Neutrinos Again

Returning to the six masses of the neutrinos and antineutrinos, we can search for further approximate relations between the values and their ratios. In particular, observe that the scale independent relation holds exactly for a universal phase not of $2/9$, but quite close at $\theta = 0.222535$. This phase does not substantially alter the predicted neutrino mass values or the $\Delta m^2$ of the MINOS experiment, for a similar scale choice. However, this $\theta$ ruins the correct $2/9$ rule for the charged lepton masses. For the charged leptons the rule above could never hold, because particles have the same mass as antiparticles.