Constraints on hard spectator scattering and annihilation corrections in   $B_{u,d}$ ${\to}$ $PV$ decays within QCD factorization
  In this paper, we investigate the contributions of hard spectator scattering and annihilation in $B\to PV$ decays within the QCD factorization framework. With available experimental data on $B\to \pi K^{\ast}$, $\rho K$, $\pi \rho$ and $K\phi$ decays, comprehensive $\chi^2$ analyses of the parameters $X_{A,H}^{i,f}({\rho}_{A,H}^{i,f},{\phi}_{A,H}^{i,f})$ are performed, where $X_A^f$ ($X_A^i$) and $X_H$ are used to parameterize the endpoint divergences of the (non)factorizable annihilation and hard spectator scattering amplitudes, respectively. Based on $\chi^2$ analyses, it is observed that (1) The topology-dependent parameterization scheme is feasible for $B\to PV$ decays; (2) At the current accuracy of experimental measurements and theoretical evaluations, $X_H=X_A^i$ is allowed by $B\to PV$ decays, but $X_{H}\neq X_A^f$ at $68%$ C. L.; (3) With the simplification $X_H=X_A^i$, parameters $X_A^f$ and $X_A^i$ should be treated individually. The above-described findings are very similar to those obtained from $B\to PP$ decays. Numerically, for $B\to PV$ decays, we obtain $(\rho_{A,H}^i,\phi_{A,H}^i[^{\circ}]) =(2.87^{+0.66}_{-1.95}, -145^{+14}_{-21})$ and $(\rho_A^f,\phi_A^f[^{\circ}]) = (0.91^{+0.12}_{-0.13}, -37^{+10}_{-9})$ at $68%$ C. L.. With the best-fit values, most of the theoretical results are in good agreement with the experimental data within errors. However, significant corrections to the color-suppressed tree amplitude $\alpha_2$ related to a large $\rho_H$ result in the wrong sign for $A^{dir}_{CP}(B^- \to \pi^0 K^{{\ast}-})$ compared with the most recent BABAR data, which presents a new obstacle in solving "$\pi\pi$" and "$\pi K$" puzzles through $\alpha_2$. A crosscheck with measurements at Belle (or Belle II) and LHCb, which offer higher precision, is urgently expected to confirm or refute such possible mismatch. 
Junfeng Sun, Qin Chang, Xiaohui Hu and Yueling Yang
hep-ph hep-ex