Nucleon decay in the minimal supersymmetric SU(5) grand unification

We make a detailed analysis on the nucleon decay in the minimal supersymmetric SU(5) grand unified model. We find that a requirement of the unification of three gauge coupling constants leads to a constraint on a mass MHC of the color-triplet Higgs multiplet as 2 × 1013 GeV ⩽ MHC ⩽ 2 × 1017 GeV, taking both weak- and GUT-scale threshold effects into account. Contrary to the results in the previous analyses, the present experimental limits on the nucleon decay turn out to be consistent with the SUSY particles lighter than 1 TeV even without a cancellation between matrix elements contributed from different generations, if one adopts a relatively large value of MHC (⩾ 2 × 1016 GeV). We also show that the Yukawa coupling constant of the color-triplet Higgs multiplet does not necessarily blow up below the gravitational scale (2.4 × 1018 GeV) even with the largest possible value of MHC. We point out that the no-scale model is still viable, though it is strongly constrained.