A massless neutrino and lepton mixing patterns from finite discrete subgroups of U(3)

Understand

Finite discrete subgroups of $U(3)$ as possible flavour symmetries $G_f$ for a massless neutrinos with predictive mixing angles are studied.

• This is done by assuming that a residual symmetry $S_\nu$ appropriate for describing a massless neutrino is contained in $G_f$.
• It is shown that all the groups $G_f$ admitting three dimensional faithful irreducible representation and generated from a specific set of $3\times 3$ matrices imply only one of the three flavour compositions for the massless state namely, unmixed, maximally mixed with equal probabilities and bimaximally mixed with probabilities (0,1/2,1/2) and their permutations.
• This result holds irrespective of the order of $G_f$ and the choice of $S_{\nu}$ within it.