Decays of $B$ meson to two charmed mesons

TL;DR

This paper uses perturbative QCD to analyze $B$ meson decays into two charmed mesons, confirming the factorization theorem's validity, predicting polarization contributions, and calculating CP asymmetries consistent with experimental data.

Contribution

It demonstrates the applicability of the factorization theorem in $B$ decays to two charmed mesons and provides detailed predictions for polarization and CP asymmetries.

Findings

Factorization theorem holds at leading order.

Branching ratios agree with experimental data.

Transverse polarization contributes 40-50%.

Abstract

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 $\Lambda_{\rm{QCD}}/m_D$ 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 $\sin 2\beta$ measurement from other channels.