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

TL;DR

This paper presents a $ ext{Δ}(27)$ flavor symmetry model extending the Standard Model, explaining quark and lepton masses and mixings, including neutrino oscillation parameters, without inducing flavor-changing neutral currents.

Contribution

The model uniquely employs gauge singlet scalars for spontaneous flavor symmetry breaking, naturally producing realistic quark and lepton mixing matrices, including a non-zero $ heta_{13}$.

Findings

Quark mass matrix is flavor diagonal with CKM from down sector.

Charged lepton mass matrix is nearly diagonal.

Neutrino mixing deviates from tri-bimaximal with $ heta_{13} eq 0$.

Abstract

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.