Flavor of product-group grand unified theories

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 nontrivial 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 mb∼mτ 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