A 4 flavour symmetry breaking scheme for understanding quark and neutrino mixing angles

Abstract

We propose a spontaneous A 4 flavour symmetry breaking scheme to understand the observed pattern of quark and neutrino mixing. The fermion mass eigenvalues are arbitrary, but the mixing angles are constrained in such a way that the overall patterns are explained while also leaving sufficient freedom to fit the detailed features of the observed values, including CP-violating phases. The scheme realises the proposal of Low and Volkas to generate zero quark mixing and tribimaximal neutrino mixing at tree level, with deviations from both arising from small corrections after spontaneous A 4 breaking. In the neutrino sector, the breaking is A 4Z 2, while in the quark and charged-lepton sectors it is A 4Z 3≅C 3. The full theory has A 4 completely broken, but the two different unbroken subgroups in the two sectors force the dominant mixing patterns to be as stated above. Radiative effects within each sector are shown to deviate neutrino mixing from tribimaximal, while maintaining zero quark mixing. Interactions between the two sectors - ''cross-talk'' - induce nonzero quark mixing, and additional deviation from tribimaximal neutrino mixing. We discuss the vacuum alignment challenge the scenario faces, and suggest three generic ways to approach the problem. We follow up one of those ways by sketching how an explicit model realising the symmetry breaking structure may be constructed. © SISSA 2006.