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We propose a realistic A4 extension of the Standard Model involving a particular quark–lepton mass relation, namely that the ratio of the third family mass to the geometric mean of the first and second family masses are equal for down-type quarks and charged leptons. This relation, which is approximately renormalization group invariant, is usually regarded as arising from the Georgi–Jarlskog relations, but in the present model there is no unification group or supersymmetry. In the neutrino sector we propose a simple modification of the so-called Zee–Wolfenstein mass matrix pattern which allows an acceptable reactor angle along with a deviation of the atmospheric and solar angles from their bi-maximal values. Quark masses, mixing angles and CP violation are well described by a numerical fit.

We present a model based on the A4 non-abelian discrete symmetry leading to a predictive five-parameter neutrino mass matrix and providing a stable dark matter candidate. We found an interesting correlation among the atmospheric and the reactor angles which predicts theta_23 ~ pi/4 for very small reactor angle and deviation from maximal atmospheric mixing for large theta_13. Only normal neutrino mass spectrum is possible and the effective mass entering the neutrinoless double beta decay rate is constrained to be |m_ee| > 4 10^{-4} eV., 7 pages, 2 figures, minor changes to match the version to appear in PLB