On unification and nucleon decay in supersymmetric grand unified theories based on SU(5)

We investigate the unification constraints in the minimal supersymmetric grand unified theories based on SU(5) gauge symmetry. The most general constraints on the spectrum of minimal supersymmetric SU(5) and flipped SU(5) are shown. The upper bound on the mass of the colored Higgs mediating proton decay is discussed in detail in the context of the minimal supersymmetric SU(5). In the case of the minimal SUSY SU(5) we show that if we stick to the strongest bound on the colored triplet mass coming from dimension five proton decay contributions there is no hope to test this model at future nucleon decay experiments through the dimension six operators. We find a lower bound on the partial proton decay lifetime for all relevant channels in the context of flipped SUSY SU(5). We conclude that flipped SUSY SU(5) might be in trouble if proton decay is found at the next generation of experiments with a lifetime below 1037 years.