Charged Higgs mass bound from the $b\to s\gamma$ process in the minimal supergravity model

We study the constraint on the mass of the charged Higgs boson in the minimal supergravity model based on the recent measurement of the inclusive $b\to s\gamma$ decay. It is shown that the lower bound for the charged Higgs mass crucially depends on the sign of the higgsino mass parameter ($\mu$). For $\mu <0$, the bound exceeds 400 GeV when the ratio of two Higgs vacuum expectation values ($\tan \beta$) is larger than 10. No strong bound is obtained for $\mu >0$ due to cancellations between charged Higgs and supersymmetric particle contributions. For $3\text{lsim}\tan \beta \text{lsim}5$, a charged Higgs lighter than 180 GeV is excluded by this process irrespective of the sign of $\mu$.