Tri-bimaximal neutrino mixing and quark masses from a discrete flavour symmetry

We build a supersymmetric model of quark and lepton masses based on the discrete flavour symmetry group T′, the double covering of A4. In the lepton sector our model is practically indistinguishable from recent models based on A4 and, in particular, it predicts a nearly tri-bimaximal mixing, in good agreement with present data. In the quark sector a realistic pattern of masses and mixing angles is obtained by exploiting the doublet representations of T′, not available in A4. To this purpose, the flavour symmetry T′ should be broken spontaneously along appropriate directions in flavour space. In this paper we fully discuss the related vacuum alignment problem, both at the leading order and by accounting for small effects coming from higher-order corrections. As a result we get the relations: md/ms≈|Vus| and md/ms≈|Vtd/Vts|.