Recent theoretical improvement of hadronic $B_s$ decays

TL;DR

This mini-review discusses recent theoretical advancements in understanding two-body hadronic B_s and B_c decays, emphasizing higher-order corrections and the role of different QCD factorization approaches in predicting decay processes and CP asymmetries.

Contribution

It highlights the inclusion of next-to-leading order power corrections and the application of k_T factorization to better calculate decay amplitudes and CP asymmetries in B meson decays.

Findings

Higher-order corrections improve decay predictions.

k_T factorization effectively handles endpoint singularities.

Predicted decay channels align with recent experimental measurements.

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.