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

Abstract

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\varphi$, $\varphi K^{\ast 0}$, $\varphi \varphi$ and $K^{\ast 0}{\bar{K}}^{\ast 0}$ 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 $f_{L,\perp }({\bar{B}}_s\to K^{\ast 0}{\bar{K}}^{\ast 0})=(20.1\pm 7.0)\%,(58.4\pm 8.5)\%$ measured by the LHCb collaboration can be reconciled through the weak annihilation corrections. However, the branching ratio of ${\bar{B}}_s\to \varphi K^{\ast 0}$ decay exhibits a tension between the data and theoretical result, which dominates the contributions to ${\chi }_{\min }^2$ 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.

Comments: 31 pages, 4 figures, 6 tables