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Finite discrete subgroups of $U(3)$ as possible flavour symmetries $G_f$ fora massless neutrinos with predictive mixing angles are studied. This is done byassuming that a residual symmetry $S_\nu$ appropriate for describing a masslessneutrino is contained in $G_f$. It is shown that all the groups $G_f$ admittingthree dimensional faithful irreducible representation and generated from aspecific set of $3\times 3$ matrices imply only one of the three flavourcompositions for the massless state namely, unmixed, maximally mixed with equalprobabilities and bimaximally mixed with probabilities (0,1/2,1/2) and theirpermutations. This result holds irrespective of the order of $G_f$ and thechoice of $S_{\nu}$ within it. All of these lead to unfavourable leading orderprediction for the solar mixing angle. Neutrino mixing pattern is thennumerically investigated in case of subgroups of $U(3)$ with order less than512 and it is found that only one of these can lead to a massless neutrino andleading order predictions for all the mixing angles close to their experimentalvalues. Ways to correct for the solar angle prediction are proposed and twoconcrete examples giving the observed mixing pattern are discussed.

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