Limit on the Color-Triplet Higgs Mass in the Minimum Supersymmetric SU(5) Model

In the minimum supersymmetric SU(5) GUT, we derive the upper limit on the mass of the color-triplet Higgs multiplets as $\mhc\leq 2.4\times 10^{16}~\GEV$ (90 \% C.L.) taking all possible corrections into account in a renormalization group analysis. If the above upper limit is compared with a limit on $\mhc$ from the negative search for the proton decay; $\mhc \geq 2.0\times 10^{16}~\GEV$ (in which effects of the larger top-quark mass are included), the minimum supersymmetric SU(5) GUT is severely constrained.