Study of the weak annihilation contributions in charmless $B_s\to VV$ decays

In this paper, in order to probe the spectator-scattering and weak annihilation contributions in charmless $B_s\to VV$ (where $V$ stands for a light vector meson) decays, we perform the $\chi^2$-analyses for the end-point parameters within the QCD factorization framework, under the constraints from the measured $\bar B_{s}\to$$\rho^0\phi$, $\phi K^{*0}$, $\phi \phi$ and $K^{*0}\bar K^{*0}$ decays. The fitted results indicate that the end-point parameters in the factorizable and nonfactorizable annihilation topologies are non-universal, which is also favored by the charmless $B\to PP$ and $PV$ (where $P$ stands for a light pseudo-scalar meson) decays observed in the previous work. Moreover, the abnormal polarization fractions $f_{L,\bot}(\bar B_{s}\to K^{*0}\bar K^{*0})=(20.1\pm7.0)\%\,,(58.4\pm8.5)\%$ measured by the LHCb collaboration can be reconciled through the weak annihilation corrections. However, the branching ratio of $\bar B_{s}\to\phi K^{*0}$ decay exhibits a tension between the data and theoretical result, which dominates the contributions to $\chi_{\rm min}^2$ in the fits. Using the fitted end-point parameters, we update the theoretical results for the charmless $B_s\to VV$ decays, which will be further tested by the LHCb and Belle-II experiments in the near future.