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Decays of $B$ meson to two charmed mesons

The factorization theorem in Decays of $B_{(s)}$ mesons to two charmed mesons (both pseudoscalar and vector) can still be proved in the leading order in $m_D/m_B$ and $Λ_{\rm{QCD}}/m_D$ expansion. Working in the perturbative QCD approach, we find that the factorizable emission diagrams are dominant. Most of branching ratios we compute agree with the experimental data well, which means that the factorization theorem seems to be reliable in predicting branching ratios for these decays. In the decays of a $B$ meson to two vector charmed mesons, the transverse polarization states contribute $40%-50%$ both in the processes with an external W emission and in the pure annihilation decays. This is in agreement with the present experimental data. We also calculate the CP asymmetry parameters. The results show that the direct CP asymmetries are very small. Thus observation of any large direct CP asymmetry will be a signal for new physics. The mixing induced CP asymmetry in the neutral modes is large. This is also in agreement with the current experimental measurements. They can give a cross check of the $\sin 2β$ measurement from other channels.