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Branching Ratio and Polarization of $B\toρ(ω)ρ(ω)$ Decays in Perturbative QCD Approach

In this work, we calculated the branching ratios, polarization fractions and CP asymmetry of decay modes $B\toρ(ω)ρ(ω)$ in the Perturbative QCD approach, which is based on $\mathbf{k}_T$ factorization. After calculation, we find the the branching ratios of $B^0 \to ρ^+ ρ^-$, $B^+ \to ρ^+ ρ^0$ and $B^+ \to ρ^+ ω$ are at the order of $10^{-5}$, and their longitudinal polarization fractions are more than 90%. The above results agree with BarBar's measurements. We also predict the branching ratios and polarizations of $B^0 \to ρ^0 ρ^0$, $B^0 \to ρ^0 ω$ and $B^0 \to ωω$, which will be measured in future. We predicted the CP asymmetry of $B^0 \to ρ^+ ρ^-$ and $B^+ \to ρ^+ ρ^0$, which will play important role in determining angle $α$.