The Flavour Problem and the Family Symmetry Beyond the Standard Model

In the framework of a two Higgs doublet model, we try to explain lepton masses and mixing matrix elements assuming that neutrinos are Dirac particles. Discrete family symmetry groups, which are subgroups of U(3) up to the order of 1025 are considered. Like in the Standard Model with one Higgs doublet, we found that discrete family symmetries do not give satisfactory answer to these basic questions in the flavour problem.