Quark-lepton mass relation and CKM mixing in an<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>A</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:math>extension of the minimal supersymmetric standard model

Abstract

An interesting mass relation between down-type quarks and charged leptons has been recently predicted within a supersymmetric $\mathrm{SU}(3{)}_{\mathrm{c}}\ensuremath{\bigotimes}\mathrm{SU}(2{)}_{\mathrm{L}}\ensuremath{\bigotimes}\mathrm{U}(1{)}_{\mathrm{Y}}$ 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.