Direct and semi-direct approaches to lepton mixing with a massless neutrino

We discuss the possibility of enforcing a massless majorana neutrino in the direct and semi-direct approaches to lepton mixing, in which the pmns matrix is partly predicted by subgroups of a discrete family symmetry, extending previous group searches up to order 1535. we find a phenomenologically viable scheme for the semi-direct approach based on q(648) which contains δ(27) and the quaternion group as subgroups. this leads to novel predictions for the first column of the pmns matrix corresponding to a normal neutrino mass hierarchy with m 1 = 0, and sum rules for the mixing angles and phase which are characterised by the solar angle being on the low side θ 12 ∼ 31° and the dirac (oscillation) cp phase δ being either about ±45° or ±π.