Final State Interaction Effect in Pure Annihilation $B_s \to \rho \rho $ Decay

We analyzed the process of $B_s\rightarrow \rho \rho$ decay in QCD factorization (QCDF) and final state interaction (FSI) effects. In QCDF for this decay we have only the annihilation graph and we expected small Branching ratio. Then we considered FSI effect as a sizable correction where the intermediate states are $\pi^0\pi^0$, $\pi^+\pi^-$, $K^0\bar{K^0}$ and $K^+K^-$ mesons. To consider the amplitudes of these intermediate states, QCDF approach was used. The experimental branching ratio of $B_s\rightarrow \rho\rho$ is less than $3.20\times 10^{-4}$ and our result is $1.08 \times 10^{-9}$ and $3.29 \times10^{-4}$ from QCDF and FSI, respectively.