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 $M_{H_c} \le 2.5\times 10^{16}~{\rm GeV}$ (90% C.L.) taking all possible corrections into account in a renormalization group analysis. If the above upper limit is compared with a lower limit on $M_{H_c}$ from the negative search for the proton decay; $M_{H_c} \ge 2.0\times 10^{16}~{\rm GeV}$ (in which effects of the larger top-quark mass are included), the minimum supersymmetric SU(5) GUT is severely constrained.