Constraints on hard spectator scattering and annihilation corrections in Bu,d → PV decays within QCD factorization

In this paper, we investigate the contributions of hard spectator scattering and annihilation in B→PVB→PV decays within the QCD factorization framework. With available experimental data on B→πK⁎,ρK,πρ and KϕB→πK⁎,ρK,πρ and Kϕ decays, comprehensive χ2χ2 analyses of the parameters XA,Hi,f(ρA,Hi,f,ϕA,Hi,f) are performed, where XAf(XAi) and XHXH are used to parameterize the endpoint divergences of the (non)factorizable annihilation and hard spectator scattering amplitudes, respectively. Based on χ2χ2 analyses, it is observed that (1) The topology-dependent parameterization scheme is feasible for B→PVB→PV decays; (2) At the current accuracy of experimental measurements and theoretical evaluations, XH=XAi is allowed by B→PVB→PV decays, but XH≠XAf at 68%68% C.L.; (3) With the simplification XH=XAi, parameters XAf and XAi should be treated individually. The above-described findings are very similar to those obtained from B→PPB→PP decays. Numerically, for B→PVB→PV decays, we obtain (ρA,Hi,ϕA,Hi[°])=(2.87−1.95+0.66,−145−21+14) and (ρAf,ϕAf[°])=(0.91−0.13+0.12,−37−9+10) at 68%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 α2α2 related to a large ρHρH result in the wrong sign for ACPdir(B−→π0K⁎−) compared with the most recent BABAR data, which presents a new obstacle in solving “ππ” and “πK  ” puzzles through α2α2. 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.