Light grand unified theory triplets and Yukawa splitting

Triplet-mediated proton decay in grand unified theories (GUTs) is usually suppressed by arranging a large triplet mass. Here we explore instead a mechanism for suppressing the couplings of the triplets to the first and second generations compared to the Yukawa couplings, so that the triplets can be light. This mechanism is based on a ``triplet symmetry'' in the context of product-group GUTs. We study two possibilities. The first possibility, which requires the top Yukawa coupling to arise from a nonrenormalizable operator at the GUT scale, is that all triplet couplings to matter are negligible, so that the triplets can be at the weak scale, giving new evidence for grand unification. The second possibility is that some triplet couplings, and in particular Ttb and $T\overline{t}\overline{l},$ are equal to the corresponding Yukawa couplings. This would give a distinct signature of grand unification if the triplets were sufficiently light. However, we derive a model-independent bound on the triplet mass in this case, which is at least ${10}^{6}\mathrm{GeV}.$ Finally, we construct an explicit viable GUT model based on Yukawa splitting, with the triplets at ${10}^{14}\mathrm{GeV},$ as required for coupling unification to work. This model requires no additional thresholds below the GUT scale.