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

TL;DR

This paper investigates the decay of B_s into rho rho mesons, highlighting the significant impact of final state interactions on the decay rate, which is much larger than the direct QCDF prediction.

Contribution

It introduces a detailed analysis of FSI effects in B_s → ρρ decay, showing their importance in accurately estimating the branching ratio beyond QCDF alone.

Findings

QCDF predicts a very small branching ratio (~10^-9)

FSI effects increase the predicted branching ratio to match experimental bounds

Final state interactions are crucial for understanding B_s decay dynamics

Abstract

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.