Recent theoretical improvement of hadronic $B_s$ decays

Abstract

In this mini-review, we show that a lot of theoretical efforts have been made for the theoretical study of two body hadronic $B_{(s)}$ and $B_c$ decays. In addition to many next-to-leading order or even next-to-next-to leading order $\alpha_s$ corrections made, we also study many of the previously unknown next-to-leading order power corrections. While the former corrections are theoretically solid, the latter corrections are phenomenologically more important. In the QCD factorization approach based on collinear factorization, there is difficulty to deal with the power correction diagrams due to the endpoint singularity. Thus many of these analysis use phenomenological method. In the perturbative QCD approach based on $k_T$ factorization, the endpoint singularity is killed by including the quark transverse momentum. Therefore we can calculate the annihilation type diagrams quantitatively, which give the right sign for the direct CP asymmetry parameters. More and more $B_{(s)}$ decays channels, especially the pure annihilation type decays have been measured by the recent experiments to confirm our theoretical predictions. More channels are predicted for future experiments, such as the charmless and charmed $B_s$ and $B_c$ hadronic decays and the decays involving a scalar, axial vector, even a tensor meson in the final states.