Study of $B_c^{\pm }\to (D^0{K}^{\pm },D^0{\pi }^{\pm })$ decays

Abstract

LHCb observes the $B_c^{+}\to D^0{K}^{+}$ decay with $R_{D^{0}K}=f_c/f_u\times \mathcal{B}(B_c^{+}\to D^0{K}^{+})=(9.3_{-2.5}^{+2.8}\pm 0.6)\times 10^{-7}$. The corresponding branching ratio (BR) of the decay can be estimated as $\mathcal{B}(B_c^{+}\to D^0{K}^{+})\approx (10.01\pm 3.40)\times 10^{-5}$; however, the theoretical estimates vary from $\sim 10^{-7}$ to $\sim 5\times 10^{-5}$. We phenomenologically investigate the $B_c^{+}\to (D^0{K}^{+},D^0{\pi }^{+})$ decays through the analysis of $B\to KK$, $B_u^{+}\to D^{+}{K}^0$, and $B_d\to D_s^{-}{K}^{+}$. With the form factor of $f_0^{B_{c}D}\approx 0.2$, it is found that the tree-annihilation contribution dominates the $B_c^{+}\to D^0{K}^{+}$ decay, and when $\mathcal{B}(B_u^{+}\to D^{+}{K}^0)\approx (1-3.1)\times 10^{-7}$ is required, we obtain $\mathcal{B}(B_c^{+}\to D^0{K}^{+})\approx (4.4-9)\times 10^{-5}$, and the magnitude of CP asymmetry is lower than approximately $10\%$. Although the $B_c^{+}\to D^0{\pi }^{+}$ decay is dominated by the tree-transition effect, the tree-annihilation also makes an important contribution, where its effect could be around $70\%$ of the tree-transition. It is found that when $\mathcal{B}(B_c^{+}\to D^0{K}^{+})\approx (4.4-9)\times 10^{-5}$ is taken, the BR and CP asymmetry for $B_c^{+}\to D^0{\pi }^{+}$ with the common values of parameters can be $\mathcal{B}(B_c^{+}\to D^0{\pi }^{+})\approx (4.9-8)\times 10^{-6}$ and of the order of one, respectively. Moreover, we conclude $\mathcal{B}(B_c^{+}\to D^{+}{K}^0)\approx \mathcal{B}(B_c^{+}\to D^0{K}^{+})$, and the BRs for $B_c^{+}\to K^{+}{\bar{K}}^0$ and $B_c^{+}\to J/\Psi {\pi }^{+}$ are $(6.99\pm 1.34)\times 10^{-7}$ and $(7.7\pm 1.1)\times 10^{-4}$, respectively.

Comments: 25 pages, 11 figures, 5 tables