b→sll¯in the minimal supergravity model

The $b\to {\mathrm{sl}}^{+}{l}^{-}$ process is studied in the minimal supergravity model in detail. Taking into account the long-distance contributions from the $c\overline{c}$ resonances, we calculate the branching ratio and the lepton forward-backward asymmetry in this model. We find that there is a strong correlation between the branching ratios of $b\to s\gamma$ and $b\to {\mathrm{sl}}^{+}{l}^{-}$ processes and that the interference effect can change the $b\to {\mathrm{sl}}^{+}{l}^{-}$ branching ratio in the off-resonance regions by up to ±15% depending on the relative phase between the long- and short-distance contributions. Using various phenomenological constraints including the branching ratio of $b\to s\gamma$, we show that there are regions in the parameter space where the branching ratio of $b\to {\mathrm{sl}}^{+}{l}^{-}$ is enhanced by about 50% compared to the standard model (SM). We also show that the branching ratio of $b\to s\nu \overline{\nu }$ is reduced at most by 10% from the SM prediction.