Rate difference between b $\to$ s mu^+ mu^- and b $\to$ s e^+e^- in SUSY with large tan$\beta$

We study the inclusive semileptonic rare decay $b \to s l^+ l^-$ in minimal supergravity model (mSUGRA). If tan$\beta$ is large, down-type quark mass matrices and their Yukawa couplings cannot be diagonalized at the same basis. This induces the flavor violating neutral Higgs boson couplings. These couplings contribute significantly to decay $b \to s mu^+ mu^-$ and $b \to s tau^+ tau^-$, but negligible to $b \to s e^+ e^-$ decay because of its negligible $m_e$ mass. The ratio $R \equiv B(b \to s mu^+ mu^-)/ B(b \to s e^+ e^-)$ can be very different from its corresponding value in the Standard Model. We find that part of parameter space can accommodate a large R value, and that maximum R value can be larger than 2. We also present our results in $b \to s tau^+ tau^-$ decay channel. Although it can be not detected now, it is potentially a new channel for the future observation of new physics.