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

Abstract

In this paper, the contributions of weak annihilation and hard spectator scattering in $B\to \rho K^*$, $ K^* \bar{K}^*$, $\phi K^*$, $\rho\rho$ and $\phi\phi$ decays are investigated within the framework of QCD factorization. Using the experimental data available, we perform $\chi^2$ 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 $(\rho_A^{i},\phi_A^{i})\neq (\rho_A^{f},\phi_A^{f})$ 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 $ (\rho_H,\phi_H)= (\rho_A^{i},\phi_A^{i})$ are challenged by ${\cal B}(\bar{B}^0\to \rho^0 \rho^0)$, even though they are allowed by $B\to PP$ and $PV$ decays and helpful for resolving "$\pi\pi$ puzzle", (iii) In the polarization-dependent scheme, the relation $(\rho_A^{L},\phi_A^{L})\neq (\rho_A^{T},\phi_A^{T})$ 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 $B_d\to \phi \phi$ decay, are also identified for probing the annihilation corrections.