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The perturbative QCD (PQCD) approach based on $k_T$ factorization has made a great achievement for the QCD calculation of the hadronic B decays. Regulating the endpoint divergence by the transverse momentum of quarks in the propagators, one can do the perturbation calculation for kinds of diagrams including the annihilation type diagrams. In this paper, we review the current status of PQCD factorization calculation of two-body charmless $B\to PP, PV, VV$ decays up to the next-to-leading order (NLO) QCD corrections. two new power suppressed terms in decaying amplitudes are also taken into account. By using the universal input (non-perturbative) parameters, we collected the branching ratios and ${\bf CP}$ asymmetry parameters for all the charmless two body $B$ decays, calculated in the PQCD approach up to the NLO, including some power suppressed terms in decaying amplitudes. The results are compared with the ones from QCD factorization approach, soft-collinear effective theory approach and the current experimental measurements. For most considered B meson decays, the PQCD results for branching ratios agree well with other approaches and the experimental data. The PQCD predictions for the ${\bf CP}$ asymmetry parameters for many of the decay channels do not agree with other approaches, but have a better agreement with the experimental data. The longstanding $K \pi $ puzzle about the pattern of the direct CP asymmetries of the penguin-dominated $B \to K \pi $ decays can be understood after the inclusion of the NLO contributions in PQCD. The NLO corrections and power suppressed terms play an important role in the color suppressed and pure annihilation type $B$ decay modes. These rare decays are more sensitive to different types of corrections, providing opportunity to examine the factorization approach with the more precise experimental measurements., Comment: 52 pages, 4 figures, 11 tables

The decay width of the $D_s^{\ast}$ meson is dominated by the electromagnetic mode $D_s^\ast \to D_s \gamma$, and it is thus the longest-lived charged vector meson. In light of this point, we perform the first QCD LCSRs calculation of $D_s^{\ast}\to \phi$ helicity form factors and discuss the experiment potential of discovering exclusive $D_s^{\ast}$ weak decays. The main result is the partial decay widths, which read as $\Gamma_{D_s^\ast \to l \nu} = 2.44 \times 10^{-12} \, {\rm GeV}$, $\Gamma_{D_s^\ast \to \phi l \nu} = (3.28^{+0.82}_{-0.71}) \times 10^{-14} \, {\rm GeV}$, $\Gamma_{D_s^{\ast} \to \phi \pi} = ( 3.81^{+1.52}_{-1.33} ) \times 10^{-14} \, {\rm GeV}$ and $\Gamma_{D_s^{\ast}\to \phi \rho} = ( 1.16^{+0.42}_{-0.39} ) \times 10^{-13} \, {\rm GeV}$. We show that these channels are promising in the near future, serving as the first experimental observation of weak decays of a vector meson, and would open up a new playground for precision test of the standard model., Comment: 14 pages, 3 figure, 4 tables, matches version accepted for publication in EPJC