The CKM suppressed $B(B_s) \to \bar D_{(s)}P,\bar D_{(s)}V,\bar D_{(s)}^*P, \bar D_{(s)}^*V$ decays in perturbative QCD approach

Abstract

Although the two-body charmed decays $B_{(s)} \to \bar D_{(s)}^{(*)}P$ and $\bar D_{(s)}^{(*)}V$, where $P$($V$) denotes a light pseudoscalar(vector) meson, are CKM suppressed comparing with the $B_{(s)} \to D_{(s)}^{(*)}P$ and $ D_{(s)}^{(*)}V$ decays, they are important in the CKM angle $\gamma=\phi_3$ extraction method. We investigated these decays in the perturbative QCD approach to the leading order of $m_D/m_B$ and $\Lambda_{\rm{QCD}}/m_D$ expansion. We find that the nonfactorizable emission diagrams and the annihilation diagrams are not negligible in many of these channels. The numerical results show that most channels have branching ratios with an order of $10^{-6}$ or $10^{-7}$. The ratio needed for the CKM angle $\gamma$ extraction is estimated as $r = \frac{|A(B^- \to \bar{D}^0 K^-)|}{|A(B^- \to D^0 K^-)|} = 0.092_{-0.003-0.003}^{+0.012+0.003},$ which is too small for the experiments. Some of the $ B_{(s)}\to \bar D_{(s)}^*V$ decays have a very large transversely polarized contribution that can reach 80%.