Quark–lepton mass relation in a realistic A4 extension of the Standard Model

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.