An interesting mass relation between down-type quarks and charged leptons has been recently predicted within a supersymmetric $\mathrm{SU}(3{)}_{\mathrm{c}}\otimes \mathrm{SU}(2{)}_{\mathrm{L}}\otimes \mathrm{U}(1{)}_{\mathrm{Y}}$ model based on the $A_4$ flavor symmetry. Here we propose a simple extension which provides an adequate full description of the quark sector. By adding a pair of vectorlike up quarks, we show how the CKM entries $V_{ub}$, $V_{cb}$, $V_{td}$ and $V_{ts}$ arise from deviations of the unitarity. We perform an analysis including the most relevant observables in the quark sector, such as oscillations and rare decays of kaons, $B_d$ and $B_s$ mesons. In the lepton sector, the model predicts an inverted hierarchy for the neutrino masses, leading to a potentially observable rate of neutrinoless double beta decay.

• Received 12 April 2013

DOI:https://doi.org/10.1103/PhysRevD.88.036001