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 → sl + l − in minimal supergravity model (mSUGRA). If tan β 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 → sµ + µ − and b → sτ + τ − , but negligible to b → se + e − decay because of its negligible m e mass. The ratio R ≡ B ( b → sµ + µ − ) /B ( b → se + 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 → sτ + τ − decay channel. Although it can not be detected now, it is potentially a new channel for the future observation of new physics.