses with a $\Delta m^2$ in perfect agreement with the new MINOS results. Note that the $\overline{m}_{2}$ mass dominates the $\Delta$, so it does not much matter if we are considering $\overline{m}_{1}$ or $\overline{m}_{3}$.

It is not yet clear why conjugation on the $\pi /12$ should correspond to antineutrinos, but recall that conjugation is a standard feature of phases for antiparticles in the braid spectrum. The $2/9$ component appears to be shared by all particles, irrespective of their quantum numbers.