Fermion masses and mixing in $\Delta(27)$ flavour model

An extension of the Standard Model (SM) based on the non-Abelian discrete group $\Delta(27)$ is considered. The $\Delta(27)$ flavour symmetry is spontaneously broken only by gauge singlet scalar fields, therefore our model is free from any flavour changing neural current. We show that the model accounts simultaneously for the observed quark and lepton masses and their mixing. In the quark sector, we find that the up quark mass matrix is flavour diagonal and the Cabbibo-Kobayashi-Maskawa (CKM) mixing matrix arises from down quarks. In the lepton sector, we show that the charged lepton mass matrix is almost diagonal. We also adopt type-I seesaw mechanism to generate neutrino masses. A deviated mixing matrix from tri-bimaximal Maki-Nakagawa-Sakata (MNS), with $\sin\theta_{13} \sim 0.13$ and $\sin^2 \theta_{23} \sim 0.41$, is naturally produced.