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 $B\to \rho K^{\ast }$, $K^{\ast }{\bar{K}}^{\ast }$, $\varphi K^{\ast }$, $\rho \rho$ and $\varphi \varphi$ 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 $({\rho }_A^i,{\varphi }_A^i)\ne ({\rho }_A^f,{\varphi }_A^f)$ 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 $({\rho }_H,{\varphi }_H)=({\rho }_A^i,{\varphi }_A^i)$ are challenged by $\mathcal{B}({\bar{B}}^0\to {\rho }^0{\rho }^0)$, 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 $({\rho }_A^L,{\varphi }_A^L)\ne ({\rho }_A^T,{\varphi }_A^T)$ 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 $B_d\to \varphi \varphi$ decay, are also identified for probing the annihilation corrections.

Comments: 25 pages, 12 figures