Search for B$^0 \rightarrow l^+ l^-$ at Belle

The decay modes $B^{0}\rightarrow l^{+}l^{-}$ are a group of very rare particle decays presenting an important test to the Standard Model. They could show evidence of physics outside the Standard model such as lepton family number violations and probe the weak interaction theory. Based on a sample of $ (771.581\pm 10.566) \times 10^6 $ $B\bar B$ pairs collected by the Belle experiment at $\sqrt{s} = 10.58 GeV$, we present a study of the rare decay $B^{0}\rightarrow l^{+}l^{-}$.