Branching Ratio and Polarization of $B\to \rho (\omega )\rho (\omega )$ Decays in Perturbative QCD Approach

In this work, we calculated the branching ratios, polarization fractions and CP asymmetry of decay modes $B\to \rho (\omega )\rho (\omega )$ in the Perturbative QCD approach, which is based on ${\mathbf{k}}_T$ factorization. After calculation, we find the the branching ratios of $B^0\to {\rho }^{+}{\rho }^{-}$, $B^+ \to \rho^+ \rho^0$and$B^+ \to \rho^+ \omega$areattheorderof$10^{-5}$, 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 $B^0\to {\rho }^0{\rho }^0$, $B^0\to {\rho }^0\omega$ and $B^0 \to \omega \omega$, which will be measured in future. We predicted the CP asymmetry of $B^0\to {\rho }^{+}{\rho }^{-}$ and $B^{+}\to {\rho }^{+}{\rho }^0$, which will play important role in determining angle $\alpha$.