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Fits of Weak Annihilation and Hard Spectator Scattering Corrections in $B_{u,d}\to VV$ Decays

In this paper, the contributions of weak annihilation and hard spectator scattering in $B\to ρK^*$, $ K^* \bar{K}^*$, $ϕK^*$, $ρρ$ and $ϕϕ$ decays are investigated within the framework of QCD factorization. Using the experimental data available, we perform $χ^2$ analyses of end-point parameters in four cases based on the topology-dependent and polarization-dependent parameterization schemes. The fitted results indicate that: (i) In the topology-dependent scheme, the relation $(ρ_A^{i},ϕ_A^{i})\neq (ρ_A^{f},ϕ_A^{f})$ gotten through $B\to PP$ and $PV$ decays is favored by the penguin-dominated $B\to VV$ decays at 95\% C. L., (ii) The large hard spectator scattering corrections and/or the simplification $ (ρ_H,ϕ_H)= (ρ_A^{i},ϕ_A^{i})$ are challenged by ${\cal B}(\bar{B}^0\to ρ^0 ρ^0)$, even though they are allowed by $B\to PP$ and $PV$ decays and helpful for resolving "$ππ$ puzzle", (iii) In the polarization-dependent scheme, the relation $(ρ_A^{L},ϕ_A^{L})\neq (ρ_A^{T},ϕ_A^{T})$ is always required. Moreover, we have updated the theoretical results for $B\to VV$ decays with the best-fit values of end-point parameters. A few observables, such as the ones of pure annihilation $B_d\to ϕϕ$ decay, are also identified for probing the annihilation corrections.