The flavor of product-group GUTs

Abstract

The doublet-triplet splitting problem can be simply solved in product-group GUT models, using a global symmetry that distinguishes the doublets from the triplets. Apart from giving the required mass hierarchy, this ``triplet symmetry'' can also forbid some of the triplet couplings to matter. We point out that, since this symmetry is typically generation-dependent, it gives rise to non-trivial flavor structure. Furthermore, because flavor symmetries cannot be exact, the triplet-matter couplings are not forbidden then but only suppressed. We construct models in which the triplet symmetry gives acceptable proton decay rate and fermion masses. In some of the models, the prediction m_b ~ m_\tau is retained, while the similar relation for the first generation is corrected. Finally, all this can be accomplished with triplets somewhat below the GUT scale, supplying the right correction for the standard model gauge couplings to unify precisely.